Abstract
A coupled theory of elasticity and continuum damage mechanics is formulated for metals in this chapter. It is assumed that the material undergoes damage with small elastic strains. The hypothesis of elastic energy equivalence is used to produce the proposed coupling. The damage variable used represents average material degradation that reflects the various types of damage at the microscale level such as nucleation and growth of voids, cavities, microcracks, and other microscopic defects. The constitutive model is numerically implemented using finite elements with an updated Lagrangian description. This chapter also explains how the model can be applied to the problems of ductile fracture. The problem of crack initiation in a thin plate with a center crack that is subjected to uniaxial tension is analyzed using the constitutive model. Damage variable has been shown to be tensorial in nature in the general case of anisotropic damage. This damage tensor was shown to be an irreducible even-rank tensor. Several other properties of the damage tensor have been outlined in a rigorous mathematical treatment using the theory of tensor functions.
Published Version
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