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Null Lagrangians in linear theories of micropolar type and few other generalizations of elasticity. (English) Zbl 1464.74030

Summary: In the context of linear theories of generalized elasticity including those for homogeneous micropolar media, quasicrystals, and piezoelectric and piezomagnetic media, we explore the concept of null Lagrangians. For obtaining the family of null Lagrangians, we employ the sufficient conditions of H. Rund [Aequationes Math. 11, 212–229 (1974; Zbl 0293.49001)]. In some cases, a nonzero null Lagrangian is found and the stored energy admits a split into a null Lagrangian and a remainder. However, the null Lagrangian vanishes whenever the relevant elasticity tensor obeys certain symmetry conditions which can be construed as an analogue of the Cauchy relations.

MSC:

74B99 Elastic materials
74A35 Polar materials
74G65 Energy minimization in equilibrium problems in solid mechanics
74F15 Electromagnetic effects in solid mechanics

Citations:

Zbl 0293.49001
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References:

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