Numerical analysis of nonlocal anisotropic continuum damage

This article deals with the numerical analysis of anisotropic continuum damage in ductile metals based on thermodynamic laws and nonlocal theories. The proposed model is based on a generalized macroscopic theory within the framework of nonlinear continuum damage mechanics taking into account the kinematic description of the damage. A generalized yield condition is employed to describe the plastic flow characteristics of the matrix material, whereas the damage criterion provides a realistic representation of material degradation. The nonlocal theory of inelastic continua is established, which incorporates the macroscopic interstate variables and their higher-order gradients which properly describe the change in the internal structure and investigate the size effect of statistical inhomogeneity of the heterogeneous material. The idea of bridging length scales is made by using the higher-order gradients only in the evolution equations of the equivalent inelastic strain measures. This leads to a system of elliptic partial differential equations which is solved using the finite difference method. The applicability of the proposed continuum damage theory is demonstrated by finite element analyses of the inelastic deformation process of tension specimens.