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We analyze a mesoscopic model of a shear stress material with a three dimensional slab geometry, under an external quasistatic deformation of a simple shear type. Relaxation is introduced in the model as a mechanism by which an unperturbed…
A variational modeling framework for hydraulically induced fracturing of elastic-plastic solids is developed in the present work. The developed variational structure provides a global minimization problem. While fracture propagation is…
With the eventual aim of describing flowing elasto-plastic materials, we focus on the elementary brick of such a flow, a plastic event, and compute the long-range perturbation it elastically induces in a medium submitted to a global shear…
We investigate mathematical properties of the system of nonlinear partial differential equations that describe, under certain simplifying assumptions, evolutionary processes in water-saturated granular materials. The unconsolidated solid…
We formulate a phenomenological elasto-plastic theory to describe a solid undergoing a structural transition from a square (p4mm) to an oblique (p2) lattice in two dimensions. Within our theory, the components of the strain may be…
When an amorphous solid is deformed homogeneously, the response exhibits heterogeneous plastic instabilities with localized cooperative rearrangement of cluster of particles. The heterogeneous behavior plays an important role in deciding…
The plastic deformation of amorphous solids is mediated by localized shear transformations involving small groups of particles rearranging irreversibly in an elastic background. We introduce and compare three different computational methods…
The elastic coupling between plastic events is generally invoked to interpret plastic properties and failure of amorphous soft glassy materials. We report an experiment where the emergence of a self-organized plastic flow is observed well…
The paper is concerned with an optimal control problem governed by the equations of elasto plasticity with linear kinematic hardening and the inertia term at small strain. The objective is to optimize the displacement field and plastic…
A new model for elucidating the mathematical foundation of plasticity yield criteria is proposed. The proposed ansatz uses differential geometry and group theory concepts in addition to elementary hypotheses based on well-established…
We derive the variational formulation of a gradient damage model by applying the energetic formulation of rate-independent processes and obtain a regularized formulation of fracture. The model exhibits different behavior at traction and…
Several experiments have demonstrated the existence of an electro-mechanical effect in many biological tissues and hydrogels, and its actual influence on growth, migration, and pattern formation. Here, to model these interactions and…
This dissertation develops, for several families of statistical mechanical and random growth models, techniques for analyzing infinite-volume asymptotics. In the statistical mechanical setting, we focus on the low-temperature phases of spin…
We develop a strain gradient plasticity formulation for composite materials with spatially varying volume fractions to characterize size effects in functionally graded materials (FGMs). The model is grounded on the mechanism-based strain…
Crystalline plasticity is strongly interlinked with dislocation mechanics and nowadays is relatively well understood. Concepts and physical models of plastic deformation in amorphous materials on the other hand - where the concept of linear…
In this paper we propose a canonical variational framework for rate-independent phenomenological geometrically linear gradient plasticity with plastic spin. The model combines the additive decomposition of the total distortion into…
We investigate the time-evolution of elastoplastic materials reinforced by randomly distributed long-range interactions. Starting from a rate-independent system on a discrete spring lattice that combines local linearized elasticity,…
The simulation of viscoelastic time-evolution problems described by a large number of internal variables and with a large spectrum of relaxation times requires high computational resources for their resolution. Furthermore, the internal…
We investigate the stability and geometrically non-linear dynamics of slender rods made of a linear isotropic poroelastic material. Dimensional reduction leads to the evolution equation for the shape of the poroelastica where, in addition…
A damage-plasticity constitutive model for the description of fracture in plain concrete is presented. Two approaches, the local model comprising the adjustment of the softening modulus and the nonlocal model based on spatial averaging of…