Modelagem de fratura através do método de campo de fase visando aplicações em géis poliméricos

Abstract

This dissertation presents theoretical and numerical modeling that describes the fracture process in elastic bodies, from their nucleation to the propagation and branching of cracks. The motivation of this work lies in the potential of applications that polymer gels have, which like other materials with fluid content internal to their solid network, when they are put to dry, may suffer fracture due to residual stresses of the process. The theoretical formulation of the problem rests on the framework of the continuum thermodynamics, thus generating thermodynamically consistent balance and constitutive equations for continuous bodies under mechanical, diffusive and microstructural effects. For the description of the theory of microstructural changes, the recent phase-field models for fracture, which represent a major advance for the numerical solution of these problems, are used as a basis. After finishing the theoretical basis, the problems to be overcome to reach the objective of the work are defined, assuming that the drying process would generate residual stresses in the body. The first one of them is based on the standard problem of fracture mode 1, where the intense regeneration of the body in regions far from the crack is verified numerically. To overcome this theoretical inconsistency, a formulation is developed that takes into account the hypothesis of irreversibility of the damage in the body. To evaluate the applicability of this formulation, the final fracture problem is defined under residual stresses in real bodies, which have heterogeneity in their composition. Numerically, such characteristic is described by considering initial random conditions of damage in the additional variable of the microstructural problem. To solve computationally all the problems defined, a personal numerical code is developed based on an open package of finite elements written in Python.