Journal of Elasticity

, Volume 135, Issue 1–2, pp 261–293 | Cite as

A Causality Setting for Elasticity Theory

  • Roger FosdickEmail author


We give a causality approach to nonlinear elasticity theory within a pure mechanics setting. Based on the notion of a fixed frame in Open image in new window and Euclidean invariance considerations, we show how a broadly general and novel evolutionary hypothesis concerning ‘cause’ and ‘effect’ must reduce to the classical statement of the balance of energy, and we obtain all of the classical balance laws of continuum mechanics. The concept of mass and its balance is derived within this theory. The mass density naturally emerges from the theory without preconception as an inertial scalar field for the body which is associated with the speed of its material particles and a measure of their kinetic behavior. Aside from the causality hypothesis and its invariance, the fundamental notions of body, motion, force and internal power are primitive.


Causality Continuum mechanics Elasticity Invariance Objectivity 

Mathematics Subject Classification (2010)




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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Department of Aerospace Engineering and MechanicsUniversity of MinnesotaMinneapolisUSA

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