Mathematical Problems Posed by the Theory
The characteristic features of all special problems in the theory of continua with microstructure stem from the basic fact that knowledge of a complete placement of a body B requires the assignment of a field v(x) whose values, in general, are not in a Euclidean space or in a linear space but in a smooth manifold, with sometimes complex topological properties; this fact by itself creates new types of mathematical problems. Other interesting questions derive from the higher order of the differential systems which describe the evolution of B or from higher-order derivatives appearing in the balance equation of momentum itself, when bodies with latent microstructure are envisaged. Numerous other problems are generated by the wealth of possibilities arising from constitutive equations which involve more variables than in the classical case. Here, in Part IV, we quote some special examples, beginning with some elementary aspects of the topological theory of defects.
KeywordsManifold Assure Incompressibility
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