A plasticity-damage theory for large deformation of solids—I. Theoretical formulation

Abstract

A coupled theory of continuum damage mechanics and finite strain plasticity (with small elastic strains) is formulated in the Eulerian reference system. The yield function used is of the von Mises type and incorporates both isotropic and kinematic hardening. An explicit matrix representation is derived for the damage effect tensor for a general state of deformation and damage. Although the theory is applicable to anisotropic damage, the matrix representation is restricted to isotropy. A linear transformation is shown to exist between the effective deviatoric Cauchy stress tensor and the total Cauchy stress tensor. It is also shown that a linear transformation between the deviatoric Cauchy stress tensor and its effective counterpart is not possible as this will lead to plastic incompressibility in damaged materials. In addition, an effective elasto-plastic stiffness tensor is derived that includes the effects of damage. The proposed model is applied to void growth through the use of Gurson's yield function. It is also shown how a modified Gurson function can be related to the proposed model. Some interesting results are obtained in this case.