Computational aspects of the mechanics of complex materials |
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Authors: | Paolo Maria Mariano Furio Lorenzo Stazi |
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Affiliation: | (1) Università di Firenze, Firenze, Italy;(2) Università di Roma “La Sapienza”, Roma, Italy |
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Abstract: | Summary Bodies with exotic properties display material substructural complexity from nano to meso-level. Various models have been
built up in condensed matter physics to represent the behavior of special classes of complex bodies. In general, they fall
within the setting of an abstract model building framework which is not only a unifying structure of existing models but—above
all—atool to construct special models of new exotic materials. We describe here basic elements of this framework, the one ofmultifield theories, trying to furnish a clear idea of the subtle theoretical and computational problems arising within it. We present the matter
in a form that allows one to construct appropriate algorithms in special cases of physical interest. We discuss also issues
related to the construction of compatible and mixed finite elements in linearized setting, the extension of extended finite
element methods to analyze the influnce of material substructures on crack growth, the evolution of sharp discontinuity surfaces
in complex bodies. Concrete examples of complex bodies are also presented with a number of details.
Dedicated to Gianfranco Capriz on occasion of his eightieth birthday |
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