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

Fadi Aldakheel, Universität Stuttgart, Universität Stuttgart
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
more » ... lassical 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-bas [...]
doi:10.18419/opus-8803 fatcat:7mi4rhplmfhqpcx32ydtedheu4