Modelos de campos de fase para problemas envolvendo fratura, plasticidade e grandes deformações

This study presents the development of mathematical models and numerical strategies to describe the initialization and crack propagation in elasto-plastic materials under the hypothesis of small and large strains. The developed models use the phase field methodology to introduce diffuse transitions in the fracture description. It allows describing the nucleation and subsequent propagation of cracks with complex geometries without any additional numerical treatment. Moreover, it leads to non-isothermal thermodynamically consistent models by considering the dissipative and free-energy potentials associated with the fracture regularization. Employing the principle of virtual powers, energy balance and the second law of thermodynamics in the form of the Clausius-Duhem entropy inequality, this methodology leads to general thermodynamically consistent models including contributions not usually considered in the literature. The energy degradation functions associated with damage processes are studied and a new degradation function is proposed alternatively to the classical expressions. This new function delays the softening process until the failure. The nonlinear equations resulting from the developed models are solved numerically and systematically, at each time step, by adopting an appropriated implicit method together with the classical Newton-Raphson method (motion, damage, and temperature). The discretization and linearization of each equation are detailed, including an accurate numerical evaluation of the tangent modulus for general free-energy densities. Numerical results, including tensile, shear and bending tests, show that these models can reproduce qualitative and quantitative fragile and ductile fractures (AU)