Related papers: Computational homogenization of heterogeneous medi…

Modern 'smart' materials have complex heterogeneous microscale structure, often with unknown macroscale closure but one we need to realise for large scale engineering and science. The multiscale Equation-Free Patch Scheme empowers us to…

The aim of this work is the numerical homogenization of a parabolic problem with several time and spatial scales using the heterogeneous multiscale method. We replace the actual cell problem with an alternate one, using Dirichlet boundary…

Real-world physical systems, like composite materials and porous media, exhibit complex heterogeneities and multiscale nature, posing significant computational challenges. Computational homogenization is useful for predicting macroscopic…

The FE$^2$ method is a very flexible but computationally expensive tool for multiscale simulations. In conventional implementations, the microscopic displacements are iteratively solved for within each macroscopic iteration loop, although…

Finite difference/element/volume methods of discretising PDEs impose a subgrid scale interpolation on the dynamics. In contrast, the holistic discretisation approach developed herein constructs a natural subgrid scale field adapted to the…

In this article, we present an extension of the formulation recently developed by the authors (A Framework for Data-Driven Computational Mechanics Based on Nonlinear Optimization, arXiv:1910.12736 [math.NA]) to the structural dynamics…

Discrete energy minimization is a ubiquitous task in computer vision, yet is NP-hard in most cases. In this work we propose a multiscale framework for coping with the NP-hardness of discrete optimization. Our approach utilizes algebraic…

Many experiments over the past half century have shown that, for a range of protocols, granular materials compact under pressure and repeated small disturbances. A recent experiment on cyclically sheared spherical grains showed significant…

Learning to sample from complex unnormalized distributions is a fundamental challenge in computational physics and machine learning. While score-based and variational methods have achieved success in continuous domains, extending them to…

We present a new method for the approximate solution of the strongly coupled, nonlinear stress-diffusion problem that appears when modeling hydrogen transport in metals. The most salient feature of the proposed approximation is that it is…

The emergence of statistical complexity in frictional systems, manifested in broad distributions of various observables, is not yet understood. We study this problem in velocity-driven, homogeneous (no quenched disorder) unstable frictional…

In the framework of virtual element discretizazions, we address the problem of imposing non homogeneous Dirichlet boundary conditions in a weak form, both on polygonal/polyhedral domains and on two/three dimensional domains with curved…

We propose a matrix-free finite element (FE) homogenization scheme that is considerably more efficient than generic FE implementations. The efficiency of our scheme follows from a preconditioned well-scaled reformulation allowing for the…

We propose a new framework for identifying mechanical properties of heterogeneous materials without a closed-form constitutive equation. Given a full-field measurement of the displacement field, for instance as obtained from digital image…

Fully resolving dynamics of materials with rapidly-varying features involves expensive fine-scale computations which need to be conducted on macroscopic scales. The theory of homogenization provides an approach to derive effective…

We derive a new effective macroscopic Cahn-Hilliard equation whose homogeneous free energy is represented by 4-th order polynomials, which form the frequently applied double-well potential. This upscaling is done for perforated/strongly…

This article offers a new perspective for the mechanics of solids using moving Cartan's frame, specifically discussing a mixed variational principle in non-linear elasticity. We treat quantities defined on the co-tangent bundles of…

Heterogeneous systems are present from powerful supercomputers, to mobile devices, including desktop computers, thanks to their excellent performance and energy consumption. The ubiquity of these architectures in both desktop systems and…

In this paper we consider a wide class of discrete diffusion load balancing algorithms. The problem is defined as follows. We are given an interconnection network and a number of load items, which are arbitrarily distributed among the nodes…

The macroscopic mechanical properties of colloidal particle gels strongly depend on the local arrangement of the powder particles. Experiments have shown that more heterogeneous microstructures exhibit up to one order of magnitude higher…