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A note on incremental equations for a new class of constitutive relations for elastic bodies |
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| Institution: | 1. Departamento de Ingeniería Mecánica, Universidad de Chile, Beauchef 851, Santiago Centro, Santiago, Chile;2. Institute of Mechanics of Materials, Department of Civil Engineering, Aristotle University of Thessaloniki 54124, Greece;1. Materials innovation institute (M2i), P.O. Box 5008, 2600 GA Delft, The Netherlands;2. Tata Steel, P.O. Box 10000, 1970 CA IJmuiden, The Netherlands;3. University of Twente, Faculty of Engineering Technology, P.O. Box 217, 7500 AE Enschede, The Netherlands;1. Department of Orthopedic Surgery, Yamaguchi University Graduate School of Medicine, Yamaguchi, Japan;2. Department of Orthopedic Surgery, Yamaguchi Rosai Hospital, Yamaguchi, Japan;3. Department of Orthopedic Surgery, Ube Kosan Central Hospital, Yamaguchi, Japan |
| Abstract: | Some new classes of constitutive relations for elastic bodies have been proposed in the literature, wherein the stresses and strains are obtained from implicit constitutive relations. A special case of the above relations corresponds to a class of constitutive equations where the linearized strain tensor is given as a nonlinear function of the stresses. For such constitutive equations we consider the problem of decomposing the stresses into two parts: one corresponds to a time-independent solution of the boundary value problem, plus a small (in comparison with the above) time-dependent stress tensor. The effect of this initial time-independent stress in the propagation of a small wave motion is studied for an infinite medium. |
| Keywords: | Wave propagation Strain limiting behaviour Nonlinear elasticity Strain plane problems Infinite medium Large stresses |
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