New universal relations for nonlinear isotropic elastic materials

@article{citeulike:1598538, abstract = {A nonlinear isotropic elastic block is subjected to a homogeneous deformation consisting of simple shear superposed on triaxial extension. Two new relations are established for this deformation which are valid for all nonlinear elastic isotropic materials, and hence are universal relations. The first is a relation between the stretch ratios in the plane of shear and the amount of shear when the deformation is supported only by shear tractions. The second relation is established for a thin-walled cylinder under combined extension, inflation and torsion. Each material element of the cylinder undergoes the same local homogeneous deformation of shear superposed on triaxial extension. The properties of this deformation are used to establish a relation between pressure, twisting moment, angle of twist and current dimensions when no axial force is applied to the cylinder. It is shown that these relations also apply for a mixture of a nonlinear isotropic solid and a fluid.}, author = {Rajagopal, K. R. and Wineman, Alan S. }, citeulike-article-id = {1598538}, doi = {10.1007/BF00042450}, journal = {Journal of Elasticity}, keywords = {elasticity}, month = {January}, number = {1}, pages = {75--83}, posted-at = {2007-08-28 13:46:14}, priority = {2}, title = {New universal relations for nonlinear isotropic elastic materials}, url = {http://dx.doi.org/10.1007/BF00042450}, volume = {17}, year = {1987} }

TY - JOUR ID - citeulike:1598538 L3 - citeulike-article-id:1598538 TI - New universal relations for nonlinear isotropic elastic materials JF - Journal of Elasticity VL - 17 IS - 1 SP - 75 EP - 83 N2 - A nonlinear isotropic elastic block is subjected to a homogeneous deformation consisting of simple shear superposed on triaxial extension. Two new relations are established for this deformation which are valid for all nonlinear elastic isotropic materials, and hence are universal relations. The first is a relation between the stretch ratios in the plane of shear and the amount of shear when the deformation is supported only by shear tractions. The second relation is established for a thin-walled cylinder under combined extension, inflation and torsion. Each material element of the cylinder undergoes the same local homogeneous deformation of shear superposed on triaxial extension. The properties of this deformation are used to establish a relation between pressure, twisting moment, angle of twist and current dimensions when no axial force is applied to the cylinder. It is shown that these relations also apply for a mixture of a nonlinear isotropic solid and a fluid. KW - elasticity AU - Rajagopal, KR AU - Wineman, Alan PY - 1987/01/01/ UR - http://dx.doi.org/10.1007/BF00042450 ER -