Semiholonomic second order connections associated with material bodies. (English) Zbl 1338.53049

Summary: The thermomechanical behavior of a material is expressed mathematically by means of one or more constitutive equations representing the response of the body to the history of its deformation and temperature. These settings induce a set of connections which can express local properties. We replace two of them by a second order connection and prove that the holonomity of this connection classifies our materials.


53C05 Connections (general theory)
70F20 Holonomic systems related to the dynamics of a system of particles
70G45 Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics
74A20 Theory of constitutive functions in solid mechanics
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