Formulation of a strain based orthotropic elasto-plastic damage theory

A strain based orthotropic elasto-plastic damage theory is derived for solv ing engineering problems. The basic ideas of the formulation are first expl ained by the one-dimensional approach. Subsequently, the approach is genera lized to develop the theory in three-dimensional space. Damage is character ized by a second order damage tensor D while its effects on mechanical prop erties are described by a fourth order damage effect tensor M. The concept of elastic energy equivalence is adopted to determine the stress-strain rel ation in terms of the effective stress and the effective strain. On the bas is of the plastic flow rule and the damage potential, the elasto-plastic da mage tangent tensor as well as the damage threshold function are obtained. Since the development of damage usually connects with deformation, the stra in based theory is easier to use in solving structural problems. An example case of uniaxial stretching of aluminium alloy 2024T3 plate is employed to justify the applicability of the theory. The results show that the theoret ical results are in good agreement with the experimental ones.