Abstract
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.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsAuthor information
Authors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer Science+Business Media New York
About this chapter
Cite this chapter
Rakotomanana, L.R. (2004). Conclusion. In: A Geometric Approach to Thermomechanics of Dissipating Continua. Progress in Mathematical Physics, vol 31. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-8132-6_8
Download citation
DOI: https://doi.org/10.1007/978-0-8176-8132-6_8
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-6411-8
Online ISBN: 978-0-8176-8132-6
eBook Packages: Springer Book Archive