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Homogenization appeared more than 100 years ago. It is an approach to study the macro-behavior of a medium by its micro-properties. In mathematics, homogenization theory considers the limitations of the sequences of the problems and its…
Equation-free macroscale modelling is a systematic and rigorous computational methodology for efficiently predicting the dynamics of a microscale system at a desired macroscale system level. In this scheme, the given microscale model is…
A new framework is introduced for constructing interpretable and truly reliable reduced models for multiscale problems in situations without scale separation. Hydrodynamic approximation to the kinetic equation is used as an example to…
Honeycomb-like microstructures have been shown to exhibit local elastic buckling under compression, with three possible geometric buckling modes, or pattern transformations. The individual pattern transformations, and consequently also…
In this work, we develop a novel technique for reconstructing images from projection-based nano- and microtomography. Our contribution focuses on enhancing reconstruction quality, particularly for specimen composed of homogeneous material…
Knitting is an effective technique for producing complex three-dimensional surfaces owing to the inherent flexibility of interlooped yarns and recent advances in manufacturing providing better control of local stitch patterns. Fully…
Determining effective elastic properties of rocks from their pore-scale digital images is a key goal of digital rock physics (DRP). Direct numerical simulation (DNS) of elastic behavior, however, incurs high computational cost; and…
In this work we continue the investigation of different approaches to conception and modeling of composite materials. The global method we focus on, is called 'stochastic homogenization'. In this approach, the classical deterministic…
In this paper, we discuss a general framework for multicontinuum homogenization. Multicontinuum models are widely used in many applications and some derivations for these models are established. In these models, several macroscopic…
Data-driven material models have many advantages over classical numerical approaches, such as the direct utilization of experimental data and the possibility to improve performance of predictions when additional data is available. One…
We propose a novel numerical homogenization method based on the edge multiscale approach for solving indefinite time-harmonic Maxwell equations in heterogeneous media with large wavenumber. Numerical methods for these equations in…
The Gaussian graphical model is a widely used tool for learning gene regulatory networks with high-dimensional gene expression data. Most existing methods for Gaussian graphical models assume that the data are homogeneous, i.e., all samples…
In this paper, we focus on multi-scale modeling and simulation of piezoelectric composite materials. A multi-scale model for piezoelectric composite materials under the framework of Heterogeneous Multi-scale Method(HMM) is proposed. For…
Machine learning models can be used to predict physical quantities like homogenized elasticity stiffness tensors, which must always be symmetric positive definite (SPD) based on conservation arguments. Two datasets of homogenized elasticity…
Coarse-grained models are a core computational tool in theoretical chemistry and biophysics. A judicious choice of a coarse-grained model can yield physical insight by isolating the essential degrees of freedom that dictate the…
We investigate volume-element sampling strategies for the stochastic homogenization of particle-reinforced composites and show, via computational experiments, that an improper treatment of particles intersecting the boundary of the…
Determining the stability of molecules and condensed phases is the cornerstone of atomistic modelling, underpinning our understanding of chemical and materials properties and transformations. Here we show that a machine learning model,…
We construct a homogeneous, nonlinear elastic constitutive law, that models aspects of the mechanical behavior of inhomogeneous fibrin networks. Fibers in such networks buckle when in compression. We model this as a loss of stiffness in…
This paper proposes the application of the waveform relaxation method to the homogenization of multiscale magnetoquasistatic problems. In the monolithic heterogeneous multiscale method, the nonlinear macroscale problem is solved using the…
Data-driven constitutive modeling with neural networks has received increased interest in recent years due to its ability to easily incorporate physical and mechanistic constraints and to overcome the challenging and time-consuming task of…