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Z. angew. Math. Phys. 58 (2007) 114 0044-2275/07/050001-14

Summary: Z. angew. Math. Phys. 58 (2007) 1­14
DOI 10.1007/s00033-007-6141-8
c 2007 Birkh¨auser Verlag, Basel
Zeitschrift f¨ur angewandte
Mathematik und Physik ZAMP
On the geometric character of stress in continuum mechanics
Eva Kanso, Marino Arroyo, Yiying Tong, Arash Yavari, Jerrold E. Marsden1
Mathieu Desbrun
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 funda-
mental 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.
Mathematics Subject Classification (2000).
Keywords. Continuum mechanics, elasticity, stress tensor, differential forms.
1. Motivation
This paper proposes a reformulation of classical continuum mechanics in terms of
bundle-valued exterior forms. Our motivation is to provide a geometric description


Source: Arroyo, Marino - Departament de Matemàtica Aplicada III, Universitat Politècnica de Catalunya
Desbrun, Mathieu - Computer Science Department, California Institute of Technology
Marsden, Jerrold - Control and Dynamical Systems Program, Division of Engineering and Applied Science, California Institute of Technology


Collections: Computer Technologies and Information Sciences; Engineering; Materials Science