Description
The classic nonlinear constitutive representation for isotropic elastic materials was given by Rivlin and Ericksen in 1955. Knowledge about similar constitutive representations for anisotropic materials has developed slowly since then, primarily by group theoretic means, but in a series of articles in the 1990s. H. Xiao showed that all anisotropic materials have a six-term representation. However, it has been difficult to find those so-called minimal representations that not only satisfy all the necessary symmetry requirements, but also reduce to linear elasticity for small strains. In addition, in the 1990s, S. Cowin and M. Mehrabadi showed that linear elasticity may always be -represented in no more than six terms even though an anisotropic material may have as many as 21 independent elastic moduli. Combining and extending these results have allowed the author to develop minimal representations for any anisotropic material that do reduce to linear elasticity. This article will illustrate the method for cubic materials.
Recommended Citation
Wright, T. (2014). Nonlinear constitutive representation for cubic materials. In A. Bajaj, P. Zavattieri, M. Koslowski, & T. Siegmund (Eds.). Proceedings of the Society of Engineering Science 51st Annual Technical Meeting, October 1-3, 2014 , West Lafayette: Purdue University Libraries Scholarly Publishing Services, 2014. https://docs.lib.purdue.edu/ses2014/honors/prager/14
Nonlinear constitutive representation for cubic materials
The classic nonlinear constitutive representation for isotropic elastic materials was given by Rivlin and Ericksen in 1955. Knowledge about similar constitutive representations for anisotropic materials has developed slowly since then, primarily by group theoretic means, but in a series of articles in the 1990s. H. Xiao showed that all anisotropic materials have a six-term representation. However, it has been difficult to find those so-called minimal representations that not only satisfy all the necessary symmetry requirements, but also reduce to linear elasticity for small strains. In addition, in the 1990s, S. Cowin and M. Mehrabadi showed that linear elasticity may always be -represented in no more than six terms even though an anisotropic material may have as many as 21 independent elastic moduli. Combining and extending these results have allowed the author to develop minimal representations for any anisotropic material that do reduce to linear elasticity. This article will illustrate the method for cubic materials.