Related papers: Multi-scale Modeling for Piezoelectric Composite M…
The paper presents two-scale numerical algorithms for stress-strain analysis of porous media featured by self-contact at pore level. The porosity is constituted as a periodic lattice generated by a representative cell consisting of elastic…
We propose an algorithm for the computational homogenization of locally periodic hyperelastic structures undergoing large deformations due to external quasi-static loading. The algorithm performs clustering of macroscopic deformations into…
Asymptotic homogenisation is considered for problems with integral constraints imposed on a slowly-varying microstructure; an insulator with an array of perfectly dielectric inclusions of slowly varying size serves as a paradigm. Although…
This article combines shape optimization and homogenization techniques by looking for the optimal design of the microstructure in composite materials and of scaffolds. The development of materials with specific properties is of huge…
Ferroelectric materials have remained one of the foci of condensed matter physics and materials science for over 50 years. In the last 20 years, the development of voltage-modulated scanning probe microscopy techniques, exemplified by…
Expressions arising from the Bruggeman approach for the homogenization of dielectric-magnetic composite materials, without ignoring the sizes of the spherical particles, are presented. These expressions exhibit the proper limit behavior.…
High-fidelity electron microscopy simulations required for quantitative crystal structure refinements face a fundamental challenge: while physical interactions are well-described theoretically, real-world experimental effects are…
The formation of microstructures in metallic alloys during hot metal forming involves simultaneous metallurgical complex phenomena. Traditional high-fidelity numerical frameworks used on the polycrystalline scale tend to focus on…
This article presents general procedures for constructing, estimating, and testing Hilbert space multi-dimensional (HSM) models, which are based on quantum probability theory. HSM models can be applied to collections of K different…
In this paper we present a fully-coupled, two-scale homogenization method for dynamic loading in the spirit of FE$^2$ methods. The framework considers the balance of linear momentum including inertia at the microscale to capture possible…
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…
Simulation in media with multiple continua where each continuum interacts with every other is often challenging due to multiple scales and high contrast. One needs some types of model reduction. One of the approaches is multi-continuum…
Shale, like many other sedimentary rocks, is typically heterogeneous, anisotropic, and is characterized by partial alignment of anisotropic clay minerals and naturally formed bedding planes. In this study, a micromechanical framework based…
An uncoupled multi-scale homogenization approach is used to estimate the effective thermal conductivities of plain weave C/C composites with a high degree of porosity. The geometrical complexity of the material system on individual scales…
Nonlinearities in piezoelectric systems can arise from internal factors such as nonlinear constitutive laws or external factors like realizations of boundary conditions. It can be difficult or even impossible to derive detailed models from…
Data driven materials discovery and optimization requires databases that are error free and experimentally verified. Performing material measurements are time-consuming and often restricted by the fact that material sample preparations are…
In this paper, we study numerical homogenization methods based on integral equations. Our work is motivated by materials such as concrete, modeled as composites structured as randomly distributed inclusions imbedded in a matrix. We…
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…
How heterogeneous multiscale methods (HMM) handle fluctuations acting on the slow variables in fast-slow systems is investigated. In particular, it is shown via analysis of central limit theorems (CLT) and large deviation principles (LDP)…
We present a Lagrangian Heterogeneous Multiscale Method (LHMM) for simulating the non-Newtonian rheology of polymer melts in complex two-dimensional flows. The method couples Dissipative Particle Dynamics (DPD) at the microscale with a…