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Spatial and Material Forces in Nonlinear Continuum Mechanics

Part of the book series: Solid Mechanics and Its Applications ((SMIA,volume 272))

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Abstract

This chapter introduces the overarching topic of this monograph. After recalling the need for continuum mechanics, it contrasts the concepts of spatial and material forces and highlights why the latter are a necessary concept in various branches of defect mechanics. It then reviews various vistas on material forces before commenting on their computational implications.

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Notes

  1. 1.

    A descriptive definition of material forces due to Eshelby [30] is the following: ... the total energy of a system ... is a function of the set of parameters necessary to specify the configuration of the imperfections. The negative gradient of the total energy wrt the position of an imperfection may conveniently be called the force on it. This force, in a sense fictitious, is introduced to give a picturesque description of energy changes, and must not be confused with the ordinary surface and body forces acting on the material.

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Steinmann, P. (2022). Introduction. In: Spatial and Material Forces in Nonlinear Continuum Mechanics. Solid Mechanics and Its Applications, vol 272. Springer, Cham. https://doi.org/10.1007/978-3-030-89070-4_1

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