On the gradient-enhanced damage model for a hyperelastic material

An approach for modeling damage in the material in a geometrically nonlinear setting is studied. We consider a gradient-enhanced damage approach where the damage variable is taken as an independent variable, and the fluxes conjugated to the damage gradient are computed. The concept of maximum dissipation is used to derive the global Kuhn-Tucker conditions. The total free energy function consists of two nonlocal terms corresponding to referential gradient of the nonlocal damage variable and a penalty term to bridge the local damage variable and the nonlocal damage variable. Based on the principle of minimum total potential energy, a coupled system of Euler-Lagrange equations is obtained and solved in weak form. These nonlinear system of equations is solved by a standard Newton-Raphson-type solution scheme. The regularization capabilities, as well as the accuracy and efficiency of the proposed damage models are demonstrated by some standard benchmark examples.