| Affiliation: | (1) Structural and Solid Mechanics Program, Department of Civil Engineering, University of Virginia, Charlottesville, VA 22904, USA;(2) Department of Mechanical Engineering, Dublin City University, Glasnevin, Dublin, 9, Ireland |
| Abstract: | For homogeneous, isotropic, compressible nonlinearly elastic materials, a wide class of strain-energy density functions are obtained that leave the equations of equilibrium invariant under simple scaling transformations of the material and spatial coordinates. These strain-energy densities are homogeneous functions of the principal stretches. Several illustrative examples of particular strain-energies are provided. For axisymmetric problems, the invariance discussed here ensures that the equations of equilibrium can be solved by quadratures and thus often leads to analytic solutions in parametric or closed-form.Mathematics Subject Classifications (2000) 74B20, 74G55. |
