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The modelling of heterogeneous and architected materials poses a significant challenge, demanding advanced homogenisation techniques. However, the complexity of this task can be considerably simplified through the application of micropolar…
Dynamic homogenization aims at describing the macroscopic characteristics of wave propagation in microstructured systems. Using a simple method, we derive frequency-dependent homogenized parameters that reproduce the exact dispersion…
It is shown, for the first time, that negative refraction with positive phase velocity refraction can be realized (and controlled) over a wide range of frequency on the first (lowest) pass band of simple photonic and phononic crystals.…
This paper is concerned with the large-scale regularity in the homogenization of elliptic systems of elasticity with periodic high-contrast coefficients. We obtain the large-scale Lipschitz estimate that is uniform with respect to the…
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 present novel variations of an earlier approach called homogeneous clustering algorithm for reducing dataset size. The intuition behind the approaches proposed in this paper is to partition the dataset into homogeneous…
We carry out the homogenization of a fluid-structure interaction problem consisting in the periodic inclusions of a viscous fluid in an elastic body. We get a macrostructure model where the body behaves as a viscoelastic material with a…
Inverse design of high-resolution and fine-detailed 3D lightweight mechanical structures is notoriously expensive due to the need for vast computational resources and the use of very fine-scaled complex meshes. Furthermore, in designing for…
Numerical homogenization, i.e. the finite-dimensional approximation of solution spaces of PDEs with arbitrary rough coefficients, requires the identification of accurate basis elements. These basis elements are oftentimes found after a…
The homogenization of auxetic cellular solids having periodic hexachiral and tetrachiral microstructure is dealt with two different techniques. The first approach is based on the representation of the cellular solid as a beam-lattice to be…
Modeling of frictional contacts is crucial for investigating mechanical performances of composite materials under varying service environments. The paper considers a linear elasticity system with strongly heterogeneous coefficients and…
The structural properties of mechanical metamaterials are typically studied with two-scale methods based on computational homogenization. Because such materials have a complex microstructure, enriched schemes such as second-order…
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…
The goal of this work is to present a fast and viable approach for the numerical solution of the high-contrast state problems arising in topology optimization. The optimization process is iterative, and the gradients are obtained by an…
The first part of the cumulative thesis contains the numerical analysis of different $hp$-finite element discretizations related to two different weak formulations of a model problem in elastoplasticity with linearly kinematic hardening.…
Ultrasound elasticity images which enable the visualization of quantitative maps of tissue stiffness can be reconstructed by solving an inverse problem. Classical model-based approaches for ultrasound elastography use deterministic finite…
The goal of this paper is to develop a reliable analytical approach to finding the effective elastic-plastic response of metal matrix composites (MMC) and porous metals (PM) with a predefined particle or void distribution, as well as to…
This paper is concerned with homogenization of systems of linear elasticity with rapidly oscillating periodic coefficients. We establish sharp convergence rates in $L^2$ for the mixed boundary value problems with bounded measurable…
Micro-structured materials consisting of an array of microstructures are engineered to provide the specific material properties. This present work investigates the design of cellular materials under the framework of level set, so as to…
Skeletonization extracts thin representations from images that compactly encode their geometry and topology. These representations have become an important topological prior for preserving connectivity in curvilinear structures, aiding…