Solution of a Riemann problem for elasticity |
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Authors: | Xabier Garaizar |
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Institution: | (1) Courant Institute of Mathematical Sciences, New York University, 10012 New York, NY, USA;(2) Present address: Department of Mathematics, North Carolina State University, 27695-8205 Raleigh, NC, USA |
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Abstract: | This paper describes a numerical algorithm for the Riemann solution for nonlinear elasticity. We assume that the material is hyperelastic, which means that the stress-strain relations are given by the specific internal energy. Our results become more explicit under further assumptions: that the material is isotropic and that the Riemann problem is uniaxial. We assume that any umbilical points lie outside the region of physical relevance. Our main conclusion is that the Riemann solution can be obtained by the iterative solution of functional equations (Godunov iterations) each defined in one- or two-dimensional spaces.Supported in part by AFOSR-88-0025. |
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Keywords: | 35L60 35L65 35L67 58G16 58G17 65C20 73C25 73C30 73C50 73G05 |
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