Related papers: Micromorphic Computational Homogenization for Mech…
Prediction of hydrogen embrittlement requires a robust modelling approach and this will foster the safe adoption of hydrogen as a clean energy vector. A generalised computational model for hydrogen embrittlement is here presented, based on…
Time-evolving perforated domains arise in many engineering and geoscientific applications, including reactive transport, particle deposition, and structural degradation in porous media. Accurately capturing the macroscopic behavior of such…
A general process is proposed to experimentally design anisotropic inhomogeneous metamaterials obtained through a change of coordinate in the Helmholtz equation. The method is applied to the case of a cylindrical transformation that allows…
We develop stochastic mixed finite element methods for spatially adaptive simulations of fluid-structure interactions when subject to thermal fluctuations. To account for thermal fluctuations, we introduce a discrete fluctuation-dissipation…
We present a multiscale modeling approach that concurrently couples quantum mechanical, classical atomistic and continuum mechanics simulations in a unified fashion for metals. This approach is particular useful for systems where chemical…
We present a new theoretical and numerical assessment methodology for a one-dimensional process chain with general applicability to management problems such as the optimization of decision chains or production chains. The process is thereby…
We introduce a new variational method for the numerical homogenization of divergence form elliptic, parabolic and hyperbolic equations with arbitrary rough ($L^\infty$) coefficients. Our method does not rely on concepts of ergodicity or…
The phase field fracture method has emerged as a promising computational tool for modelling a variety of problems including, since recently, hydrogen embrittlement and stress corrosion cracking. In this work, we demonstrate the potential of…
We develop a new spatial semidiscrete multiscale method based upon the edge multiscale methods to solve semilinear parabolic problems with heterogeneous coefficients and smooth initial data. This method allows for a cheap spatial…
This article is the first part of a two-fold study, the objective of which is the theoretical analysis and numerical investigation of new approximate corrector problems in the context of stochastic homogenization. We present here three new…
Architected metamaterials like foams and lattices exhibit complex responses governed by microstructural instabilities, localization, and phase-transition-like phenomena. Their behavior is further affected by heterogeneities inherent in…
The computational analysis of fiber network fracture is an emerging field with application to paper, rubber-like materials, hydrogels, soft biological tissue, and composites. Fiber networks are often described as probabilistic structures of…
We consider the problem of homogenizing the Maxwell equations for periodic composites. The analysis is based on Bloch-Floquet theory. We calculate explicitly the reflection coefficient for a half-space, and derive and implement a…
The simulation of heat flow through heterogeneous material is important for the design of structural and electronic components. Classical analytical solutions to the heat equation PDE are not known for many such domains, even those having…
We consider a linear system of differential equations describing a joint motion of elastic porous body and fluid occupying porous space. The rigorous justification, under various conditions imposed on physical parameters, is fulfilled for…
Simulation of multiphase poromechanics involves solving a multi-physics problem in which multiphase flow and transport are tightly coupled with the porous medium deformation. To capture this dynamic interplay, fully implicit methods, also…
We introduce a general-purpose framework for interconnecting scientific simulation programs using a homogeneous, unified interface. Our framework is intrinsically parallel, and conveniently separates all component numerical modules in…
Heterogeneous materials, crucial in various engineering applications, exhibit complex multiscale behavior, which challenges the effectiveness of traditional computational methods. In this work, we introduce the Micromechanics Transformer…
This paper presents an immersed, isogeometric finite element framework to predict the response of multi-material, multi-physics problems with complex geometries using locally refined discretizations. To circumvent the need to generate…
A cornerstone of numerical homogenization is the equivalence of the microscopic and the macroscopic energy densities, which is referred to as Hill-Mandel condition. Among these coupling conditions, the cases of periodic, linear displacement…