On Maximally Dissipative Shock Waves in Nonlinear Elasticity
Source abstract
Abstract
Shock waves in nonlinearly elastic solids are, in general, dissipative. We study the following question: among all plane shock waves that can propagate with a given speed in a given one-dimensional nonlinearly elastic bar, which one—if any—maximizes the rate of dissipation? We find that the answer to this question depends strongly on the qualitative nature of the stress-strain relation characteristic of the given material. When maximally dissipative shocks do occur, they propagate according to a definite kinetic relation, which we characterize and illustrate with examples.
Source: expertdata · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Navier-Stokes equation solutions · Gas Dynamics and Kinetic Theory · Elasticity and Material Modeling
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (11)
Show source-provided references
1. LeFloch, P.G.: Hyperbolic Systems of Conservation Laws. Birkhäuser, Basel (2002)10.1007/978-3-0348-8150-0 ↗
2. Abeyaratne, R., Knowles, J.K.: On the propagation of maximally dissipative phase boundaries in solids. Q. Appl. Math. 50, 149–172 (1992)10.1090/qam/1146630 ↗
3. Abeyaratne, R., Knowles, J.K.: Evolution of Phase Transitions: A Continuum Theory. Cambridge University Press, New York (2006)10.1017/CBO9780511547133 ↗
4. Abeyaratne, R., Knowles, J.K.: On a shock-induced martensitic phase transition. J. Appl. Phys. 87, 1123–1134 (2000)10.1063/1.371989 ↗
5. Erskine, D.J., Nellis, W.J.: Shock-induced martensitic transformation of highly oriented graphite to diamond. J. Appl. Phys. 71, 4882–4886 (1992)10.1063/1.350633 ↗
6. Rice, J.R.: On the structure of stress-strain relations for time-dependent plastic deformation in metals. J. Appl. Mech. 37, 728–737 (1970)10.1115/1.3408603 ↗
7. Lubliner, J.: A maximum dissipation principle in generalized plasticity. Acta Mech. 52, 225–237 (1984)10.1007/BF01179618 ↗
8. Dafermos, C.M.: The entropy rate admissibility criterion for solutions of hyperbolic conservation laws. J. Diff. Equs. 14, 202–212 (1973)10.1016/0022-0396(73)90043-0 ↗
9. Dafermos, C.M.: Hyperbolic systems of conservation laws. In: Ball, J.M. (ed.) Systems of Nonlinear Partial Differential Equations, pp. 25–70. Reidel, Dordrecht (1983)10.1007/978-94-009-7189-9_2 ↗
10. Knowles, J.K.: Impact-induced tensile waves in a rubberlike material. SIAM J. Appl. Math. 62, 1153–1175 (2002)10.1137/S0036139901388234 ↗
11. Knowles, J.K.: Sudden tensile loading of a rubberlike bar. Mech. Res. Commun. 30, 581–587 (2003)10.1016/S0093-6413(03)00070-3 ↗