Related papers: Continuum Representation of Systems of Dislocation…

This paper deals with the solution of delay differential equations describing evolution of dislocation density in metallic materials. Hardening, restoration, and recrystallization characterizing the evolution of dislocation populations…

Moving-habitat models track the density of a population whose suitable habitat shifts as a consequence of climate change. Whereas most previous studies in this area consider 1-dimensional space, we derive and study a spatially 2-dimensional…

Using linearized elasticity as a convenient mechanical framework, we show that volumetric growth can be formulated as an optimization-driven process in which the growth tensor is determined implicitly by constrained optimization rather than…

Creep in single crystal Nickel-based superalloys has been a topic of interest since decades, and nowadays simulations are more and more able to complement experiments. In these alloys, the $\gamma/\gamma'$ phase microstructure co-evolves…

We are interested in exploring interacting particle systems that can be seen as microscopic models for a particular structure of coupled transport flux arising when different populations are jointly evolving. The scenarios we have in mind…

We present a general formalism which allows us to derive the evolution equations describing one-dimensional (1D) and isotropic 2D interfacelike systems, that is based on symmetries, conservation laws, multiple scale arguments, and exploits…

We study a class of time evolution models that contain dissipation mech- anisms exhibited by geophysical materials during deformation: plasticity, viscous dissipation and fracture. We formally prove that they satisfy a Clausius-Duhem type…

Relationships between sediment flux and geomorphic processes are combined with statements of mass conservation, in order to create continuum models of hillslope evolution. These models have parameters which can be calibrated using available…

Cross-slip is a thermally activated process by which screw dislocation changes its glide plane to another slip plane sharing the same Burgers vector. The rate at which this process happens is determined by a Boltzmann type expression that…

A formal hierarchy of exact evolution equations are derived for physically relevant space-time averages of state functions of microscopic dislocation dynamics. While such hierarchies are undoubtedly of some value, a primary goal here is to…

We study particle transport in a class of open channels of finite length, made of identical cells of connected open polygonal billiards with parallel boundaries. In these systems the Mean Square Displacement (MSD) grows in time faster than…

Uniqueness of solutions in the linear theory of non-singular dislocations, studied as a special case of plasticity theory, is examined. The status of the classical, singular Volterra dislocation problem as a limit of plasticity problems is…

Fatigue simulation requires accurate modeling of unloading and reloading. However, classical ductile damage models treat deformations after complete failure as irrecoverable -- which leads to unphysical behavior during unloading. This…

Discovering relationships between materials' microstructures and mechanical properties is a key goal of materials science. Here, we outline a strategy exploiting Bayesian optimization to efficiently search the multidimensional space of…

The Discrete Dislocation (DD) analysis and its computional modeling have been advanced significantly over the past decade. This progress has been further magnified by the idea to couple DD with continuum mechanics analysis in association…

The use of discrete material representation in numerical models is advantageous due to the straightforward way it takes into account material heterogeneity and randomness, and the discrete and orientated nature of cracks. Unfortunately, it…

We propose an energy-consistent mathematical model for motion of dislocation curves in elastic materials using the idea of phase field model. This reveals a hidden gradient flow structure in the dislocation dynamics. The model is derived as…

In this paper, we study the statistical evolution of the large-scale structure (LSS), focusing on the joint probability distribution function (PDF) of the coarse-grained cosmic field and its role in constructing effective dynamics. As the…

The goal of this paper is the analytical validation of a model of Cermelli and Gurtin for an evolution law for systems of screw dislocations under the assumption of antiplane shear. The motion of the dislocations is restricted to a discrete…

Flexible slender structures such as rods, ribbons, plates, and shells exhibit extreme nonlinear responses bending, twisting, buckling, wrinkling, and self contact, that defy conventional simulation frameworks. Discrete Differential Geometry…