Related papers: Multi-scale Modeling for Piezoelectric Composite M…
This work deals with the modelling and simulation of curing phenomena in adhesively bonded piezo metal composites which consist of an adhesive layer with integrated piezoelectric module and two surrounding metal sheet layers. In a first…
This paper proposes a novel higher-order multi-scale (HOMS) computational method, which is highly targeted for efficient, high-accuracy and low-computational-cost simulation of hygro-thermo-mechanical (H-T-M) coupling problems in…
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…
We present a Heterogeneous Multiscale Method for the Landau-Lifshitz equation with a highly oscillatory diffusion coefficient, a simple model for a ferromagnetic composite. A finite element macro scheme is combined with a finite difference…
This short paper presents the potential of using machine learning to predict materials behaviour in the context of hydrogen interaction with steel. Effort has been made to understand the quality, and amount of data needed to get improved…
In this paper we address three aspects of nonlinear computational homogenization of elastic solids by two-scale finite element methods. First, we present a nonlinear formulation of the finite element heterogeneous multiscale method FE-HMM…
In this paper, we develop a novel unfitted multiscale framework that combines two separate scales represented by only one single computational mesh. Our framework relies on a mixed zooming technique where we zoom at regions of interest to…
Owing to additive manufacturing techniques, a structure at millimeter length scale (macroscale) can be produced by using a lattice substructure at micrometer length scale (microscale). Such a system is called a metamaterial at the…
Peridynamics provides a versatile tool for fracture modelling in materials where fracture pathways cannot be predicted beforehand, but must be envisaged as an emergent features of the deformation process. One class of materials where this…
High-frequency homogenization is used to study dispersive media, containing inclusions placed periodically, for which the properties of the material depend on the frequency (Lorentz or Drude model with damping, for example). Effective…
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 a companion paper, equations for partially molten media were derived using two-scale homogenization theory. One advantage of homogenization is that material properties, such as permeability and viscosity, readily emerge. A caveat is that…
Computational multiscale methods for analyzing and deriving constitutive responses have been used as a tool in engineering problems because of their ability to combine information at different length scales. However, their application in a…
Here homogenization theory is used to establish a connection between the symmetries of a periodic elastic structure associated with the microscopic properties of an elastic material and the material symmetries of the effective, macroscopic…
We extend the FE-DMN method to fully coupled thermomechanical two-scale simulations of composite materials. In particular, every Gauss point of the macroscopic finite element model is equipped with a deep material network (DMN). Such a DMN…
We present a formulation for high-order generalized periodicity conditions in the context of a high-order electromechanical theory including flexoelectricity, strain gradient elasticity and gradient dielectricity, with the goal of studying…
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…
The dynamic behavior of jointed assemblies exhibiting friction nonlinearities features amplitude-dependent dissipation and stiffness. To develop numerical simulations for predictive and design purposes, macro-scale High Fidelity Models…
We analyze the random fluctuations of several multi-scale algorithms such as the multi-scale finite element method (MsFEM) and the finite element heterogeneous multiscale method (HMM), that have been developed to solve partial differential…
The present work attempts to present a consistent and efficient approach to piezoelectric laminated beams. The influence of hypotheses on three-dimensional sectional deformations and stress distributions on the estimate of the beam…