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The Finite Element Method (FEM) is the gold standard for spatial discretization in numerical simulations for a wide spectrum of real-world engineering problems. Prototypical areas of interest include linear heat transfer and linear…
In this work, we present a numerical scheme for the approximate solutions of a 2D crawling cell migration problem. The model, defined on a non-deformable discoidal domain, consists in a Darcy fluid problem coupled with a Poisson problem and…
We reformulate the theory of polycrystalline plasticity, in externally driven, nonequilibrium situations, by writing equations of motion for the flow of energy and entropy associated with dislocations. Within this general framework, and…
We present a multiscale simulation algorithm for amorphous materials, which we illustrate and validate in a canonical case of dense granular flow. Our algorithm is based on the recently proposed Spot Model, where particles in a dense random…
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…
We introduce the Fixed Point Diffusion Model (FPDM), a novel approach to image generation that integrates the concept of fixed point solving into the framework of diffusion-based generative modeling. Our approach embeds an implicit fixed…
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…
The sedimentation process of granular materials exists ubiquitously in nature and many fields which involve the solid-liquid separation. This paper employs the coupled computational fluid dynamics and discrete element method (CFD-DEM) to…
The interaction of screw dislocations with an applied stress is studied using atomistic simulations in conjunction with a continuum treatment of the role played by the far field boundary condition. A finite cell of atoms is used to consider…
The finite element method is one of the widely employed numerical techniques in electrical engineering for the study of electric and magnetic fields. When applied to the moving conductor problems, the finite element method is known to have…
In medical imaging, the diffusion models have shown great potential for synthetic image generation tasks. However, these approaches often lack the interpretable connections between the generated and real images and can create anatomically…
Most of the FFT methods available for homogenization of the mechanical response use the strain/deformation gradient as unknown, imposing their compatibility using Green's functions or projection operators. This implies the allocation of…
Material properties controlled by evolving defect structures, such as mechanical response, often involve processes spanning many length and time scales which cannot be modeled using a single approach. We present a variety of new results…
In this paper we construct numerical schemes to approximate linear transport equations with slab geometry by diffusion equations. We treat both the case of pure diffusive scaling and the case where kinetic and diffusive scalings coexist.…
By means of linear theory of elastoplasticity, solutions are given for screw and edge dislocations situated in an isotropic solid. The force stresses, strain fields, displacements, distortions, dislocation densities and moment stresses are…
The presence of interfaces and grain boundaries significantly impacts the mechanical properties of materials, particularly when dealing with micro- or nano-scale samples. Distinct interactions between dislocations and grain boundaries can…
Despite its numerical challenges, finite element method is used to compute viscous fluid flow. A consensus on the cause of numerical problems has been reached; however, general algorithms---allowing a robust and accurate simulation for any…
We study the relaxation dynamics of systems of straight, parallel crystal dislocations, starting from initially random and uncorrelated positions of the individual dislocations. A scaling model of the relaxation process is constructed by…
Accurate numerical simulations of interaction between fluid and solid play an important role in applications. The task is challenging in practical scenarios as the media are usually highly heterogeneous with very large contrast. To overcome…
We present a dislocation density-based strain hardening model for single crystal copper through a systematic coarse-graining analysis of more than 200 discrete dislocation dynamics (DDD) simulations of plastic deformation under uniaxial…