On the geometric character of stress in continuum mechanics

Eva Kanso; Marino Arroyo; Yiying Tong; Arash Yavari; Jerrold G. Marsden; Mathieu Desbrun

doi:10.1007/s00033-007-6141-8

On the geometric character of stress in continuum mechanics

Eva Kanso
, Marino Arroyo
, Yiying Tong
, Arash Yavari
, Jerrold G. Marsden
, Mathieu Desbrun

Research output: Contribution to journal › Article › peer-review

Abstract

This paper shows that the stress field in the classical theory of continuum mechanics may be taken to be a covector-valued differential two-form. The balance laws and other fundamental laws of continuum mechanics may be neatly rewritten in terms of this geometric stress. A geometrically attractive and covariant derivation of the balance laws from the principle of energy balance in terms of this stress is presented.

Original language	English
Pages (from-to)	843-856
Number of pages	14
Journal	Zeitschrift fur Angewandte Mathematik und Physik
Volume	58
Issue number	5
DOIs	https://doi.org/10.1007/s00033-007-6141-8
Publication status	Published - 1 Sept 2007
Externally published	Yes

Keywords

Continuum mechanics
Differential forms
Elasticity
Stress tensor

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10.1007/s00033-007-6141-8

Cite this

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AU - Desbrun, Mathieu

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KW - Continuum mechanics

KW - Differential forms

KW - Elasticity

KW - Stress tensor

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On the geometric character of stress in continuum mechanics

Abstract

Keywords

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