Any rational theory of continuum thermomechanics presupposes, for the formulation of both conservation laws and constitutive laws, some basic geometry. The choice of this geometical structure predetermines the effectiveness of the model to describe “abnormal phenomena” due to defects, which can be attributed to the change of local topology in the continuum. The present work is an attempt at giving some theoretical basis to the elaboration of the thermomechanics of a material in the presence of field singularity (distribution of scalar and vector discontinuity). Defects in various mechanical systems, such as fluids or solids, have the common property that, within the continuum limit, certain closed contour integrals over field either scalar or vector variables do not vanish because of the presence of singularity (in other words, there are jumps of fields). This process comes under the range of the Cartan path.
KeywordsBasic Geometry Affine Connection Local Topology Affine Structure Abnormal Phenomenon
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