Formulation, implementation and validation of a scalar damage model for brittle materials applied to three-dimensional solid elements

G. González del Solar, P. Martín, N. Maldonado


Continuum Damage Mechanics describes the progressive degradation of the material properties based on a phenomenological model. This work presents the formulation, implementation and validation of a scalar damage model applied to three-dimensional solid elements. It is a highly versatile model defined from a fault surface and a scalar damage variable. Isotropic elastic materials with softening behavior and a single threshold surface can be simulated by this model. Four parameters are necessary to define the model and they derive from the classical stress-strain test. The model is implemented through a user-defined UMAT subroutine in software ABAQUS. The non-linear equilibrium equations are solved by an implicit algorithm based on the Backward Euler Method. The tensile stress validation shows an adequate correlation between the numerical and experimental results, with a 6% dispersion of dissipated energy. Finally, an illustrative example is presented. The results show that it is a simple but powerful tool for the numerical analysis of brittle materials.


Damage model, non-linear analysis, softening, fracture energy, finite elements



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