The present study focuses on theoretical modeling of a “continuum with a singularity distribution” in the sense that the distribution of matter is assumed continuous but that discontinuity of scalar fields (density, temperature,...) and discontinuity of vectorial fields (micro-cracks, inter-granular de-cohesions, growth of adiabatic shear bands, e.g., ...) may appear in the continuum. These two types of discontinuity constitute the singularity type we deal with. For a single surface singularity, jump conditions across this surface (e.g., Green and Nagdhi ) were derived from the balance equations of mass, linear momentum, moment of momentum, energy, and entropy. The density of singularity is assumed sufficiently high to accept a continuous volume distribution of singularity.
KeywordsAdiabatic Shear Band Affine Connection Field Singularity Gauge Connection Creep Fracture
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