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Publication

Non-Associative Plasticity and Fracture: Variational Formulation of Multi-Field Coupled Models

Book - Dissertation

The field of continuum solid mechanics has seen a great deal of progress during the past century, allowing for substantial developments in several branches of engineering science. Most notably, many material models that describe inelastic material behavior are now available in the literature, mainly concerning (but not limited to) plasticity and damage. Moreover, enhanced continuum theories that describe strain localization are, by now, well established, offering essential tools for fracture mechanics and material failure analysis. Of particular interest in these developments are theories based on variational formulations, which provide mathematically and thermodynamically consistent material models. Despite this progress, the description of solids under failure conditions remains one of the most challenging topics in mechanics. Often, existing models are either too simple to describe the broad spectrum of material responses or too complex and heuristic to be framed within a rigorous variational setting. This problem calls for a revisited modeling framework that owns the following features: (i) the ability to embed complex material behavior, (ii) a suitable description of strain localization and fracture, and (iii) a variational structure that ensures mathematical and thermodynamic consistency. The present dissertation provides some steps in this direction. The approach for point (i) is the use of non-associative models, which offer great flexibility to describe, for instance, the response of ductile materials under cyclic loading, or frictional plasticity in geomaterials under compressive/shear loading. Concerning point (ii), localized failure is resolved by employing the phase-field approach to fracture, a topic that has received significant attention in the past decade due to its ability to describe complex fracture processes naturally. Finally, point (iii) is approached using a variational/energetic formulation, building upon the thermodynamically consistent theory of generalized standard materials. Incidentally, several complications arise when considering these three approaches simultaneously. It is widely presumed that non-associative models do not fit within the framework of generalized standard materials and, therefore, lack a variational structure. Consequently, these models have been mainly developed from a heuristic perspective, while more rigorous formulations have received little attention in the mechanics community. Moreover, phase-field models that capture complex failure responses (beyond mode I brittle fracture) often employ ad hoc techniques without a clear physical meaning and typically drop the variational structure of the underlying theory in favor of greater flexibility. In order to address these shortcomings, a variational treatment of non-associative models is elaborated in this thesis. This is achieved by extending the theory of generalized standard materials and the variational/energetic formulation through the notion of state-dependent dissipation potentials, i.e., dissipation potentials that depend on the current generalized stress state. The underlying mathematical argument represents a generalized principle of maximum dissipation, as coined in this work. Non-associative models for frictional plasticity and cyclic plasticity are studied as particular examples of the general framework. The extended variational framework is further applied to develop three novel phase-field models coupled to non-associative plasticity, resulting in multi-field coupled systems that provide thermodynamically consistent descriptions of strain localization in various scenarios. The first application consists of a phase-field approach to fatigue that provides a unified representation of low- and high-cycle effects. A central aspect of the model is a non-associative ratcheting variable that captures a variety of material responses. The second application presents a micromechanics-based theory for brittle-tensile and compressive-ductile fracture in geomaterials, where non-associative frictional plasticity plays an essential role. The model offers a physically meaningful representation of the material behavior, requiring little phenomenological assumptions and providing links to the underlying micromechanical processes. Moreover, mode I and mode II fracture are captured without resorting to the usual heuristic modifications of previous phase-field models. Finally, as a third application, the micromechanics-based phase-field approach is extended to consider hydromechanical fracture in saturated porous media. In this model, the versatility of the variational framework is further exploited to include multiphysics coupled effects.
Publication year:2022
Accessibility:Open