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Equivalent histories, minimal state and initial value problem in viscoelasticity
Author(s) -
Fabrizio M.,
Morro A.
Publication year - 2004
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.581
Subject(s) - uniqueness , mathematics , equivalence (formal languages) , viscoelasticity , initial value problem , state (computer science) , infinity , mathematical analysis , calculus (dental) , pure mathematics , algorithm , medicine , dentistry , physics , thermodynamics
The modelling of materials with memory is characterized by the process and the initial state. Because of the equivalence between histories, the state is identified with the response generated by the trivial process on the given initial strain. The process is the strain since the initial time. The occurrence of histories up to past infinity is then avoided. Within this setting, the inversion of the constitutive equation and a variational formulation are examined. Moreover a virtual‐work type formulation provides a simpler weak form of the initial‐value problem. Uniqueness of the solution to the initial‐value problem is then established. Copyright © 2004 John Wiley & Sons, Ltd.