Abstract
The present work deals with the geometrical desingularization of a well-known asymptotic realization of the ideal holonomic constraints in analytical mechanics. A structure of this kind is extended to the theory of continuous materials—in particular, to elastic materials with internal constraints. By using the same geometrical structure, another aim of this paper can be fulfilled: a new type of generalized hyperelastic material is introduced and some physical examples are discussed. This definition of a generalized hyperelastic material globalizes and unifies the usual definition of a hyperelastic material and its analogue for crystalline solids according to Ericksen and Pitteri. We recall that generalized hyperelastic materials can display a multi-valued strain-stress behaviour, as discussed by Ericksen. Such a behaviour can be used to describe phenomena usually regarded as typical of plasticity.
Sommario
In questo lavoro si considera una desingolarizzazione geometrica di una ben nota realizzazione asintotica dei vincoli lisci olonomi in meccanica analitica. Tale struttura è estesa allla meccanica dei continui, in particolare, al caso dei materiali elastici con vincoli interni. Utilizzando lo stesso ambiente geometrico di quest'ultima costruzione si realizza un altro scopo di questa nota: viene introdotta una nuova definizione di materiale iperelastico in senso generalizzato e sono discussi alcuni esempi fisici noti in letteratura. Questa definizione globalizza e unifica l'usuale definizione di materiale iperelastico e il suo analogo per i solidi cristallini secondo Ericksen e Pitteri. Tali materiali possono manifestare una risposta stress-strain multivoca. Questo comportamento può essere utilizzato per la descrizione di fenomenologie tipiche della plasticità.
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Cardin, F. Morse families and constrained mechanical systems. Generalized hyperelastic materials. Meccanica 26, 161–167 (1991). https://doi.org/10.1007/BF00429884
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DOI: https://doi.org/10.1007/BF00429884