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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…

Computational Engineering, Finance, and Science · Computer Science 2020-10-20 Erik Tamsen , Daniel Balzani

The growing use of composite materials in engineering applications has accelerated the demand for computational methods to accurately predict their complex behavior. Multiscale modeling based on computational homogenization is a potentially…

Numerical Analysis · Mathematics 2024-10-18 N. Kovács , M. A. Maia , I. B. C. M. Rocha , C. Furtado , P. P. Camanho , F. P. van der Meer

Pattern-forming metamaterials feature microstructures specifically designed to change the material's macroscopic properties due to internal instabilities. These can be triggered either by mechanical deformation or, in the case of active…

The aim of this article is to introduce a new methodology for constructing morphings between shapes that have identical topology. The morphings are obtained by deforming a reference shape, through the resolution of a sequence of linear…

Numerical Analysis · Mathematics 2025-02-04 Abbas Kabalan , Fabien Casenave , Felipe Bordeu , Virginie Ehrlacher , Alexandre Ern

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…

Achieving strongly symmetric stress approximations for linear elasticity problems in high-contrast media poses a significant computational challenge. Conventional methods often struggle with prohibitively high computational costs due to…

Numerical Analysis · Mathematics 2025-09-03 Eric T. Chung , Changqing Ye , Xiang Zhong

The paper addresses the problem of a Mode III interfacial crack advancing quasi-statically in a heterogeneous composite material, that is a two-phase material containing elastic inclusions, both soft and stiff, and defects, such as…

Mathematical Physics · Physics 2011-10-25 Andrea Piccolroaz , Gennady Mishuris , Alexander Movchan , Natasha Movchan

This work presents a study on the computational homogenization of electro-magneto-mechanically coupled problems through the Virtual Element Method (VEM). VE-approaches have great potential for the homogenization of the physical properties…

Computational Engineering, Finance, and Science · Computer Science 2021-04-07 Christoph Böhm , Blaž Hudobivnik , Michele Marino , Peter Wriggers

Digital stiffness programmability is fulfilled with a heterogeneous mechanical metamaterial. The prototype consists of an elastomer matrix containing tessellations of diamond shaped cavities selectively confined with semi-rigid plastic beam…

Soft Condensed Matter · Physics 2021-08-13 H. Tao , F. Danzi , C. E. Silva , J. M. Gibert

While the design of always new metamaterials with exotic static and dynamic properties is attracting deep attention in the last decades, little effort is made to explore their interactions with other materials. This prevents the conception…

Applied Physics · Physics 2020-07-30 Gianluca Rizzi , Manuel Collet , Félix Demore , Bernhard Eidel , Patrizio Neff , Angela Madeo

This paper focuses on the homogenization of high-contrast dielectric elastomer composites, materials that deform in response to electrical stimulation. The considered heterogeneous material consisting of an ambient material with inserted…

Analysis of PDEs · Mathematics 2024-12-17 Thuyen Dang , Yuliya Gorb , Silvia Jiménez Bolaños

This work presents a machine learning approach to predict peak-stress clusters in heterogeneous polycrystalline materials. Prior work on using machine learning in the context of mechanics has largely focused on predicting the effective…

Analysis of PDEs · Mathematics 2024-05-10 Ankit Shrivastava , Jingxiao Liu , Kaushik Dayal , Hae Young Noh

Fracture processes in heterogeneous materials comprise a large number of disordered spatial degrees of freedom, representing the dynamical state of a sample over the entire domain of interest. This complexity is usually modeled directly,…

Statistical Mechanics · Physics 2014-08-25 Yon Visell , Guillaume Millet

In the paper, we present an integrated data-driven modeling framework based on process modeling, material homogenization, mechanistic machine learning, and concurrent multiscale simulation. We are interested in the injection-molded short…

Computational Engineering, Finance, and Science · Computer Science 2020-03-24 Zeliang Liu , Haoyan Wei , Tianyu Huang , C. T. Wu

We present a self-contained, soft robotic hand composed of soft pneumatic actuator modules that are equipped with strain and pressure sensing. We show how this data can be used to discern whether a grasp was successful. Co-locating sensing…

Robotics · Computer Science 2016-05-03 Nicholas Farrow , Yang Li , Nikolaus Correll

Soft robots achieve functionality through tight coupling among geometry, material composition, and actuation. As a result, effective design optimization requires these three aspects to be considered jointly rather than in isolation. This…

Robotics · Computer Science 2026-03-09 Vittorio Candiello , Manuel Mekkattu , Mike Y. Michelis , Robert K. Katzschmann

Modeling microstructural evolution at large strains requires mechanical formulations that remain thermodynamically consistent while capturing significant lattice rotations and transformation-induced stresses. However, most existing…

Materials Science · Physics 2025-11-21 Tushar Jogi

The structural complexity of metamaterials is limitless, although in practice, most designs comprise periodic architectures which lead to materials with spatially homogeneous features. More advanced tasks, arising in e.g. soft robotics,…

Soft Condensed Matter · Physics 2016-08-03 Corentin Coulais , Eial Teomy , Koen de Reus , Yair Shokef , Martin van Hecke

The presence of prestrain can have a tremendous effect on the mechanical behavior of slender structures. Prestrained elastic plates show spontaneous bending in equilibrium -- a property that makes such objects relevant for the fabrication…

Analysis of PDEs · Mathematics 2023-01-18 Klaus Böhnlein , Stefan Neukamm , David Padilla-Garza , Oliver Sander

Mechanical metamaterials exhibit size-effects when a few unit-cells are subjected to static loading because no clear micro-macro scale separation holds and the characteristic length of the deformation becomes comparable to the unit-cell…

Numerical Analysis · Mathematics 2025-12-23 Mohammad Sarhil , Leonardo Andres Perez Ramirez , Max Jendrik Voss , Angela Madeo