Mechanics of nonlocal dissipative solids: gradient plasticity and phase field modeling of ductile fracture

Abstract

The underlying work is concerned with the development of physically-motivated constitutive models for the description of size effects within the context of inelastic deformations. A key aspect of this thesis is to develop a theoretical and computational framework for gradient-extended dissipative solids. It incorporates spatial gradients of selected micro-structural fields that account for length scale effects and describe the evolving dissipative mechanisms. In contrast to classical theories of local continuum mechanics, where the internal variables are determined by ordinary differential equations (ODEs), these global micro-structural (order parameter) fields are governed by partial differential equations (PDEs) and boundary conditions reflecting the continuity of these variables. The proposed framework for gradient-extended dissipative solids is first used to address the development of phenomenological theories of strain gradient plasticity. The corresponding model guarantees from the computational side a mesh-objective response in the post-critical ranges of softening materials. In this regard, a mixed variational principle for the evolution problem of gradient plasticity undergoing small and large strains is developed. A novel finite element formulation of the coupled problem incorporating a long-range hardening/softening parameter and its dual driving force is also proposed. A second employment of the introduced framework is related to the thermo-mechanical coupling in gradient plasticity theory within small strain deformations. Two global solution procedures for the thermo-mechanically coupled problem are introduced, namely the product formula algorithm and the coupled-simultaneous solution algorithm. For this purpose, a family of mixed finite element formulations is derived to account for the coupled thermo-mechanical boundary-value problem. A further application of the proposed framework deals with the phase-field modeling of ductile fracture undergoing large strains. To this end, a novel variational-based framework for the phase-field modeling of ductile fracture in gradient-extended elastic-plastic solids is proposed. Herein, two independent length scales, that regularize both the plastic response as well as the crack discontinuities, are introduced. This ensures that the failure zone of ductile fracture takes place inside the plastic zone, and guarantees from the computational perspective mesh objectivity in the post-critical range. The performance of these models is tested on a broad range of homogeneous and heterogeneous representative numerical simulations.