Formulation of a strain based orthotropic elasto-plastic damage theory

A strain based orthotropic elasto-plastic damage theory is derived for solving engineering problems. The basic ideas of the formulation are first explained by the one-dimensional approach. Subsequently, the approach is generalized to develop the theory in three-dimensional space. Damage is characterized by a second order damage tensor D while its effects on mechanical properties are described by a fourth order damage effect tensor M. The concept of elastic energy equivalence is adopted to determine the stress-strain relation in terms of the effective stress and the effective strain. On the basis of the plastic flow rule and the damage potential, the elasto-plastic damage tangent tensor as well as the damage threshold function are obtained. Since the development of damage usually connects with deformation, the strain based theory is easier to use in solving structural problems. An example case of uniaxial stretching of aluminum alloy 2024T3 plate is employed to justify the applicability of the theory. The results show that the theoretical results are in good agreement with the experimental ones.