Macroscopic stress, couple stress and flux tensors derived through energetic equivalence from microscopic continuous and discrete heterogeneous finite representative volumes

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26110%2F26%3A0197723" target="_blank" >RIV/00216305:26110/26:0197723 - isvavai.cz</a>

Result on the web

<a href="https://www.sciencedirect.com/science/article/pii/S0045782524009423" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0045782524009423</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.cma.2024.117688" target="_blank" >10.1016/j.cma.2024.117688</a>

Result language

angličtina

Original language name

Macroscopic stress, couple stress and flux tensors derived through energetic equivalence from microscopic continuous and discrete heterogeneous finite representative volumes

Original language description

This paper presents a rigorous derivation of equations to evaluate the macroscopic stress tensor, the couple stress tensor, and the flux vector equivalent to underlying microscopic fields in continuous and discrete heterogeneous systems with independent displacements and rotations. Contrary to the classical asymptotic expansion homogenization, finite size representative volume is considered. First, the macroscopic quantities are derived for a heterogeneous Cosserat continuum. The resulting continuum equations are discretized to provide macroscopic quantities in discrete heterogeneous systems. Finally, the expressions for discrete system are derived once again, this time considering the discrete nature directly. The formulations are presented in two variants, considering either internal or external forces, couples, and fluxes. The derivation is based on the virtual work equivalence and elucidates the fundamental significance of the couple stress tensor in the context of balance equations and admissible virtual deformation modes. Notably, an additional term in the couple stress tensor formula emerges, explaining its dependence on the reference system and position of the macroscopic point. The resulting equations are verified by comparing their predictions with known analytical solutions and results of other numerical models under both steady state and transient conditions.

Czech name

—

Czech description

—

Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

—

OECD FORD branch

20102 - Construction engineering, Municipal and structural engineering

Project

<a href="/en/project/GA23-04974S" target="_blank" >GA23-04974S: Coupled chemo-mechanical model of normal and cancer microenvironment</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2025

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING

ISSN

0045-7825

e-ISSN

1879-2138

Volume of the periodical

431

Issue of the periodical within the volume

117688

Country of publishing house

NL - THE KINGDOM OF THE NETHERLANDS

Number of pages

23

Pages from-to

1-23

UT code for WoS article

001397749700001

EID of the result in the Scopus database

2-s2.0-85213280408