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Finite volume methods for nonlinear elasticity in heterogeneous media. (English) Zbl 1024.74044

Summary: We develop an approximate Riemann solver for equations of nonlinear elasticity in a heterogeneous medium, where each grid cell has an associated density and stress-strain relation. The nonlinear flux function is spatially varying, and a wave decomposition of flux difference across the cell interface is used to approximate the wave structure of the Riemann solution. This solver is used in conjunction with a high-resolution finite volume method using the CLAWPACK software. As a test problem, we study elastic waves in a periodic layered medium. Dispersive effects from the heterogeneity, combined with the nonlinearity, lead to solitary wave solutions that are well captured by the present numerical method.

MSC:

74S10 Finite volume methods applied to problems in solid mechanics
74J30 Nonlinear waves in solid mechanics
74B20 Nonlinear elasticity
74E05 Inhomogeneity in solid mechanics

Software:

CLAWPACK
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References:

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[2] CLAWPACK software. http: //www.amath.washington.edu/?claw
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