Stress and Strain

Strain describes deformation, while stress describes internal resistance to deformation. In small-strain linear analysis, strain is derived from spatial gradients of the displacement field.

For a displacement field u, the infinitesimal strain tensor is defined as the symmetric part of the displacement gradient. In matrix form, the strain vector is commonly written as:

epsilon = B u_e

where B is the strain-displacement matrix and u_e is the element nodal displacement vector.

Stress is related to strain through the material constitutive law. For linear elastic materials:

sigma = D epsilon

where D is the material stiffness matrix. Stress components are usually evaluated at element integration points and may later be extrapolated or averaged for visualization.