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Deformation (mechanics)
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This article is about deformation in mechanics. For the term's use in engineering, see Deformation (engineering).
The deformation of a thin straight rod into a closed loop. The length of the rod remains almost unchanged during the deformation, which indicates that the strain is small. In this particular case of bending, displacements associated with rigid translations and rotations of material elements in the rod are much greater than displacements associated with straining.
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Deformation in continuum mechanics is the transformation of a body from a reference configuration to a current configuration.[1] A configuration is a set containing the positions of all particles of the body.
A deformation may be caused by external loads,[2] body forces (such as gravity or electromagnetic forces), or changes in temperature, moisture content, or chemical reactions, etc.
Strain is a description of deformation in terms of relative displacement of particles in the body that excludes rigid-body motions. Different equivalent choices may be made for the expression of a strain field depending on whether it is defined with respect to the initial or the final configuration of the body and on whether the metric tensor or its dual is considered.
In a continuous body, a deformation field results from a stress field induced by applied forces or is due to changes in the temperature field inside the body. The relation between stresses and induced strains is expressed by constitutive equations, e.g., Hooke's law for linear elastic materials. Deformations which are recovered after the stress field has been removed are called elastic deformations. In this case, the continuum completely recovers its original configuration. On the other hand, irreversible deformations remain even after stresses have been removed. One type of irreversible deformation is plastic deformation, which occurs in material bodies after stresses have attained a certain threshold value known as the elastic limit or yield stress, and are the result of slip, or dislocation mechanisms at the atomic level. Another type of irreversible deformation is viscous deformation, which is the irreversible part of viscoelastic deformation.
In the case of elastic deformations, the response function linking strain to the deforming stress is the compliance tensor of the material.
Contents
[hide]
1 Strain
1.1 Strain measures
1.1.1 Engineering strain
1.1.2 Stretch ratio
1.1.3 True strain
1.1.4 Green strain
1.1.5 Almansi strain
1.2 Normal and shear strain
1.2.1 Normal strain
1.2.2 Shear strain
1.3 Metric tensor
2 Description of deformation
2.1 Affine deformation
2.2 Rigid body motion
3 Displacement
3.1 Displacement gradient tensor
4 Examples of deformations
4.1 Plane deformation
4.1.1 Isochoric plane deformation
4.1.2 Simple shear
5 See also
6 References
7 Further reading
Strain[edit]
See also: Stress measures and Strain rate
Strain is a measure of deformation representing the displacement between particles in the body relative to a reference length.
A general deformation of a body can be expressed in the form x = F(X) where X is the reference position of material points in the body. Such a measure does not distinguish between rigid body motions (translations and rotations) and changes in shape (and size) of the body. A deformation has units of length.
We could, for example, define strain to be
ε ≐ ∂ ∂ X ( x − X ) = F ′ − I , {\displaystyle {\boldsymbol {\varepsilon }}\doteq {\cfrac {\partial }{\partial \mathbf {X} }}\left(\mathbf {x} -\mathbf {X} \right)={\boldsymbol {F}}'-{\boldsymbol {I}},}
where I is the identity tensor. Hence strains are dimensionless and are usually expressed as a decimal fraction, a percentage or in parts-per notation. Strains measure how much a given deformation differs locally from a rigid-body deformation.[3]
A strain is in general a tensor quantity. Physical insight into strains can be gained by observing that a given strain can be decomposed into normal and shear components. The amount of stretch or compression along material line elements or fibers is the normal strain, and the amount of distortion associated with the sliding of plane layers over each other is the shear strain, within a deforming body.[4] This could be applied by elongation, shortening, or volume changes, or angular distortion.[5]
The state of strain at a material point of a continuum body is defined as the totality of all the changes in length of material lines or fibers, the normal strain, which pass through that point and also the totality of all the changes in the angle between pairs of lines initially perpendicular to each other, the shear strain, radiating from this point. However, it is sufficient to know the normal and shear components of strain on a set of three mutually perpendicular directions.
If there is an increase in length of the material line, the normal strain is called tensile strain, otherwise, if there is reduction or compression in the length of the material line, it is called compressive strain.
Strain measures[edit]
Depending on the amount of strain, or local deformation, the analysis of deformation is subdivided into three deformation theories:
Finite strain theory, also called large strain theory, large deformation theory, deals with deformations in which both rotations and strains are arbitrarily large. In this case, the undeformed and deformed configurations of the continuum are significantly different and a clear distinction has to be made between them. This is commonly the case with elastomers, plastically-deforming materials and other fluids and biological soft tissue.
Infinitesimal strain theory, also called small strain theory, small deformation theory, small displacement theory, or small displacement-gradient theory where strains and rotations are both small. In this case, the undeformed and deformed configurations of the body can be assumed identical. The infinitesimal strain theory is used in the analysis of deformations of materials exhibiting elastic behavior, such as materials found in mechanical and civil engineering applications, e.g. concrete and steel.
Large-displacement or large-rotation theory, which assumes small strains but large rotations and displacements.
In each of these theories the strain is then defined differently. The engineering strain is the most common definition applied to materials used in mechanical and structural engineering, which are subjected to very small deformations. On the other hand, for some materials, e.g. elastomers and polymers, subjected to large deformations, the engineering definition of strain is not applicable, e.g. typical engineering strains greater than 1%,[6] thus other more complex definitions of strain are required, such as stretch, logarithmic strain, Green strain, and Almansi strain.
Engineering strain[edit]
The Cauchy strain or engineering strain is expressed as the ratio of total deformation to the initial dimension of the material body in which the forces are being applied. The engineering normal strain or engineering extensional strain or nominal strain e of a material line element or fiber axially loaded is expressed as the change in length ΔL per unit of the original length L of the line element or fibers. The normal strain is positive if the material fibers are stretched and negative if they are compressed. Thus, we have
e = Δ L L = l − L L {\displaystyle \ e={\frac {\Delta L}{L}}={\frac {l-L}{L}}}
where e is the engineering normal strain, L is the original length of the fiber and l is the final length of the fiber. Measures of strain are often expressed in parts per million or microstrains.
The true shear strain is defined as the change in the angle (in radians) between two material line elements initially perpendicular to each other in the undeformed or initial configuration. The engineering shear strain is defined as the tangent of that angle, and is equal to the length of deformation at its maximum divided by the perpendicular length in the plane of force application which sometimes makes it easier to calculate.
Stretch ratio[edit]
The stretch ratio or extension ratio is a measure of the extensional or normal strain of a differential line element, which can be defined at either the undeformed configuration or the deformed configuration. It is defined as the ratio between the final length l and the initial length L of the material line.
λ = l L {\displaystyle \ \lambda ={\frac {l}{L}}}
The extension ratio is approximately related to the engineering strain by
e = l − L L = λ − 1 {\displaystyle \ e={\frac {l-L}{L}}=\lambda -1}
This equation implies that the normal strain is zero, so that there is no deformation when the stretch is equal to unity.
The stretch ratio is used in the analysis of materials that exhibit large deformations, such as elastomers, which can sustain stretch ratios of 3 or 4 before they fail. On the other hand, traditional engineering materials, such as concrete or steel, fail at much lower stretch ratios.
True strain[edit]
The logarithmic strain ε, also called, true strain or Hencky strain [7]. Considering an incremental strain (Ludwik)
δ ε = δ l l {\displaystyle \ \delta \varepsilon ={\frac {\delta l}{l}}}
the logarithmic strain is obtained by integrating this incremental strain:
∫ δ ε = ∫ L l δ l l ε = ln  ( l L ) = ln  ( λ ) = ln  ( 1 + e ) = e − e 2 2 + e 3 3 − ⋯ {\displaystyle \ {\begin{aligned}\int \delta \varepsilon &=\int _{L}^{l}{\frac {\delta l}{l}}\\\varepsilon &=\ln \left({\frac {l}{L}}\right)=\ln(\lambda )\\&=\ln(1+e)\\&=e-{\frac {e^{2}}{2}}+{\frac {e^{3}}{3}}-\cdots \\\end{aligned}}}
where e is the engineering strain. The logarithmic strain provides the correct measure of the final strain when deformation takes place in a series of increments, taking into account the influence of the strain path.[4]
Green strain[edit]
Main article: Finite strain theory
The Green strain is defined as:
ε G = 1 2 ( l 2 − L 2 L 2 ) = 1 2 ( λ 2 − 1 ) {\displaystyle \ \varepsilon _{G}={\tfrac {1}{2}}\left({\frac {l^{2}-L^{2}}{L^{2}}}\right)={\tfrac {1}{2}}(\lambda ^{2}-1)}
Almansi strain[edit]
Main article: Finite strain theory
The Euler-Almansi strain is defined as
ε E = 1 2 ( l 2 − L 2 l 2 ) = 1 2 ( 1 − 1 λ 2 ) {\displaystyle \ \varepsilon _{E}={\tfrac {1}{2}}\left({\frac {l^{2}-L^{2}}{l^{2}}}\right)={\tfrac {1}{2}}\left(1-{\frac {1}{\lambda ^{2}}}\right)}
Normal and shear strain[edit]
Two-dimensional geometric deformation of an infinitesimal material element.
Strains are classified as either normal or shear. A normal strain is perpendicular to the face of an element, and a shear strain is parallel to it. These definitions are consistent with those of normal stress and shear stress.
Normal strain[edit]
For an isotropic material that obeys Hooke's law, a normal stress will cause a normal strain. Normal strains produce dilations.
Consider a two-dimensional, infinitesimal, rectangular material element with dimensions dx × dy, which, after deformation, takes the form of a rhombus. From the geometry of the adjacent figure we have
l e n g t h ( A B ) = d x {\displaystyle \mathrm {length} (AB)=dx\,}
and
l e n g t h ( a b ) = ( d x + ∂ u x ∂ x d x ) 2 + ( ∂ u y ∂ x d x ) 2 = d x 1 + 2 ∂ u x ∂ x + ( ∂ u x ∂ x ) 2 + ( ∂ u y ∂ x ) 2 {\displaystyle {\begin{aligned}\mathrm {length} (ab)&={\sqrt {\left(dx+{\frac {\partial u_{x}}{\partial x}}dx\right)^{2}+\left({\frac {\partial u_{y}}{\partial x}}dx\right)^{2}}}\\&=dx~{\sqrt {1+2{\frac {\partial u_{x}}{\partial x}}+\left({\frac {\partial u_{x}}{\partial x}}\right)^{2}+\left({\frac {\partial u_{y}}{\partial x}}\right)^{2}}}\\\end{aligned}}\,\!}
For very small displacement gradients the squares of the derivatives are negligible and we have
l e n g t h ( a b ) ≈ d x + ∂ u x ∂ x d x {\displaystyle \mathrm {length} (ab)\approx dx+{\frac {\partial u_{x}}{\partial x}}dx}
The normal strain in the x-direction of the rectangular element is defined by
ε x = extension original length = l e n g t h ( a b ) − l e n g t h ( A B ) l e n g t h ( A B ) = ∂ u x ∂ x {\displaystyle \varepsilon _{x}={\frac {\text{extension}}{\text{original length}}}={\frac {\mathrm {length} (ab)-\mathrm {length} (AB)}{\mathrm {length} (AB)}}={\frac {\partial u_{x}}{\partial x}}}
Similarly, the normal strain in the y- and z-directions becomes
ε y = ∂ u y ∂ y , ε z = ∂ u z ∂ z {\displaystyle \varepsilon _{y}={\frac {\partial u_{y}}{\partial y}}\quad ,\qquad \varepsilon _{z}={\frac {\partial u_{z}}{\partial z}}\,\!}
Shear strain[edit]
Shear strain
Common symbols
γ or ε
SI unit
1, or radian
Derivations from
other quantities
γ = τ/G
The engineering shear strain (γxy) is defined as the change in angle between lines AC and AB. Therefore,
γ x y = α + β {\displaystyle \gamma _{xy}=\alpha +\beta \,\!}
From the geometry of the figure, we have
tan  α = ∂ u y ∂ x d x d x + ∂ u x ∂ x d x = ∂ u y ∂ x 1 + ∂ u x ∂ x tan  β = ∂ u x ∂ y d y d y + ∂ u y ∂ y d y = ∂ u x ∂ y 1 + ∂ u y ∂ y {\displaystyle {\begin{aligned}\tan \alpha &={\frac {{\tfrac {\partial u_{y}}{\partial x}}dx}{dx+{\tfrac {\partial u_{x}}{\partial x}}dx}}={\frac {\tfrac {\partial u_{y}}{\partial x}}{1+{\tfrac {\partial u_{x}}{\partial x}}}}\\\tan \beta &={\frac {{\tfrac {\partial u_{x}}{\partial y}}dy}{dy+{\tfrac {\partial u_{y}}{\partial y}}dy}}={\frac {\tfrac {\partial u_{x}}{\partial y}}{1+{\tfrac {\partial u_{y}}{\partial y}}}}\end{aligned}}}
For small displacement gradients we have
∂ u x ∂ x ≪ 1 ; ∂ u y ∂ y ≪ 1 {\displaystyle {\cfrac {\partial u_{x}}{\partial x}}\ll 1~;~~{\cfrac {\partial u_{y}}{\partial y}}\ll 1}
For small rotations, i.e. α and β are ≪ 1 we have tan α ≈ α, tan β ≈ β. Therefore,
α ≈ ∂ u y ∂ x ; β ≈ ∂ u x ∂ y {\displaystyle \alpha \approx {\cfrac {\partial u_{y}}{\partial x}}~;~~\beta \approx {\cfrac {\partial u_{x}}{\partial y}}}
thus
γ x y = α + β = ∂ u y ∂ x + ∂ u x ∂ y {\displaystyle \gamma _{xy}=\alpha +\beta ={\frac {\partial u_{y}}{\partial x}}+{\frac {\partial u_{x}}{\partial y}}\,\!}
By interchanging x and y and ux and uy, it can be shown that γxy = γyx.
Similarly, for the yz- and xz-planes, we have
γ y z = γ z y = ∂ u y ∂ z + ∂ u z ∂ y , γ z x = γ x z = ∂ u z ∂ x + ∂ u x ∂ z {\displaystyle \gamma _{yz}=\gamma _{zy}={\frac {\partial u_{y}}{\partial z}}+{\frac {\partial u_{z}}{\partial y}}\quad ,\qquad \gamma _{zx}=\gamma _{xz}={\frac {\partial u_{z}}{\partial x}}+{\frac {\partial u_{x}}{\partial z}}\,\!}
The tensorial shear strain components of the infinitesimal strain tensor can then be expressed using the engineering strain definition, γ, as
ε _ _ = [ ε x x ε x y ε x z ε y x ε y y ε y z ε z x ε z y ε z z ] = [ ε x x 1 2 γ x y 1 2 γ x z 1 2 γ y x ε y y 1 2 γ y z 1 2 γ z x 1 2 γ z y ε z z ] {\displaystyle {\underline {\underline {\boldsymbol {\varepsilon }}}}=\left[{\begin{matrix}\varepsilon _{xx}&\varepsilon _{xy}&\varepsilon _{xz}\\\varepsilon _{yx}&\varepsilon _{yy}&\varepsilon _{yz}\\\varepsilon _{zx}&\varepsilon _{zy}&\varepsilon _{zz}\\\end{matrix}}\right]=\left[{\begin{matrix}\varepsilon _{xx}&{\tfrac {1}{2}}\gamma _{xy}&{\tfrac {1}{2}}\gamma _{xz}\\{\tfrac {1}{2}}\gamma _{yx}&\varepsilon _{yy}&{\tfrac {1}{2}}\gamma _{yz}\\{\tfrac {1}{2}}\gamma _{zx}&{\tfrac {1}{2}}\gamma _{zy}&\varepsilon _{zz}\\\end{matrix}}\right]\,\!}
Metric tensor[edit]
Main article: Finite strain theory § Deformation tensors in curvilinear coordinates
A strain field associated with a displacement is defined, at any point, by the change in length of the tangent vectors representing the speeds of arbitrarily parametrized curves passing through that point. A basic geometric result, due to Fréchet, von Neumann and Jordan, states that, if the lengths of the tangent vectors fulfil the axioms of a norm and the parallelogram law, then the length of a vector is the square root of the value of the quadratic form associated, by the polarization formula, with a positive definite bilinear map called the metric tensor.
Description of deformation[edit]
Deformation is the change in the metric properties of a continuous body, meaning that a curve drawn in the initial body placement changes its length when displaced to a curve in the final placement. If none of the curves changes length, it is said that a rigid body displacement occurred.
It is convenient to identify a reference configuration or initial geometric state of the continuum body which all subsequent configurations are referenced from. The reference configuration need not be one the body actually will ever occupy. Often, the configuration at t = 0 is considered the reference configuration, κ0(B). The configuration at the current time t is the current configuration.
For deformation analysis, the reference configuration is identified as undeformed configuration, and the current configuration as deformed configuration. Additionally, time is not considered when analyzing deformation, thus the sequence of configurations between the undeformed and deformed configurations are of no interest.
The components Xi of the position vector X of a particle in the reference configuration, taken with respect to the reference coordinate system, are called the material or reference coordinates. On the other hand, the components xi of the position vector x of a particle in the deformed configuration, taken with respect to the spatial coordinate system of reference, are called the spatial coordinates
There are two methods for analysing the deformation of a continuum. One description is made in terms of the material or referential coordinates, called material description or Lagrangian description. A second description is of deformation is made in terms of the spatial coordinates it is called the spatial description or Eulerian description.
There is continuity during deformation of a continuum body in the sense that:
The material points forming a closed curve at any instant will always form a closed curve at any subsequent time.
The material points forming a closed surface at any instant will always form a closed surface at any subsequent time and the matter within the closed surface will always remain within.
Affine deformation[edit]
A deformation is called an affine deformation if it can be described by an affine transformation. Such a transformation is composed of a linear transformation (such as rotation, shear, extension and compression) and a rigid body translation. Affine deformations are also called homogeneous deformations.[8]
Therefore, an affine deformation has the form
x ( X , t ) = F ( t ) ⋅ X + c ( t ) {\displaystyle \mathbf {x} (\mathbf {X} ,t)={\boldsymbol {F}}(t)\cdot \mathbf {X} +\mathbf {c} (t)}
where x is the position of a point in the deformed configuration, X is the position in a reference configuration, t is a time-like parameter, F is the linear transformer and c is the translation. In matrix form, where the components are with respect to an orthonormal basis,
[ x 1 ( X 1 , X 2 , X 3 , t ) x 2 ( X 1 , X 2 , X 3 , t ) x 3 ( X 1 , X 2 , X 3 , t ) ] = [ F 11 ( t ) F 12 ( t ) F 13 ( t ) F 21 ( t ) F 22 ( t ) F 23 ( t ) F 31 ( t ) F 32 ( t ) F 33 ( t ) ] [ X 1 X 2 X 3 ] + [ c 1 ( t ) c 2 ( t ) c 3 ( t ) ] {\displaystyle {\begin{bmatrix}x_{1}(X_{1},X_{2},X_{3},t)\\x_{2}(X_{1},X_{2},X_{3},t)\\x_{3}(X_{1},X_{2},X_{3},t)\end{bmatrix}}={\begin{bmatrix}F_{11}(t)&F_{12}(t)&F_{13}(t)\\F_{21}(t)&F_{22}(t)&F_{23}(t)\\F_{31}(t)&F_{32}(t)&F_{33}(t)\end{bmatrix}}{\begin{bmatrix}X_{1}\\X_{2}\\X_{3}\end{bmatrix}}+{\begin{bmatrix}c_{1}(t)\\c_{2}(t)\\c_{3}(t)\end{bmatrix}}}
The above deformation becomes non-affine or inhomogeneous if F = F(X,t) or c = c(X,t).
Rigid body motion[edit]
A rigid body motion is a special affine deformation that does not involve any shear, extension or compression. The transformation matrix F is proper orthogonal in order to allow rotations but no reflections.
A rigid body motion can be described by
x ( X , t ) = Q ( t ) ⋅ X + c ( t ) {\displaystyle \mathbf {x} (\mathbf {X} ,t)={\boldsymbol {Q}}(t)\cdot \mathbf {X} +\mathbf {c} (t)}
where
Q ⋅ Q T = Q T ⋅ Q = 1 {\displaystyle {\boldsymbol {Q}}\cdot {\boldsymbol {Q}}^{T}={\boldsymbol {Q}}^{T}\cdot {\boldsymbol {Q}}={\boldsymbol {\mathit {1}}}}
In matrix form,
[ x 1 ( X 1 , X 2 , X 3 , t ) x 2 ( X 1 , X 2 , X 3 , t ) x 3 ( X 1 , X 2 , X 3 , t ) ] = [ Q 11 ( t ) Q 12 ( t ) Q 13 ( t ) Q 21 ( t ) Q 22 ( t ) Q 23 ( t ) Q 31 ( t ) Q 32 ( t ) Q 33 ( t ) ] [ X 1 X 2 X 3 ] + [ c 1 ( t ) c 2 ( t ) c 3 ( t ) ] {\displaystyle {\begin{bmatrix}x_{1}(X_{1},X_{2},X_{3},t)\\x_{2}(X_{1},X_{2},X_{3},t)\\x_{3}(X_{1},X_{2},X_{3},t)\end{bmatrix}}={\begin{bmatrix}Q_{11}(t)&Q_{12}(t)&Q_{13}(t)\\Q_{21}(t)&Q_{22}(t)&Q_{23}(t)\\Q_{31}(t)&Q_{32}(t)&Q_{33}(t)\end{bmatrix}}{\begin{bmatrix}X_{1}\\X_{2}\\X_{3}\end{bmatrix}}+{\begin{bmatrix}c_{1}(t)\\c_{2}(t)\\c_{3}(t)\end{bmatrix}}}
Displacement[edit]
Figure 1. Motion of a continuum body.
A change in the configuration of a continuum body results in a displacement. The displacement of a body has two components: a rigid-body displacement and a deformation. A rigid-body displacement consists of a simultaneous translation and rotation of the body without changing its shape or size. Deformation implies the change in shape and/or size of the body from an initial or undeformed configuration κ0(B) to a current or deformed configuration κt(B) (Figure 1).
If after a displacement of the continuum there is a relative displacement between particles, a deformation has occurred. On the other hand, if after displacement of the continuum the relative displacement between particles in the current configuration is zero, then there is no deformation and a rigid-body displacement is said to have occurred.
The vector joining the positions of a particle P in the undeformed configuration and deformed configuration is called the displacement vector u(X,t) = uiei in the Lagrangian description, or U(x,t) = UJEJ in the Eulerian description.
A displacement field is a vector field of all displacement vectors for all particles in the body, which relates the deformed configuration with the undeformed configuration. It is convenient to do the analysis of deformation or motion of a continuum body in terms of the displacement field. In general, the displacement field is expressed in terms of the material coordinates as
u ( X , t ) = b ( X , t ) + x ( X , t ) − X or u i = α i J b J + x i − α i J X J {\displaystyle \ \mathbf {u} (\mathbf {X} ,t)=\mathbf {b} (\mathbf {X} ,t)+\mathbf {x} (\mathbf {X} ,t)-\mathbf {X} \qquad {\text{or}}\qquad u_{i}=\alpha _{iJ}b_{J}+x_{i}-\alpha _{iJ}X_{J}}
or in terms of the spatial coordinates as
U ( x , t ) = b ( x , t ) + x − X ( x , t ) or U J = b J + α J i x i − X J {\displaystyle \ \mathbf {U} (\mathbf {x} ,t)=\mathbf {b} (\mathbf {x} ,t)+\mathbf {x} -\mathbf {X} (\mathbf {x} ,t)\qquad {\text{or}}\qquad U_{J}=b_{J}+\alpha _{Ji}x_{i}-X_{J}\,}
where αJi are the direction cosines between the material and spatial coordinate systems with unit vectors EJ and ei, respectively. Thus
E J ⋅ e i = α J i = α i J {\displaystyle \ \mathbf {E} _{J}\cdot \mathbf {e} _{i}=\alpha _{Ji}=\alpha _{iJ}}
and the relationship between ui and UJ is then given by
u i = α i J U J or U J = α J i u i {\displaystyle \ u_{i}=\alpha _{iJ}U_{J}\qquad {\text{or}}\qquad U_{J}=\alpha _{Ji}u_{i}}
Knowing that
e i = α i J E J {\displaystyle \ \mathbf {e} _{i}=\alpha _{iJ}\mathbf {E} _{J}}
then
u ( X , t ) = u i e i = u i ( α i J E J ) = U J E J = U ( x , t ) {\displaystyle \mathbf {u} (\mathbf {X} ,t)=u_{i}\mathbf {e} _{i}=u_{i}(\alpha _{iJ}\mathbf {E} _{J})=U_{J}\mathbf {E} _{J}=\mathbf {U} (\mathbf {x} ,t)}
It is common to superimpose the coordinate systems for the undeformed and deformed configurations, which results in b = 0, and the direction cosines become Kronecker deltas:
E J ⋅ e i = δ J i = δ i J {\displaystyle \ \mathbf {E} _{J}\cdot \mathbf {e} _{i}=\delta _{Ji}=\delta _{iJ}}
Thus, we have
u ( X , t ) = x ( X , t ) − X or u i = x i − δ i J X J = x i − X i {\displaystyle \ \mathbf {u} (\mathbf {X} ,t)=\mathbf {x} (\mathbf {X} ,t)-\mathbf {X} \qquad {\text{or}}\qquad u_{i}=x_{i}-\delta _{iJ}X_{J}=x_{i}-X_{i}}
or in terms of the spatial coordinates as
U ( x , t ) = x − X ( x , t ) or U J = δ J i x i − X J = x J − X J {\displaystyle \ \mathbf {U} (\mathbf {x} ,t)=\mathbf {x} -\mathbf {X} (\mathbf {x} ,t)\qquad {\text{or}}\qquad U_{J}=\delta _{Ji}x_{i}-X_{J}=x_{J}-X_{J}}
Displacement gradient tensor[edit]
The partial differentiation of the displacement vector with respect to the material coordinates yields the material displacement gradient tensor ∇XU. Thus we have:
u ( X , t ) = x ( X , t ) − X ∇ X u = ∇ X x − I ∇ X u = F − I {\displaystyle {\begin{aligned}\mathbf {u} (\mathbf {X} ,t)&=\mathbf {x} (\mathbf {X} ,t)-\mathbf {X} \\\nabla _{\mathbf {X} }\mathbf {u} &=\nabla _{\mathbf {X} }\mathbf {x} -\mathbf {I} \\\nabla _{\mathbf {X} }\mathbf {u} &=\mathbf {F} -\mathbf {I} \\\end{aligned}}} or u i = x i − δ i J X J = x i − X i ∂ u i ∂ X K = ∂ x i ∂ X K − δ i K {\displaystyle {\begin{aligned}u_{i}&=x_{i}-\delta _{iJ}X_{J}=x_{i}-X_{i}\\{\frac {\partial u_{i}}{\partial X_{K}}}&={\frac {\partial x_{i}}{\partial X_{K}}}-\delta _{iK}\\\end{aligned}}}
where F is the deformation gradient tensor.
Similarly, the partial differentiation of the displacement vector with respect to the spatial coordinates yields the spatial displacement gradient tensor ∇xU. Thus we have,
U ( x , t ) = x − X ( x , t ) ∇ x U = I − ∇ x X ∇ x U = I − F − 1 {\displaystyle {\begin{aligned}\mathbf {U} (\mathbf {x} ,t)&=\mathbf {x} -\mathbf {X} (\mathbf {x} ,t)\\\nabla _{\mathbf {x} }\mathbf {U} &=\mathbf {I} -\nabla _{\mathbf {x} }\mathbf {X} \\\nabla _{\mathbf {x} }\mathbf {U} &=\mathbf {I} -\mathbf {F} ^{-1}\\\end{aligned}}} or U J = δ J i x i − X J = x J − X J ∂ U J ∂ x k = δ J k − ∂ X J ∂ x k {\displaystyle {\begin{aligned}U_{J}&=\delta _{Ji}x_{i}-X_{J}=x_{J}-X_{J}\\{\frac {\partial U_{J}}{\partial x_{k}}}&=\delta _{Jk}-{\frac {\partial X_{J}}{\partial x_{k}}}\\\end{aligned}}}
Examples of deformations[edit]
Homogeneous (or affine) deformations are useful in elucidating the behavior of materials. Some homogeneous deformations of interest are
uniform extension
pure dilation
equibiaxial tension
simple shear
pure shear
Plane deformations are also of interest, particularly in the experimental context.
Plane deformation[edit]
A plane deformation, also called plane strain, is one where the deformation is restricted to one of the planes in the reference configuration. If the deformation is restricted to the plane described by the basis vectors e1, e2, the deformation gradient has the form
F = F 11 e 1 ⊗ e 1 + F 12 e 1 ⊗ e 2 + F 21 e 2 ⊗ e 1 + F 22 e 2 ⊗ e 2 + e 3 ⊗ e 3 {\displaystyle {\boldsymbol {F}}=F_{11}\mathbf {e} _{1}\otimes \mathbf {e} _{1}+F_{12}\mathbf {e} _{1}\otimes \mathbf {e} _{2}+F_{21}\mathbf {e} _{2}\otimes \mathbf {e} _{1}+F_{22}\mathbf {e} _{2}\otimes \mathbf {e} _{2}+\mathbf {e} _{3}\otimes \mathbf {e} _{3}}
In matrix form,
F = [ F 11 F 12 0 F 21 F 22 0 0 0 1 ] {\displaystyle {\boldsymbol {F}}={\begin{bmatrix}F_{11}&F_{12}&0\\F_{21}&F_{22}&0\\0&0&1\end{bmatrix}}}
From the polar decomposition theorem, the deformation gradient, up to a change of coordinates, can be decomposed into a stretch and a rotation. Since all the deformation is in a plane, we can write[8]
F = R ⋅ U = [ cos  θ sin  θ 0 − sin  θ cos  θ 0 0 0 1 ] [ λ 1 0 0 0 λ 2 0 0 0 1 ] {\displaystyle {\boldsymbol {F}}={\boldsymbol {R}}\cdot {\boldsymbol {U}}={\begin{bmatrix}\cos \theta &\sin \theta &0\\-\sin \theta &\cos \theta &0\\0&0&1\end{bmatrix}}{\begin{bmatrix}\lambda _{1}&0&0\\0&\lambda _{2}&0\\0&0&1\end{bmatrix}}}
where θ is the angle of rotation and λ1, λ2 are the principal stretches.
Isochoric plane deformation[edit]
If the deformation is isochoric (volume preserving) then det(F) = 1 and we have
F 11 F 22 − F 12 F 21 = 1 {\displaystyle F_{11}F_{22}-F_{12}F_{21}=1}
Alternatively,
λ 1 λ 2 = 1 {\displaystyle \lambda _{1}\lambda _{2}=1}
Simple shear[edit]
A simple shear deformation is defined as an isochoric plane deformation in which there is a set of line elements with a given reference orientation that do not change length and orientation during the deformation.[8]
If e1 is the fixed reference orientation in which line elements do not deform during the deformation then λ1 = 1 and F·e1 = e1. Therefore,
F 11 e 1 + F 21 e 2 = e 1 ⟹ F 11 = 1 ; F 21 = 0 {\displaystyle F_{11}\mathbf {e} _{1}+F_{21}\mathbf {e} _{2}=\mathbf {e} _{1}\quad \implies \quad F_{11}=1~;~~F_{21}=0}
Since the deformation is isochoric,
F 11 F 22 − F 12 F 21 = 1 ⟹ F 22 = 1 {\displaystyle F_{11}F_{22}-F_{12}F_{21}=1\quad \implies \quad F_{22}=1}
Define
γ := F 12 {\displaystyle \gamma :=F_{12}\,}
Then, the deformation gradient in simple shear can be expressed as
F = [ 1 γ 0 0 1 0 0 0 1 ] {\displaystyle {\boldsymbol {F}}={\begin{bmatrix}1&\gamma &0\\0&1&0\\0&0&1\end{bmatrix}}}
Now,
F ⋅ e 2 = F 12 e 1 + F 22 e 2 = γ e 1 + e 2 ⟹ F ⋅ ( e 2 ⊗ e 2 ) = γ e 1 ⊗ e 2 + e 2 ⊗ e 2 {\displaystyle {\boldsymbol {F}}\cdot \mathbf {e} _{2}=F_{12}\mathbf {e} _{1}+F_{22}\mathbf {e} _{2}=\gamma \mathbf {e} _{1}+\mathbf {e} _{2}\quad \implies \quad {\boldsymbol {F}}\cdot (\mathbf {e} _{2}\otimes \mathbf {e} _{2})=\gamma \mathbf {e} _{1}\otimes \mathbf {e} _{2}+\mathbf {e} _{2}\otimes \mathbf {e} _{2}}
Since
e i ⊗ e i = 1 {\displaystyle \mathbf {e} _{i}\otimes \mathbf {e} _{i}={\boldsymbol {\mathit {1}}}}
we can also write the deformation gradient as
F = 1 + γ e 1 ⊗ e 2 {\displaystyle {\boldsymbol {F}}={\boldsymbol {\mathit {1}}}+\gamma \mathbf {e} _{1}\otimes \mathbf {e} _{2}}
See also[edit]
Euler–Bernoulli beam theory
Deformation (engineering)
Finite strain theory
Infinitesimal strain theory
Moiré pattern
Shear modulus
Shear stress
Shear strength
Stress (mechanics)
Stress measures
References[edit]
Jump up ^ Truesdell, C.; Noll, W. (2004). The non-linear field theories of mechanics (3rd ed.). Springer. p. 48.
Jump up ^ Wu, H.-C. (2005). Continuum Mechanics and Plasticity. CRC Press. ISBN 1-58488-363-4.
Jump up ^ Lubliner, Jacob (2008). Plasticity Theory (PDF) (Revised ed.). Dover Publications. ISBN 0-486-46290-0. Archived from the original (PDF) on 2010-03-31.
^ Jump up to: a b Rees, David (2006). Basic Engineering Plasticity: An Introduction with Engineering and Manufacturing Applications. Butterworth-Heinemann. ISBN 0-7506-8025-3.
Jump up ^ "Earth."Encyclopædia Britannica from Encyclopædia Britannica 2006 Ultimate Reference Suite DVD .[2009].
Jump up ^ Rees, David (2006). Basic Engineering Plasticity: An Introduction with Engineering and Manufacturing Applications. Butterworth-Heinemann. p. 41. ISBN 0-7506-8025-3.
Jump up ^ Hencky, H. (1928). "Über die Form des Elastizitätsgesetzes bei ideal elastischen Stoffen". Zeitschrift für technische Physik. 9: 215–220.
^ Jump up to: a b c Ogden, R. W. (1984). Non-linear Elastic Deformations. Dover.
Further reading[edit]
Bazant, Zdenek P.; Cedolin, Luigi (2010). Three-Dimensional Continuum Instabilities and Effects of Finite Strain Tensor, chapter 11 in "Stability of Structures", 3rd ed. Singapore, New Jersey, London: World Scientific Publishing. ISBN 9814317039.
Dill, Ellis Harold (2006). Continuum Mechanics: Elasticity, Plasticity, Viscoelasticity. Germany: CRC Press. ISBN 0-8493-9779-0.
Hutter, Kolumban; Jöhnk, Klaus (2004). Continuum Methods of Physical Modeling. Germany: Springer. ISBN 3-540-20619-1.
Jirasek, M; Bazant, Z.P. (2002). Inelastic Analysis of Structures. London and New York: J. Wiley & Sons. ISBN 0471987166.
Lubarda, Vlado A. (2001). Elastoplasticity Theory. CRC Press. ISBN 0-8493-1138-1.
Macosko, C. W. (1994). Rheology: principles, measurement and applications. VCH Publishers. ISBN 1-56081-579-5.
Mase, George E. (1970). Continuum Mechanics. McGraw-Hill Professional. ISBN 0-07-040663-4.
Mase, G. Thomas; Mase, George E. (1999). Continuum Mechanics for Engineers (2nd ed.). CRC Press. ISBN 0-8493-1855-6.
Nemat-Nasser, Sia (2006). Plasticity: A Treatise on Finite Deformation of Heterogeneous Inelastic Materials. Cambridge: Cambridge University Press. ISBN 0-521-83979-3.
Prager, William (1961). Introduction to Mechanics of Continua. Boston: Ginn and Co. ISBN 0486438090.
Retrieved from "https://en.wikipedia.org/w/index.php?title=Deformation_(mechanics)&oldid=802911124"
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text:
Gregg Sulkin
From Wikipedia, the free encyclopedia
Jump to: navigation, search
Gregg Sulkin
Sulkin at the 2014 PaleyFest Fall TV Premiere presentation for MTV's Faking It.
Born
(1992 -05-29) 29 May 1992 (age 25)
City of Westminster, London, England[1]
Residence
Los Angeles, California
Occupation
Actor
Years active
2002—present
Gregg Sulkin (/ˈsʌlkɪn/; born 29 May 1992) is an English actor. At age ten he made his film debut in the 2002 Doctor Zhivago mini-series. He later landed the starring role in the 2006 British release Sixty Six, and subsequently became known for appearing in the Disney Channel comedy series As the Bell Rings and Wizards of Waverly Place. In 2010, he starred in the Disney Channel television movie Avalon High. He also appeared in the television special The Wizards Return: Alex vs. Alex. He starred on MTV's show Faking It as Liam Booker from 2014 until its cancellation in 2016. He also appeared on Pretty Little Liars as Ezra's brother, Wesley "Wes" Fitzgerald. In 2016, he starred in the role of Sam Fuller in the horror-thriller film, Don't Hang Up.[2] He is currently starring as Chase Stein in the TV show Runaways, based on the Marvel Comics series of the same name.[3]
Contents
[hide]
1 Early life
2 Career
3 Personal life
4 Filmography
4.1 Film
4.2 Television
5 Awards and nominations
6 References
7 External links
Early life[edit]
Sulkin was born in Westminster, London. He is Jewish and had his Bar Mitzvah at the Western Wall in Jerusalem.[4][5][6][7] He attended Highgate School in North London.[8]
Career[edit]
Sulkin posing with a fan in January 2012
Sulkin made his acting debut in the 2002 mini-series Doctor Zhivago. He subsequently starred in the comedy Sixty Six,[9] as Bernie Rubens, alongside Helena Bonham Carter, Eddie Marsan and Catherine Tate.[10] Sulkin also played the role of JJ in the Disney Channel comedy, As the Bell Rings,[9] worked on a CBBC children sci-fi show The Sarah Jane Adventures (spin-off of Doctor Who), playing Adam in series 3 two-episode story The Mad Woman in the Attic.
Sulkin was on Disney Channel's Pass the Plate as Gregg from the UK. He had a recurring guest role on the Disney Channel series Wizards of Waverly Place, where he played Alex's love interest Mason Greyback he reprised his role in 4 episodes of season 3 and returned to the series in its fourth season,[11] and through to its finale.[12] Sulkin has also landed a role in the thriller The Heavy.[13]
In 2010, he went to New Zealand making a Disney Channel film Avalon High, which premiered on 12 November 2010.[14][15] In an interview with Kyle Martino, aired on Soccer Talk Live on the Fox Soccer Channel in the US, Sulkin announced that he was a fan of Arsenal. Sulkin was on the Disney Channel's Friends for Change Games and was on the Yellow Team.[16] He reprised his role as Mason Greyback in The Wizards Return : Alex vs. Alex on Friday, 15 March on Disney Channel.
In 2012, Sulkin starred in the American teen drama series Pretty Little Liars as a recurring character, Wesley Fitzgerald, brother of Ezra Fitz. In February 2013, it was announced that Sulkin would play Julian Fineman in FOX's television adaptation of Lauren Oliver's young adult novel, Delirium. On 8 May, it was reported that Fox has decided not to pick up Delirium.[17] Since 2014, Sulkin has starred in the MTV comedy Faking It. Sulkin portrays Liam Booker. Sulkin defeated Victoria Justice on 30 July 2015 episode of Spike TV's Lip Sync Battle, where he wore a wig and went shirtless to perform the hit Kelis song "Milkshake".[18]
Sulkin starred in the leading role of Sam Fuller in the horror-thriller film, Don't Hang Up which was released in theatres on 10 February 2017.[19][20]
Sulkin currently plays Chase Stein on Marvels Runaways a Marvel original show airing on Hulu. The show was renewed for a second season 2 days after season 1 ended.
Personal life[edit]
Sulkin dated Bella Thorne from 2015 to 2016.[21][22] He is also a fan of Arsenal F.C..[23]
Filmography[edit]
Film[edit]
Year
Title
Role
Notes
2006 Sixty Six Bernie Rubens
2009 The Heavy Teen Two
2011 Camilla Dickinson Frank Rowan
2012 White Frog Randy Goldman
2013 Another Me Drew
2014 Affluenza Dylan Carson
2015 A Mouse Tale The Dark Rodent Voice role; direct-to-DVD
2015 Yak: The Giant King Flapper Voice role
2015 Anti-Social Dee
2016 Don't Hang Up Sam Fuller
2018 Status Update Derek Lowe Post-production
Television[edit]
Year
Title
Role
Notes
2002 Doctor Zhivago Seryozha Television miniseries (ITV)
2006 Pass the Plate Himself
2006 Man on the Moon Michael Aldrin Television special (Channel 4)
2007–2008 As the Bell Rings JJ Main role
2009 The Sarah Jane Adventures Adam 2 episodes
2010 Avalon High Will Wagner Disney Channel Original Movie
2010–2012 Wizards of Waverly Place Mason Greyback Recurring role (seasons 3–4); 15 episodes
2011 R. L. Stine's The Haunting Hour Matt Episode: "The Perfect Brother"
2011 Get the Look Himself
2012 Melissa & Joey Haskell Davis 3 episodes
2012 Pretty Little Liars Wesley Fitzgerald Recurring role; 4 episodes
2013 The Wizards Return: Alex vs. Alex Mason Greyback Television special (Disney Channel)
2013 Delirium Julian Fineman Unsold television pilot
2014 A Daughter's Nightmare Ben Woods Television movie (Lifetime)
2014–2016 Faking It Liam Booker Main role
2016 Life in Pieces Jake Episode: "Prank Assistant Gum Puppy"
2016 Young & Hungry Rick Episode: "Young & Assistant"
2017 Drink, Slay, Love Jadrien Television movie (Lifetime)[citation needed]
2017–present Runaways Chase Stein Main role
Awards and nominations[edit]
Year
Awards
Category
Recipient
Result
Refs
2015 Teen Choice Awards Choice Summer TV Star: Male Faking It Nominated [citation needed]
2016 Teen Choice Awards Choice Summer TV Star: Male Faking It Nominated [citation needed]
References[edit]
Jump up ^ "Person Details for Gregg Sulkin, "England and Wales Birth Registration Index, 1837-2008" — FamilySearch.org".
Jump up ^ Thomas Commonwealth. "{TB EXCLUSIVE} JOE JOHNSON BEGS YOU – "DON'T HANG UP"". The Tracking Board. Retrieved 19 March 2015.
Jump up ^ Fujikawa, Jenn (20 November 2017). "'Marvel's Runaways: Meet the Steins'". Marvel.com. Retrieved 6 December 2017.
Jump up ^ "Gregg Sulkin on Twitter". Twitter. Retrieved 30 March 2015.
Jump up ^ Gorov, Lynda (17 August 2008). "Just a Jewish mum (no corset, cauldron)". Boston Globe. Retrieved 25 August 2014.
Jump up ^ "EXCLUSIVE: Gregg Sulkin Talks Disney, Turning 21 and his Bar Mitzvah". Shalom Life. Archived from the original on 16 June 2013. Retrieved 30 March 2015.
Jump up ^ Srulowitz, Rebecca (23 July 2009). "Miley Cyrus' boyfriend kicks around Israel". JWeekly. Retrieved 29 March 2010.
Jump up ^ Wallis, Lauren. "The barmitzvah boy". TotallyJewish.com. Retrieved 28 May 2010.
^ Jump up to: a b McPartland, Ben (20 April 2007). "Highgate's Sixty Six star is getting dizzy with his Disney days". Hampstead and Highgate Express. Archived from the original on 9 May 2009. Retrieved 20 April 2009.
Jump up ^ Jury, Louise (22 October 2005). "Four goals and a Bar Mitzvah: '66 World Cup made into film". The Independent. Retrieved 20 April 2009.
Jump up ^ "The magic continues as Disney Channel orders fourth season of Emmy award-winning series "Wizards of Waverly Place"". Disney Channel. 3 June 2010. Retrieved 4 June 2010.
Jump up ^ "Gregg Sulkin Talks About Wizards Finale". Sinchronicity. 11 December 2011. Retrieved 15 January 2012.
Jump up ^ "Sixty Six Production Notes" (PDF). p. 15. Retrieved 20 April 2009.
Jump up ^ "Production has begun in New Zealand on "Avalon High," a Disney Channel original film that brings Arthurian legend alive at a contemporary high school". Disney Channel. 3 May 2010. Retrieved 4 June 2010.
Jump up ^ "Disney Channel & Disney XD Present Programming Plans for 2010-11". TVbytheNumbers.com. 3 March 2010. Retrieved 5 June 2010.
Jump up ^ Help People and the Planet, Friends for Change.
Jump up ^ Hibberd, James (8 May 2013). "Fox rejects 'Delirium' pilot starring Emma Roberts". Entertainment Weekly. Retrieved 8 May 2013.
Jump up ^ Emery, Debbie (30 July 2015). "Nickelodeon Star Victoria Justice Takes on Gregg Sulkin in Sticky Lip Sync Battle Video". The Wrap. Retrieved 21 August 2015.
Jump up ^ Thomas Commonwealth. "{TB EXCLUSIVE} JOE JOHNSON BEGS YOU – "DON'T HANG UP"". The Tracking Board. Retrieved 19 March 2015.
Jump up ^ http://www.the-numbers.com/movie/Dont-Hang-Up-(UK)#tab=summary
Jump up ^ "Gregg Sulkin, Bella Thorne's Boyfriend: 5 Fast Facts You Need to Know". Heavy.com. Retrieved 4 March 2016.
Jump up ^ Briones, Isis (15 August 2016). "Bella Thorne and Gregg Sulkin Have Broken Up". Teen Vogue. Retrieved 12 November 2016.
Jump up ^ "Gregg Sulkin: Arsenal Fan". Twitter.com.
External links[edit]
Wikimedia Commons has media related to Gregg Sulkin.
Gregg Sulkin on IMDb
Gregg Sulkin at the Music Television
Gregg Sulkin on Twitter
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LCCN: no2015120414
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Blood In Blood Out
From Wikipedia, the free encyclopedia
Jump to: navigation, search
This article is about the 1993 film. For other uses, see Blood In, Blood Out (disambiguation).
Bound by Honor
Theatrical release poster
Directed by
Taylor Hackford
Produced by
Taylor Hackford
Jerry Gershwin
Screenplay by
Jimmy Santiago Baca
Jeremy Iacone
Floyd Mutrux
Story by
Ross Thomas
Starring
Jesse Borrego
Benjamin Bratt
Enrique Castillo
Damian Chapa
Music by
Bill Conti
Cinematography
Gabriel Beristain
Edited by
Fredric Steinkamp
Karl F. Steinkamp
Production
company
Hollywood Pictures
Distributed by
Buena Vista Pictures
Release date
April 16, 1993 (1993-04-16)
Running time
180 minutes[1]
190 minutes (Director's cut)
Country
United States
Language
English
Spanish
Budget
$35 million
Box office
$4,496,583
Blood In Blood Out (also known as Bound by Honor) is a 1993 American crime-drama film directed by Taylor Hackford. It follows the intertwining lives of three Chicano relatives from 1972 to 1984. They start out as members of a street gang in East Los Angeles, and as dramatic incidents occur, their lives and friendships are forever changed. Blood In Blood Out was filmed in 1991 throughout the Spanish-speaking areas of Los Angeles and inside California's San Quentin State Prison.
Contents
[hide]
1 Plot
2 Cast
3 Production
4 Reception
5 References
6 External links
Plot[edit]
Miklo is a man of Mexican and White American ethnicity who grew up in El Pico Aliso barrio in east Los Angeles. Upon moving back home from Las Vegas, Nevada, Miklo goes to stay with his two cousins Paco and Cruz. Miklo tells Cruz that he wants to join their gang Vatos Locos. While Paco is initially skeptical, Miklo later proves himself when he performs an attack on a rival gang, Tres Puntos. Afterwards he is made a member of Vatos Locos.
However, the Tres Puntos gang soon takes revenge by brutally attacking Cruz who is a budding artist, and damages his back for life. When Vatos Locos learn of the attack, they perform a well-planned counterattack. However, things go wrong when Miklo ends up getting shot by their rival gang's leader, "Spider". Miklo is able to shoot and kill Spider, but has to be rushed to the hospital by Paco while being chased by police. Paco crashes into another car at the El Pino tree and they are both arrested.
From here, the trio's paths diverges: Miklo is sent to San Quentin State Prison for murder, Paco volunteers for military service in the United States Marine Corps as an alternative choice to prison, and Cruz continues his passion for art. He also becomes a heroin addict due to the recurring back pain. His addiction leads to him being disowned by his family after his 12-year-old brother, Juanito, dies from injecting heroin into his veins thinking it's Cruz's heroin supply. Paco becomes an L.A.P.D. narcotics detective after leaving the Marine Corps.
Miklo finds trouble adapting to prison life. The prison is run by three prison gangs, all of whom are based on their racial backgrounds. The Black Guerrilla Army (B.G.A.) is led by "Bonafide", the Aryan Vanguard is led by "Red Ryder", and La Onda is led by Montana Segura. La Onda's members do not initially accept Miklo and one of them, Popeye, tries to rape Miklo at knife-point, but is stopped by Montana. After meeting Montana, he is told the only way into La Onda is killing an enemy inmate, in Miklo's case a white inmate named Big Al who runs the gambling in San Quentin. After gaining Big Al's trust, Miklo stabs him to death during a sexual encounter in the prison kitchen. Miklo is initiated into La Onda, is later promoted to its Ruling Council, and is granted parole after serving nine years in prison.
On the outside, Miklo is disgusted by his menial job on which his supervisor is extorting money from him, so he joins in an armed robbery. The heist goes poorly and Miklo is intercepted by Paco, now a decorated cop. Miklo tries to run away, but Paco shoots him in the leg, which later has to be amputated. Miklo is sent back to prison where he notices the cocaine addictions of several inmates. Onda Council Member Carlos has entered the cocaine trade and is competing with the B.G.A. for customers. The Aryan Vanguard want to partner with Carlos in the cocaine business by becoming his new supplier. In return, Carlos moves on the B.G.A. and take them out of the cocaine business. Montana, however, is fiercely against allowing La Onda to enter the drug trade, saying that drugs will destroy La Onda and that the Aryan Vanguard want to start a war between the Black and Chicano inmates. The other Council members agree with Montana and vote against it. This causes Carlos to leave La Onda to work with the Aryan Vanguard, causing other members to follow him. Carlos murders a B.G.A. soldier named "Pockets" who is running the B.G.A.'s cocaine operation. He also contacts his brother, Smokey, outside of prison to bomb a B.G.A. hangout where they move their drugs. After all of this happens, Carlos' usefulness has come to an end and the Aryan Vanguard drops their protection of him. The B.G.A. then takes the opportunity to murder Carlos. Despite his death, Miklo agrees with Carlos's outlook after being convinced by Carlos's old drug supplier.
With hostility high between the Black and Hispanic inmates, Montana and Bonafide meet in the prison yard. Montana convinces Bonafide to agree to a truce if Montana reaches out to La Onda leaders in the Folsom and Chino prisons to end the violence. The warden grants Montana special permission to visit the Chino and Folsom prisons and Miklo is left in charge during his absence. Montana is granted a special request, and he gets to stay overnight at Delano penitentiary where he can see his daughter. On the morning of the visit, Montana is stabbed to death outside his cell by a member of the B.G.A.. Believing that the Aryan Vanguard sent forged orders to the hitman, Paco arranges a peace conference between La Onda and the B.G.A. However, Miklo, La Onda's new leader, manipulates the peace talks in order to build an alliance with the B.G.A. and they agree to kill the Aryan Vanguard leaders.
Later, enforcers for La Onda and the B.G.A. sweep through the walls of San Quentin, killing the leaders of the Aryan Vanguard. After the killings are done, however, Miklo's men promptly exterminate the B.G.A. leaders as well. Paco is enraged that his own cousin has played him for a fool and angrily confronts Miklo in the prison visiting room. Paco leaves his cousin in disgust, disowning him forever.
The members of La Onda hold a final gathering after the warden vows to split the council up transporting some members to their home states. Miklo plans on using this to expand La Onda to other states in the South West. Later, Miklo and his cellmate "Magic" destroy the mold which they used to send the forged orders to the B.G.A. hit man to kill Montana. Magic says "We both loved him, but we did what we had to do for La Onda." Back in East Los Angeles, Paco visits one of Cruz's murals after the family re-accepts him to see a portrait of his former life. In a pep talk with Cruz, Paco realizes that by ordering Miklo to go after Spider, Paco is responsible for all of the things that have happened to Miklo. This causes Paco to feel guilty for his actions and ultimately forgive Miklo.
Cast[edit]
Damian Chapa as Miklo Velka
Jesse Borrego as Cruz Candelaria
Benjamin Bratt as Paco Aguilar
Enrique Castillo as Montana Segura
Delroy Lindo as Bonafide
Victor Rivers as Magic
Geoffrey Rivas as Carlos
Tom Towles as Red Ryder
Carlos Carrasco as Popeye
Theodore Wilson as Wallace
Raymond Cruz as Chuey
Valente Rodriguez as Frankie
Lanny Flaherty as Big Al
Billy Bob Thornton as Lightning
Danny Trejo as Geronimo
Victor Mohica as Mano
Luis Contreras as Realthing
Paulo Tocha as Apache
Ving Rhames as Ivan
Richard Masur (uncredited) as Prison librarian
Thomas F. Wilson as Rollie McCann
Lupe Ontiveros as Carmen
Ashley Judd as Paco's Girlfriend ("deleted scene")
Peter Mark Vasquez as Chivo
Mark Rich as Miklo's Stunt Double
Production[edit]
This section does not cite any sources. Please help improve this section by adding citations to reliable sources. Unsourced material may be challenged and removed. (February 2015) (Learn how and when to remove this template message)
The three prison gangs in the film are fictional creations of screenwriter Jimmy Santiago Baca and director Taylor Hackford. However, they were all loosely based on actual prison gangs, with the Aryan Vanguard, Black Guerrilla Army and La Onda representing the Aryan Brotherhood, Black Guerrilla Family, and the Mexican Mafia, respectively.
Actor Theodore Wilson died shortly after filming his scenes in the film.
Artist Adan Hernandez was hired to create the paintings the character of Cruz Candelaria was supposed to have painted. All of the paintings that were used in the film were created by him. The mural in the reservoir seen in the film's climax has unfortunately been painted over. Hernandez made a cameo appearance in the film as the drug dealer Gilbert in the art gallery scene.
The film was shot in and around Los Angeles and East Los Angeles and inside the walls of San Quentin State Prison. The main character Miklo is sent to San Quentin, where much of the film's plot takes place. Several of the then-inmates appear in the film as extras. In addition, several of the prison staff members also appear as others and some facilitated the production of the film by serving as technical advisors. Many members of the staff were given small lines in the film, with the warden giving an extended cameo in a part that is somewhat integral to the plot. In addition, actor Danny Trejo, who appears in the film as Geronimo, had served time in San Quentin before deciding to become an actor.
In addition to prison inmates and staff and artist Hernandez, screenwriter and barrio poet Jimmy Santiago Baca cameos as a prison inmate and member of the La Onda council.
The film was initially entitled Blood in Blood Out but was retitled Bound by Honor before the film's release. Blood in blood out refers to the initiation ritual of having to kill someone to enter a gang and, on the reverse end, not being able to leave the gang unless killed. This is a common initiation in many gangs, including prison gangs, and is also the motto of La Onda in the film. Hollywood Pictures insisted on the name change as the studio felt that it would incite violence in East Los Angeles. In addition, executives at Hollywood Pictures, a subsidiary of Disney, were cautious about the potential effect the film would have following the 1992 LA Riots and the attribution given to Boyz N the Hood as a partial cause/inspiration of the riots. Director Taylor Hackford has stated that he was very unhappy with this decision as the film's message was the exact opposite of the one that the studio feared would be transmitted.
Reception[edit]
The film received mixed reviews from critics. It holds a 55% rating on Rotten Tomatoes, based on 11 reviews.[2] The TV Guide review stated "similarity to Edward James Olmos' American Me, in which a tormented drug dealer travels the same route through prison society as Miklo. The principal difference between the two films is that Bound By Honor is by far the glossier effort, relentlessly picturesque in the seamlessly anesthetized manner of mainstream Hollywood films."[3] Film critic Jonathan Rosenbaum for the Chicago Reader wrote that this "ugly three-hour snoozefest is apparently supposed to do for East Los Angeles Chicanos what the Godfather movies did for New York mafiosi…"[4] Roger Ebert wrote "The East Los Angeles milieu and some of the characters seem familiar, because some of the same ground was covered by American Me... Bound by Honor covers similar material in a less passionate and finally less meaningful way."[5] Roger Ebert gave the film 2 stars out of 4. A critic from Entertainment Weekly, Owen Gleiberman gave Bound By Honor a B-, falling on the high end of the movie spectrum. He states "Bound By Honor comes fully alive when it moves behind bars. There's an exploitative thrill built into the genre…"[6] This film critic was definitely more interested in the second half of the movie once Miklo was in jail running La Onda. Vincent Canby from The New York Times wrote "The film is big and long, passionate and flat. It's full of heroic and tragic incident, but skimpy about the details of quotidian lives."[7] Giving a very detailed review on the plot of the story he later exalts some of the characters in the movie one in particular, Enrique Castillo. Although Vincent Canby does not give an official rating for the film, he concludes "Though it's not the epic it means to be, it is not a failure."[8]
References[edit]
Jump up ^ "BLOOD IN BLOOD OUT (18)". British Board of Film Classification. 1993-05-19. Retrieved 2012-11-06.
Jump up ^ Blood In, Blood Out (Bound by Honor) – Rotten Tomatoes
Jump up ^ "Bound By Honor". TVGuide.com. Retrieved 2015-11-03.
Jump up ^ "Bound by Honor". Chicago Reader. Retrieved 2015-11-03.
Jump up ^ Ebert, Roger. "Bound By Honor Movie Review & Film Summary (1993) | Roger Ebert". www.rogerebert.com. Retrieved 2015-11-03.
Jump up ^ "Bound by Honor | EW.com". Entertainment Weekly's EW.com. Retrieved 2015-11-03.
Jump up ^ "Movie Review - - Review/Film; The Chicano Experience, in Its Glory and Tedium – NYTimes.com". www.nytimes.com. Retrieved 2015-11-03.
Jump up ^ "Movie Review – Bound By Honor – Review/Film; The Chicano Experience, in Its Glory and Tedium – NYTimes.com". www.nytimes.com. Retrieved 2015-11-03.
External links[edit]
Blood In Blood Out on IMDb
Blood In Blood Out at AllMovie
Blood In Blood Out at Box Office Mojo
[hide]
v
t
e
Films directed by Taylor Hackford
Teenage Father (1978)
The Idolmaker (1980)
An Officer and a Gentleman (1982)
Against All Odds (1984)
White Nights (1985)
Hail! Hail! Rock 'n' Roll (1987)
Everybody's All-American (1988)
Blood In Blood Out (1993)
Dolores Claiborne (1995)
The Devil's Advocate (1997)
Proof of Life (2000)
Ray (2004)
Love Ranch (2010)
Parker (2013)
The Comedian (2016)
Retrieved from "https://en.wikipedia.org/w/index.php?title=Blood_In_Blood_Out&oldid=833954643"
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1993 films
1990s crime thriller films
1990s crime drama films
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Films scored by Bill Conti
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Films set in the 1970s
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