Representations for implicit constitutive relations describing non-dissipative response of isotropic materials Academic Article uri icon

abstract

  • © 2017, Springer International Publishing AG. A methodology for obtaining implicit constitutive representations involving the Cauchy stress and the Hencky strain for isotropic materials undergoing a non-dissipative process is developed. Using this methodology, a general constitutive representation for a subclass of implicit models relating the Cauchy stress and the Hencky strain is obtained for an isotropic material with no internal constraints. It is shown that even for this subclass, unlike classical Green elasticity, one has to specify three potentials to relate the Cauchy stress and the Hencky strain. Then, a procedure to obtain implicit constitutive representations for isotropic materials with internal constraints is presented. As an illustration, it is shown that for incompressible materials the Cauchy stress and the Hencky strain could be related through a single potential. Finally, constitutive approximations are obtained when the displacement gradient is small.

author list (cited authors)

  • Gokulnath, C., Saravanan, U., & Rajagopal, K. R.

citation count

  • 12

publication date

  • October 2017