No Cover Image

Journal article 315 views

Novel multiscale models in a multicontinuum approach to divide and conquer strategies

Raúl A. Feijóo, Pablo J. Blanco Orcid Logo, Eduardo De Souza Neto Orcid Logo, Pablo J. Sánchez

Computational and Applied Mathematics, Volume: 42, Issue: 4

Swansea University Author: Eduardo De Souza Neto Orcid Logo

Full text not available from this repository: check for access using links below.

Check full text

DOI (Published version): 10.1007/s40314-023-02288-9

Abstract

This contribution presents a comprehensive, in-depth analysis of the solution of the mechanical equilibrium problem for a generic solid with microstructure. The exact solution to this problem, referred to here as the reference solution, corresponds to the full-scale model of the problem that takes i...

Full description

Published in: Computational and Applied Mathematics
ISSN: 2238-3603 1807-0302
Published: Springer Science and Business Media LLC 2023
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa63228
Tags: Add Tag
No Tags, Be the first to tag this record!
Abstract: This contribution presents a comprehensive, in-depth analysis of the solution of the mechanical equilibrium problem for a generic solid with microstructure. The exact solution to this problem, referred to here as the reference solution, corresponds to the full-scale model of the problem that takes into account the kinematics and constitutive behavior of its entire microstructure. The analysis is carried out based on the Principle of Multiscale Virtual Power (PMVP) previously proposed by the authors. The PMVP provides a robust theoretical setting whereby the strong links between the reference solution and solutions of the mechanical equilibrium obtained using coarser scale models are brought to light. In this context, some fundamental properties of coarser scale solutions are identified by means of variational arguments. These findings unveil a new homogenization landscape for Representative Volume Element (RVE) multiscale theories, leading to the construction of new Minimal Kinematical Restriction (MKR)-based models where either displacements or tractions may be prescribed on the RVE boundary. A careful observation of the aforementioned landscape leads naturally to the proposal of a new, multicontinuum strategy (a generalized continuum counterpart of multigrid strategies) to approximate the reference solution at low computational cost. In the proposed strategy, the mechanical interactions among neighboring microcells are accounted for in an iterative fashion by means of suitably chosen boundary conditions enforced alternately on the new MKR-based models. The proposed developments are presented assuming a classical continuum at all scales, but the results are equally valid when different kinematical and constitutive assumptions are made at different scales.
Keywords: Multiscale modeling, Virtual power, Boundary conditions, Multigrid approach, Direct Numerical Solution
College: Faculty of Science and Engineering
Funders: PJB and RAF acknowledge the support of the Brazilian agencies CNPq (grant numbers 301224/2016-1, 407751/2018-1, and 301636/2019-2), and FAPESP (grant numbers 2014/50889-7 and 2018/14221-2). PJS acknowledges the financial support from CONICET and ANPCyT (grant PICT-2020-SERIEA-02793).
Issue: 4

Similar Items