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The mechanical behaviour of solid biological tissues has long been described using models based on classical continuum mechanics. However, the classical continuum theories of elasticity and viscoelasticity cannot easily capture the…
In this study, we use the mechanism-based strain gradient plasticity theory to evaluate both crack tip dislocation density behaviour and the coupled effect of the material plastic properties and the intrinsic material length on non-linear…
We rigorously derive a strain-gradient model of plasticity as a $\Gamma$-limit of continuum bodies containing finitely-many edge-dislocations (in two dimensions). The key difference from previous such derivations is the elemental notion of…
This paper presents a modeling framework to describe the driving mechanisms of cyclic failure in brittle and ductile materials, including cyclic plasticity and fatigue crack growth. A variational model is devised using the energetic…
In this paper we study the twist disclination within the elastoplastic defect theory. Using the stress function method, we found exact analytical solutions for all characteristic fields of a straight twist disclination in an infinitely…
This work rigorously implements a recent model of large-strain elasto-plastic evolution in single crystals where the plastic flow is driven by the movement of discrete dislocation lines. The model is geometrically and elastically nonlinear,…
The endochronic theory, developed in the early 70s, allows the plastic behavior of materials to be represented by introducing the notion of intrinsic time. With different viewpoints, several authors discussed the relationship between this…
We present a new theoretical and numerical framework for modelling mechanically-assisted corrosion in elastic-plastic solids. Both pitting and stress corrosion cracking (SCC) can be captured, as well as the pit-to-crack transition.…
The viscoplastic deformation (creep) of crystalline materials under constant stress involves the motion of a large number of interacting dislocations. Analytical methods and sophisticated `dislocation-dynamics' simulations have proved very…
The two-phase composite approach of Estrin et al. (1998) describes an evolving dislocation cell structure. Mckenzie et al. (2007) enhanced the model to capture the effects of hydrostatic pressure and temperature during severe plastic…
Shear strain localization refers to the phenomenon of accumulation of material deformation in narrow slip zones. Many materials exhibit strain localization under different spatial and temporal scales, particularly rocks, metals, soils, and…
Residual stresses may appear in elastic bodies due to the formation of misfits in the micro-structure, driven by plastic deformations, thermal or growth processes. They are especially widespread in living matter, resulting from the dynamic…
Dislocation based modeling of plasticity is one of the central challenges at the crossover of materials science and continuum mechanics. Developing a continuum theory of dislocations requires the solution of two long standing problems: (i)…
Modeling arbitrarily large deformations of surfaces smoothly embedded in three-dimensional space is challenging. The difficulties come from two aspects: the existing geometry processing or forward simulation methods penalize the difference…
Plastic flow is conventionally treated as continuous in finite element (FE) codes, whether in isotropic, anisotropic plasticity, or crystal plasticity. This approach, derived from continuum mechanics, contradicts the intermittent nature of…
Predicting the failure and plasticity of solids remains a longstanding challenge, with broad implications for materials design and functional reliability. Disordered solids like metallic glasses can fail either abruptly or gradually without…
Discrete dislocation dynamics (DDD) simulations offer valuable insights into the plastic deformation and work-hardening behavior of metals by explicitly modeling the evolution of dislocation lines under stress. However, the computational…
We present a time-dependent Ginzburg-Landau model of nonlinear elasticity in solid materials. We assume that the elastic energy density is a periodic function of the shear and tetragonal strains owing to the underlying lattice structure.…
Plastic deformation of most crystalline materials is due to the motion of lattice dislocations. Therefore, the simulation of the interaction and dynamics of these defects has become state-of-the-art method to study work hardening, size…
We study a continuum model of dislocation transport in order to investigate the formation of heterogeneous dislocation patterns. We propose a physical mechanism which relates the formation of heterogeneous patterns to the dynamics of a…