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Integrated Computational Materials Engineering (ICME) for Metals: Using Multiscale Modeling to Invigorate Engineering Design with Science by Mark F. Horstemeyer

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2.3 KINEMATICS OF DEFORMATION AND STRAIN

Strain is the geometrical expression of deformation caused by the action of stress on a physical body. When a body is changed, it is the strain that defines the relative position of any two points. On the other hand, a body is called rigid if the distance between every pair of points in the body remains constant during the body’s motion. The rigid body displacements and deformations comprise translations and rotations. The strain at a point is therefore defined as the same for elastic and plastic deforming bodies. If we make no assumptions about the size of deformation, then the resulting strain tensor is valid for every situation. However, this strain tensor is nonlinear and leads to a complex analysis. Therefore, if the deformation is small (typically less than 2%), then we can use a small deformation analysis, which is linear and simpler to use. If the deformation is large, then rotations become important and texture needs to be analyzed (Chapter 3 discusses in detail the large strain formulation with texture).

Given that strain results in a body’s deformation, it can be measured by calculating the change in length of a line or by the change in angle between two lines (where these lines are theoretical constructs within the deformed body). The change in length of a line is termed the stretch, absolute strain, or extension, and may be written as δl. Then the (relative) strain ε is given by

 (2.22)

where ε is the strain in measured direction, ...

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