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The notion of periodic two-scale convergence and the method of periodic unfolding are prominent and useful tools in multiscale modeling and analysis of PDEs with rapidly oscillating periodic coefficients. In this paper we are interested in…
In this paper, a new data-driven multiscale material modeling method, which we refer to as deep material network, is developed based on mechanistic homogenization theory of representative volume element (RVE) and advanced machine learning…
Modeling the unusual mechanical properties of metamaterials is a challenging topic for the mechanics community and enriched continuum theories are promising computational tools for such materials. The so-called relaxed micromorphic model…
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…
A new framework for two-fluids flow using a Finite Element/Level Set method is presented and verified through the simulation of the rising of a bubble in a viscous fluid. This model is then enriched to deal with vesicles (which mimic red…
The paper addresses the homogenization of a micro-model of poroelasticity coupled with thermal effects for two-constituent media and with imperfect interfacial contact.The homogenized model is obtained by means of the two-scale convergence…
We study a finite element approximation of a coupled fluid-structure interaction consisting of a three-dimensional incompressible viscous fluid governed by the unsteady Stokes equations and a two-dimensional elastic plate. To avoid the use…
We present a finite element framework for the numerical prediction of cavitating turbulent flows interacting with flexible structures. The vapor-fluid phases are captured through a homogeneous mixture model, with a scalar transport equation…
In this article we study a mixed finite element formulation for solving the Stokes problem with general surface forces that induce a jump of the normal trace of the stress tensor, on an interface that splits the domain into two subdomains.…
We analyze the asymptotic behavior of a multiscale problem given by a sequence of integral functionals subject to differential constraints conveyed by a constant-rank operator with two characteristic length scales, namely the film thickness…
The paper is devoted to homogenization of two-phase incompressible viscoelastic flows with disordered microstructure. We study two cases. In the first case, both phases are modeled as Kelvin-Voight viscoelastic materials. In the second…
Diffusion behaviors of heterogeneous materials are of paramount importance in many engineering problems. Numerical models that take into account the internal structure of such materials are robust but computationally very expensive. This…
It is well known that the classical energetically consistent micropolar model has limits in simulating the frequency band structure of packed granular materials (see Merkel et al., 2011). It is here shown that if a standard continualization…
Two-scale models pose a promising approach in simulating reactive flow and transport in evolving porous media. Classically, homogenized flow and transport equations are solved on the macroscopic scale, while effective parameters are…
We present a novel platform for the large-scale simulation of fibrous structures immersed in a Stokesian fluid and evolving under confinement or in free-space. One of the main motivations for this work is to study the dynamics of fiber…
We propose a methodology for the homogenization of periodic elastic lattices that covers the case of unstable lattices, having affine (macroscopic) or periodic (microscopic) mechanisms. The singular cell problems that are encountered when a…
We consider mechanics of composite materials in which thin inclusions are modeled by lower-dimensional manifolds. By successively applying the dimensional reduction to junctions and intersections within the material, a geometry of…
In our previous papers we have described efficient and reliable methods of generation of representative volume elements (RVE) perfectly suitable for analysis of composite materials via stochastic homogenization. In this paper we profit from…
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…
A temporal homogenization approach for the numerical simulation of atherosclerotic plaque growth is extended to fully coupled fluid-structure interaction (FSI) simulations. The numerical results indicate that the two-scale approach yields…