The elasticity of elasticity

by: K Rajagopal

Zeitschrift für Angewandte Mathematik und Physik (ZAMP), Vol. 58, No. 2. (30 March 2007), pp. 309-317.

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Abstract

Abstract. In this note we assert that the usual interpretation of what one means by “elasticity” is much too insular and illustrates our thesis by introducing implicit constitutive theories that can describe the non-dissipative response of solids. There is another important aspect to the introduction of such an implicit approach to the non-dissipative response of solids, the development of a hierarchy of approximations wherein, while the strains are infinitesimal the relationship between the stress and the linearized strain is non-linear. Such approximations would not be logically consistent within the context of explicit theories of Cauchy elasticity or Green elasticity that are currently popular.

@article{citeulike:1780952, abstract = {Abstract.\ \ In this note we assert that the usual interpretation of what one means by “elasticity” is much too insular and illustrates our thesis by introducing implicit constitutive theories that can describe the non-dissipative response of solids. There is another important aspect to the introduction of such an implicit approach to the non-dissipative response of solids, the development of a hierarchy of approximations wherein, while the strains are infinitesimal the relationship between the stress and the linearized strain is non-linear. Such approximations would not be logically consistent within the context of explicit theories of Cauchy elasticity or Green elasticity that are currently popular.}, author = {Rajagopal, K. }, citeulike-article-id = {1780952}, doi = {10.1007/s00033-006-6084-5}, journal = {Zeitschrift f\"{u}r Angewandte Mathematik und Physik (ZAMP)}, keywords = {elasticity}, month = {March}, number = {2}, pages = {309--317}, posted-at = {2007-10-17 19:40:53}, priority = {2}, title = {The elasticity of elasticity}, url = {http://dx.doi.org/10.1007/s00033-006-6084-5}, volume = {58}, year = {2007} }

RIS record

TY - JOUR ID - citeulike:1780952 L3 - citeulike-article-id:1780952 TI - The elasticity of elasticity JF - Zeitschrift für Angewandte Mathematik und Physik (ZAMP) VL - 58 IS - 2 SP - 309 EP - 317 N2 - Abstract.  In this note we assert that the usual interpretation of what one means by “elasticity” is much too insular and illustrates our thesis by introducing implicit constitutive theories that can describe the non-dissipative response of solids. There is another important aspect to the introduction of such an implicit approach to the non-dissipative response of solids, the development of a hierarchy of approximations wherein, while the strains are infinitesimal the relationship between the stress and the linearized strain is non-linear. Such approximations would not be logically consistent within the context of explicit theories of Cauchy elasticity or Green elasticity that are currently popular. KW - elasticity AU - Rajagopal, K PY - 2007/03/30/ UR - http://dx.doi.org/10.1007/s00033-006-6084-5 ER -

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