A Geometric Approach to Thermomechanics of Dissipating Continua

the long version

This monograph focuses on the modeling of continua that exhibit the property of singularities in fields. A rational theory of continuum thermomechanics that takes into account the existence and distribution of scalar and vector discontinuities is presented. Guiding the work is the notion that discontinuities should be modeled by the torsion and curvature tensors (Cartan), thus forming an attractive alternative way of representing dissipating continua with singularities. Also emphasized in this study is the relationship between singularities and certain irreversible properties that occur in solid and fluid models. The required mathematical background is given in several appendices, although some basic understanding of differential geometry and tensor analysis would be helpful. The book is largely self-contained and should serve a readership of graduate students, researchers, and engineers in applied mathematics, mechanics, and physics.