• L. R. Rakotomanana
Part of the Progress in Mathematical Physics book series (PMP, volume 31)


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., [4]...) 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 [69]) 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.


Adiabatic Shear Band Affine Connection Field Singularity Gauge Connection Creep Fracture 
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Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • L. R. Rakotomanana
    • 1
  1. 1.Institut Mathématique de Rennes Campus de BeaulieuUniversité de Rennes 1Rennes CedexFrance

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