2010/07/23 by Shoujun Huang, Shou-Jun Huang, Huang, Shou-Jun
Engineering · Mathematics · Physics and Astronomy · #35L45 #74B20 #74J30 #74N20 #Elasticity and Material Modeling #FOS: Physical sciences #Fluid Dynamics Simulations and Interactions #Mathematical Physics (math-ph) #Numerical methods in engineering #math-ph #math.MP #msc:35L45 #msc:74B20 #msc:74J30 #msc:74N20
paper · pdf · doi:10.48550/arxiv.1007.4227
14 pages; 5 figures; submitted to IMA Journal of Applied Mathematics
arxiv created 2010/07/23 · openalex publication_date 2010/07/23 · arxiv updated 2010/07/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper concerns the global propagation of impact-induced tensile waves in a kind of phase-transforming materials. It is well-known that the governing system of partial differential equations is hyperbolic-elliptic and the initial-boundary value problem is not well-posed at all levels of loading. By making use of fully nonlinear stress-strain curve to model this material, Dai and Kong succeeded in constructing a physical solution of the above initial-boundary value problem. For the impact of intermediate range, they assumed that β<3α in the stress-response function for simplicity. In this paper, we revisit the impact problem and consider the propagation of impact-induced tensile waves for all values of the parameters α and β. The physical solutions for all levels of loading are obtained completely.