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Applications of Hamilton’s principle to continua with singular surfaces. (English) Zbl 0604.73004

The authors discuss applications of Hamilton’s principle to continua with singular surfaces. The early sections of the paper are devoted to the basics and preliminary results which are to be used in Hamilton’s principle. The examples of an elastic fluid and an elastic solid are then examined. It is shown that Hamilton’s principle provides an alternative approach for the derivation of the known momentum jump condition and energy jump condition. Application to mixtures of elastic fluids with and without micro-inertia are carried out separately after some preliminary results on mixtures.
This is a clearly written and detailed paper enriched with references. It should be of interest to theoreticians in the field of continuum mechanics.
Reviewer: H.Ramkissoon

MSC:

74A99 Generalities, axiomatics, foundations of continuum mechanics of solids
74S30 Other numerical methods in solid mechanics (MSC2010)
76A99 Foundations, constitutive equations, rheology, hydrodynamical models of non-fluid phenomena
70H25 Hamilton’s principle
74J99 Waves in solid mechanics
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