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Variational multisymplectic formulations of nonsmooth continuum mechanics. (English) Zbl 1256.37039
Kaplan, Ehud (ed.) et al., Perspectives and problems in nonlinear science. A celebratory volume in honor of Lawrence Sirovich. New York, NY: Springer (ISBN 0-387-00312-6/hbk). 229-261 (2003).
Summary: This paper develops the foundations of the multisymplectic formulation of nonsmooth continuum mechanics. It may be regarded as a PDE generalization of previous techniques that developed a variational approach to collision problems. These methods have already proved of value in computational mechanics, particularly in the developments of asynchrounos integrators and efficient collision methods. The present formulation also includes solid-fluid interactions and material interfaces and, in addition, lays the groundwork for a treatment of shocks.
MSC:
37N10Dynamical systems in fluid mechanics, oceanography and meteorology
37N15Dynamical systems in solid mechanics
37K05Hamiltonian structures, symmetries, variational principles, conservation laws