English
Related papers

Related papers: A Newton Solver for Micromorphic Computational Hom…

200 papers

Metasurfaces have provided a novel and promising platform for the realization of compact and large-scale optical devices. The conventional metasurface design approach assumes periodic boundary conditions for each element, which is…

Homogenisation empowers the efficient macroscale system level prediction of physical scenarios with intricate microscale structures. Here we develop an innovative powerful, rigorous and flexible framework for asymptotic homogenisation of…

Dynamical Systems · Mathematics 2025-04-08 A. J. Roberts

Theories of localised pattern formation are important to understand a broad range of natural patterns, but are less well-understood than more established mechanisms of domain-filling pattern formation. Here, we extend recent work on pattern…

Pattern Formation and Solitons · Physics 2025-07-22 Andrew L. Krause , Václav Klika , Edgardo Villar-Sepúlveda , Alan R. Champneys , Eamonn A. Gaffney

Composite materials with different microstructural material symmetries are common in engineering applications where grain structure, alloying and particle/fiber packing are optimized via controlled manufacturing. In fact these…

Materials Science · Physics 2024-04-30 Ravi Patel , Cosmin Safta , Reese E. Jones

Classical atomistic simulations based on interatomic potentials resolve lattice instabilities, defect nucleation, and microstructure evolution with high fidelity, but their accessible system sizes remain far below those required for…

Numerical Analysis · Mathematics 2026-05-26 Aagashram Neelakandan , Karsten Albe , Bernhard Eidel

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…

Numerical Analysis · Mathematics 2022-06-07 Kaushik Bhattacharya , Burigede Liu , Andrew M. Stuart , Margaret Trautner

Material nonlinearities such as hyperelasticity, viscoelasticity, and plasticity have recently emerged as design paradigms for metamaterials based on buckling. These metamaterials exhibit properties such as shape morphing, transition waves,…

Soft Condensed Matter · Physics 2024-10-23 Wenfeng Liu , Bernard Ennis , Corentin Coulais

Heterogeneity and uncertainty in a composite microstructure lead to either computational bottlenecks if modeled rigorously or to solution inaccuracies in the stress field and failure predictions if approximated. Although methods suitable…

Machine Learning · Computer Science 2024-05-31 Emil Pitz , Kishore Pochiraju

This paper aims at an accurate and efficient computation of effective quantities, e.g., the homogenized coefficients for approximating the solutions to partial differential equations with oscillatory coefficients. Typical multiscale methods…

Numerical Analysis · Mathematics 2021-03-08 Assyr Abdulle , Doghonay Arjmand , Edoardo Paganoni

Machine learning models can assist with metamaterials design by approximating computationally expensive simulators or solving inverse design problems. However, past work has usually relied on black box deep neural networks, whose reasoning…

Machine Learning · Computer Science 2022-10-04 Zhi Chen , Alexander Ogren , Chiara Daraio , L. Catherine Brinson , Cynthia Rudin

Direct numerical simulations of mechanical metamaterials are prohibitively expensive due to the separation of scales between the lattice and the macrostructural size. Hence, multiscale continuum analysis plays a pivotal role in the…

Materials Science · Physics 2024-10-29 J. Ulloa , M. P. Ariza , J. E. Andrade , M. Ortiz

This work is directed to uncertainty quantification of homogenized effective properties for composite materials with complex, three dimensional microstructure. The uncertainties arise in the material parameters of the single constituents as…

Machine Learning · Computer Science 2021-10-27 Alexander Henkes , Ismail Caylak , Rolf Mahnken

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…

Soft Condensed Matter · Physics 2021-04-27 Andrea Bacigalupo , Luigi Gambarotta

When used in bulk applications, mechanical metamaterials set forth a multiscale problem with many orders of magnitude in scale separation between the micro and macro scales. However, mechanical metamaterials fall outside conventional…

Analysis of PDEs · Mathematics 2025-01-28 M. P. Ariza , S. Conti , M. Ortiz

An algorithm is devised for solving minimization problems with equality constraints. The algorithm uses first-order derivatives of both the objective function and the constraints. The step is computed as a sum between a steepest-descent…

Numerical Analysis · Mathematics 2017-11-15 Cristian Barbarosie , Sérgio Lopes , Anca-Maria Toader

This work presents a multilevel approach to large--scale topology optimization accounting for linearized buckling criteria. The method relies on the use of preconditioned iterative solvers for all the systems involved in the linear buckling…

Numerical Analysis · Mathematics 2020-03-03 Federico Ferrari , Ole Sigmund

Architected metamaterials like foams and lattices exhibit complex responses governed by microstructural instabilities, localization, and phase-transition-like phenomena. Their behavior is further affected by heterogeneities inherent in…

Materials Science · Physics 2026-04-29 Sarvesh Joshi , Jingye Tan , Craig M. Hamel , Stavros Gaitanaros , Nikolaos Bouklas

Magneto-active elastomers exhibit large, nonlinear deformations under combined mechanical loading and magnetic fields, and their effective behavior is strongly governed by microstructural heterogeneity. Predictive modeling of these…

Computational Engineering, Finance, and Science · Computer Science 2026-03-30 L. River Spencer , Manuel K. Rausch , Chad M. Landis , Jan N. Fuhg

Effective properties of materials with random heterogeneous structures are typically determined by homogenising the mechanical quantity of interest in a window of observation. The entire problem setting encompasses the solution of a local…

Numerical Analysis · Mathematics 2021-10-22 Felipe Rocha , Simone Deparis , Pablo Antolin , Annalisa Buffa

Rod-like metamaterials are the structures that are obtained by periodically assembling its microstructural unit (network of rods) in just one direction. In this work, we present a scheme for obtaining the nonlinear constitutive response of…

Materials Science · Physics 2026-05-13 Vinayak , Ajeet Kumar