Nonlinear analysis formulation > Inelastic stress-strain behavior

A material is called nonlinear if a strain-dependent matrix rather than a matrix of constants relate stresses and strains. Plastic flow is a cause of material non-linearity. During plastic straining, the material may flow in an "associated" manner, that the vector of plastic strain increment may be normal to the yield or failure surface. Alternatively, normality may not exist and the flow may be "non-associated". For frictional materials, whose ultimate state is described by the Mohr-Coulomb criterion, non-associated flow rules may be preferred in which plastic straining is described by a plastic potential potential function.

In order to formulate a theoretical description, three requirements have to be addressed, yield criterion, flow rule and hardening rule.