Relativistic Continuum Mechanics: A 20th Century Adventure

  • Gérard A. Maugin
Part of the Solid Mechanics and Its Applications book series (SMIA, volume 196)


Relativity theory as understood by Einstein is a true Twentieth century development. After the introduction of the four-dimensional version of special relativity by Minkowski and that of energy-moment tensor, to which must be added the fact that general relativity is per se a continuum theory, there was need for a true relativistic theory of the continuum. The present chapter reports in a critical manner the progress made in this theory in two distinct periods, one extending before World War II, and the second in the rough time interval 1950–1980, when solutions were finally proposed in an inclusive way. The first period dealt with attempts at discussing the ad hoc introduction of classical concepts in this new landscape. This included the notion of perfect fluids and a debated discussion of the possible generalization of the notion of rigid-body motion—without which the notion of elasticity could not be introduced. A breakthrough is represented by Eckart’s introduction of a systematic covariant space-and-time resolution of four-dimensional objects and of early elements of continuum thermodynamics. This, combined with the natural influence of the then new trends in classical continuum mechanics (rationalization à la Truesdell), then led to a modern, more axiomatic, formulation that allowed a rational construct of relativistic elasticity, and its generalization to more complex thermomechanical schemes (including generalized continua) and electromagnetic deformable bodies, a development in which the author has been more than a passive witness.


Momentum Tensor Perfect Fluid Generalize Continuum Discontinuity Wave Relativistic Elasticity 
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© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Institut Jean Le Rond D’Alembert UniversitéParis CedexFrance

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