Newtonian and Eshelbian Mechanics

  • Marcus Olavi RüterEmail author
Part of the Lecture Notes in Applied and Computational Mechanics book series (LNACM, volume 88)


The objective of this chapter is to present an introduction to the theory of continuum mechanics of elastic structures. Classical continuum mechanics deals with finding the spatial configuration of an elastic body that is subjected to external forces. This forward problem is attributed to Sir Isaac Newton and therefore termed Newtonian mechanics. In the associated inverse problem, which is attributed to John Douglas Eshelby and therefore termed Eshelbian mechanics, we are concerned with the forces applied to the spatial configuration. In Newtonian mechanics, the applied forces are of a physical nature, and as a result, the associated stress that arises in the spatial configuration of the elastic body is well known as the (physical) Cauchy stress. In Eshelbian mechanics, on the other hand, the deformed elastic body is subjected to so-called material forces, and the resulting stress in the initial configuration (of the forward problem) is termed the (material) Eshelby stress. In this chapter, the stress tensors that naturally appear in both Newtonian and Eshelbian mechanics are systematically derived for both compressible and (nearly) incompressible materials.


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Authors and Affiliations

  1. 1.Department of Civil and Environmental EngineeringUniversity of California Los AngelesLos AngelesUSA

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