Continuum modelling and numerical simulation of material damage at finite strains

Summary This paper describes in detail a general framework for the continuum modelling and numerical simulation of internal damage in finitely deformed solids. The development of constitutive models for material deterioration is addressed within the context of Continuum Damage Mechanics. Links between micromechanical aspects of damage and phenomenological modelling within continuum thermodynamics are discussed and a brief historical review of Continuum Damage Mechanics is presented. On the computational side, an up-to-date approach to the finite element solution of large strain problems involving dissipative materials is adopted. It relies on an implicit finite element discretization set on the spatial configuration in conjunction with the full Newton-Raphson scheme for the iterative solution of the corresponding non-linear systems of equations. Issues related to the numerical integration of the path dependent damage constitutive equations are discussed in detail and particular emphasis is placed on the consistent linearization of associated algorithms. A model for elastic damage in polymers and finite strain extensions to Lemaitre's and Gurson's models for ductile damage in metals are formulated within the described framework. The adequacy of the constitutive-numerical framework for the simulation of damage in large scale industrial problems is demonstrated by means of numerical examples.