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Computational aspects of the mechanics of complex materials. (English) Zbl 1152.74315

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 – a tool to construct special models of new exotic materials. We describe here basic elements of this framework, the one of multifield 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 influence 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.

MSC:

74A30 Nonsimple materials
74S05 Finite element methods applied to problems in solid mechanics
74-02 Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids
74E30 Composite and mixture properties
74J40 Shocks and related discontinuities in solid mechanics
74Q99 Homogenization, determination of effective properties in solid mechanics
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