A continuum damage modeling based on the theory of materials of type N is proposed and its nonlinear finite element approximation and numerical simulation are carried out. To solve the finite elastoplasticity problems, the reasonable kinematical strain measure for large deformed solids are introduced and constitutive relations based on the theory of materials of type N are derived. These highly nonlinear equations are reduced to the incremental weak formulation and approximated by the theory of nonlinear finite element method. To verify the theory and the computer code, the computational simulation of the uniaxial elongation is carried out and the results are compared with the actual experiment. Two example problems, bending problem and billet forming problem, are simulated, and the deformed shapes and the progressive results of the damage variable are presented.

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