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Locally homogeneous configurations of uniform elastic bodies. (English) Zbl 0785.73020
Summary: This paper deals with one of the fundamental problems of the mathematical theory of inhomogeneities in simple elastic material bodies, namely the availability of local homogeneous configurations. Utilizing the original differential geometric approach of W. Noll [Arch. Ration. Mech. Anal. 27, 1-32 (1967; Zbl 0168.457)] and C.-C. Wang [Arch. Ration. Mech. Anal. 27, 33-94 (1967; Zbl 0187.488)] adopted for our particular needs and restricted to the hyperelastic case, we develop a system of partial differential equations for the locally homogeneous material configurations. The existence and the form of solutions of this system are discussed by means of examples.

MSC:
74B20 Nonlinear elasticity
35Q72 Other PDE from mechanics (MSC2000)
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