A Top–Down Thermodynamically Motivated Perspective on Multiscale Material Modeling

ABSTRACT Established multiscale strategies such as QM/MM coupling, computational homogenization, quasi‐continuum approaches, and thermodynamically formulated continuum models provide powerful scale‐bridging tools, however, each of them is formulated on a different effective energetic level, and an explicit recursive energy reference structure connecting all scales is currently not available. In this contribution, a thermodynamically grounded top–down framework is discussed, in which the internal energy of a system is defined recursively as the sum of the total energies of its subsystems. Within this nested hierarchy, energetic contributions on each scale are conditioned by their hierarchical embedding, and multiscale modeling appears as the problem of truncating the hierarchy in a thermodynamically consistent manner. The framework is not intended as a competing numerical method but as an inspection tool: it is employed to make silent assumptions of classical volume‐average homogenization explicit and to embed a molecular‐mechanics/QM‐coupled description into a discrete homogenization scheme, recovering the averaging operator of the condensed method as a special case.

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Publication Details

Journal
PAMM
Published
2026-08-24
DOI
https://doi.org/10.1002/pamm.70188
Primary Topic
Advanced Mathematical Modeling in Engineering
Type
article
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article

A Top–Down Thermodynamically Motivated Perspective on Multiscale Material Modeling

Andreas Warkentin
PAMM
Advanced Mathematical Modeling in Engineering
article

A Top–Down Thermodynamically Motivated Perspective on Multiscale Material Modeling

Andreas Warkentin
article en

Abstract

ABSTRACT Established multiscale strategies such as QM/MM coupling, computational homogenization, quasi‐continuum approaches, and thermodynamically formulated continuum models provide powerful scale‐bridging tools, however, each of them is formulated on a different effective energetic level, and an explicit recursive energy reference structure connecting all scales is currently not available. In this contribution, a thermodynamically grounded top–down framework is discussed, in which the internal energy of a system is defined recursively as the sum of the total energies of its subsystems. Within this nested hierarchy, energetic contributions on each scale are conditioned by their hierarchical embedding, and multiscale modeling appears as the problem of truncating the hierarchy in a thermodynamically consistent manner. The framework is not intended as a competing numerical method but as an inspection tool: it is employed to make silent assumptions of classical volume‐average homogenization explicit and to embed a molecular‐mechanics/QM‐coupled description into a discrete homogenization scheme, recovering the averaging operator of the condensed method as a special case.

PAMMVol. 26(4)
University of Kassel (DE)
Affordable and clean energy
Openalex Percentile: Top 8%
Advanced Mathematical Modeling in Engineering
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A Top–Down Thermodynamically Motivated Perspective on Multiscale Material Modeling — Andreas Warkentin · PAMM (2026) | TGRS Research Map | TGRS