Enfoque energético a la modelización de fractura no lineal unidimensional

Abstract

As a result of highly demanding stresses and strains, dissipative phenomena are observed in engineering materials. Therefore, it is of great interest to study the evolution of these materials by means of computational models. In this thesis, the implementation of two nite element one-dimensional models is proposed for the analysis of ductile materials with softening behavior. Two formulations are explored: the classical approach and the energetic approach. The former is based on the application of a local plasticity model derived from the generalized standard materials theory, coupled to a nonlocal damage model. Because the resulting problem's solution lacks uniqueness, regularization through viscoplasticity is applied. On the other hand, the energetic approach uses variational tools to develop the model on three fundamental concepts: stability condition, energy balance and irreversibility condition. Then, the evolution of the system is obtained by the minimization of a convex energy functional with respect to the state variables. This allows for the global solution to be obtained with numerical stability, avoiding the need for regularization. The classical algorithm with viscoplasticity is a rate-dependent problem, resulting in a di erent evolution from the response obtained through the energetic approach. However, it is shown numerically that as the loading rate tends to zero, the models converge. As a nal result, the material evolution generated with both models is presented, as well as a comparative analysis.