Doctor of Philosophy (PhD)


Civil and Environmental Engineering

Document Type



The aim of this dissertation is developing a framework to describe damage evolution as a phase transformation in solid materials and couple it to the well-known Perzyna type viscoplastic model to account for inelastic behavior of ductile materials. To accomplish this task, the following steps have been performed. First, a new nonlocal, gradient based damage model is proposed for isotropic elastic damage using the phase field method in order to show the evolution of damage in brittle materials. The general framework of the phase field model (PFM) is discussed and the order parameter is related to the damage variable in continuum damage mechanics (CDM). The time dependent Ginzburg-Landau equation which is also termed the Allen-Cahn equation is used to describe the damage evolution process. Specific length scale which addresses the transition region in which the process of changing the undamaged solid to the fully damaged material (microcracks) occurs is defined in order to capture the effect of the damaged localization zone. A new implicit damage variable is proposed through the phase field theory. Finite Difference Method is used and details of the different aspects and regularization capabilities are illustrated by means of numerical examples and the validity and usefulness of the phase field modeling approach is demonstrated. Subsequently, the theory is developed to address the anisotropic damage evolution and simulation in materials. The anisotropic damage is discussed and appropriate nonconserved order parameters in three mutually perpendicular directions are defined to find the growth of the components of a second order diagonal damage tensor corresponding to the principle directions of a general second order damage tensor. In contrast to the previous models, two new tensors are proposed to act as interpolation and potential functions along with three coupled Allen - Cahn equations in order to obtain the evolution of the order parameters, which is the basis of the definition of the damage rate. The tensor formulation of the growth of the components of the damage tensor using the phase field theory is proposed for the first time. It is shown that by introducing a set of material parameters, there is a robust and simplified way to model the nonlocal behavior of damage and predict the corresponding material behavior along the principal axes of the second order damage tensor. Finally, the framework of coupled nonlocal damage model through phase field method and viscoplasticity in continuum scale is developed. It is shown that the recently proposed non local gradient type damage model through the phase field method can be coupled to a viscoplastic model to capture the inelastic behavior of the rate dependent material. Free energy functional of the system containing two main parts including damage propagation as a phase transformation and viscoplastic deformation is proposed. Analogous to conventional viscoplastic models, two terms are incorporated in the viscoplastic free energy functional to appropriately address dissipation and the von Mises type viscoplastic surface. In this framework it is assumed that the damage variable covers summation of evolution of microcracks density in elastic and plastic region and the total strain represents the summation of the elastic and viscoplastic counterparts. Since all the examples of chapters two and three are solved using the Finite Element Method, appropriate algorithms and derivations are also summarized in the last chapter.



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Committee Chair

Voyiadjis, George Z.