Multifield theories in mechanics of solids

Publisher Summary Multifield theories indicate the wide range of models in which some graphic fields must be introduced to describe the influence of material substructures on the gross mechanical behavior of solids. Solidification of metal alloys and their possible shape memory, damage states and evolution, and the influence of long chains of macromolecules on the behavior of polymers can be successfully analyzed with the help of multifield theories. Models with internal variables can be derived from multifield theories by appropriate internal constraints. The chapter focuses on the multifield description of continua that is a flexible framework to study physical situations in which the analysis of substructures is important for both practical and theoretical reasons. The chapter discusses the configurations and deduction of balance equations for bodies lacking in discontinuity surfaces, the behavior of the substructure, the influence of the substructure on the axial decay of energy in linear elastic cylinders, the derivation of thermomechanical balance at discontinuity surfaces, constitutive restrictions arising from a mechanical version, the second law of thermodynamics and the measures of substructural interactions, the analysis of the influence of substructures on configurational forces that drive the evolution of interfaces, the evaluation of the influence of material substructures on macrocrack propagation, the case where the substructure becomes latent in presence of appropriate internal constraints, and the application of the general theory to special cases.

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