Formulation of elastoplastic matrices
The finite element method – material nonlinear analysis

Given the non-linear nature of the elastoplastic behavior of structures, it is essential to employ an incremental formulation to enable the state of the structure to be progressively followed throughout the loading history. The latter plays a fundamental role in the development of plastic deformation and material strain-hardening.

To describe the elastoplastic behavior, we assume the following:

• total deformation can be broken down into elastic and plastic components: ${\epsilon }_{\text{ij}}={\epsilon }_{\text{ij}}^{\text{e}}+{\epsilon }_{\text{ij}}^{\text{p}}$;

• the law of elasticity remains applicable, but only as a function of elastic...