# OOF: Finite Element Analysis of Microstructures

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#

Plane Stress and Plane Strain

*Plane strain*is defined by the strain state ; it is the limiting condition in the center plane of a very thick specimen. An out-of-plane stress is required to maintain plane strain.

*Plane stress* is defined by the stress state
;
it holds at the surface of a thin specimen. The displacement field in
the direction is not zero nor is it uniform in an heterogeneous
grid.

Using plane stress or plane strain, the stiffness tensor can be reduced from three to two dimensions, because the components of stress and strain have been eliminated from the problem. In the matrix representation, becomes a matrix, with rows labeled 11, 22, and 12 in the original tensor indices.

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