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A principal fiber bundle formulation of the dynamics of pseudo-rigid bodies. (English) Zbl 0731.73011

Continuum mechanics and its applications, Proc. Conf., Burnaby/Can. 1988, 915-924 (1989).
[For the entire collection see Zbl 0706.00028.]
The paper aims at a fibre bundle theoretical approach to hyperelastic pseudo-ring bodies with emphasis on field theoretical methods. It contains one lemma and three theorems. Theorems 1 and 2 state the equivalence of local mass conservation and the conservation of the Euler deformation tensor. Theorem 3 expresses the external gauge invariance: If the stored-energy function is world observer invariant, then the Lagrangian (kinetic energy minus stored energy) is also world observer invariant.

MSC:

74A99 Generalities, axiomatics, foundations of continuum mechanics of solids
74B20 Nonlinear elasticity
74A20 Theory of constitutive functions in solid mechanics
57R22 Topology of vector bundles and fiber bundles
57R25 Vector fields, frame fields in differential topology

Citations:

Zbl 0706.00028