2025/06/04 by C. O. Horgan, Cornelius O. Horgan, J. G. Murphy · 1 citation
Engineering · #Composite Structure Analysis and Optimization #Elasticity and Material Modeling #Elasticity and Wave Propagation
paper · pdf · doi:10.1007/s10659-025-10142-8
openalex publication_date 2025/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
Abstract It is well-known that analytic solutions for problems in nonlinear elasticity for incompressible isotropic hyperelastic materials can be obtained either by using constitutive models in terms of classical invariants of the right Cauchy-Green tensor or alternatively by using the principal stretches directly. In this paper, we describe an efficient procedure for transforming strain-energy densities expressed in terms of the principal stretches into their counterparts in terms of the invariants. To illustrate the results, applications to the problems of simple shear and pure torsion are described. It is demonstrated that the stretch formulation has some advantages in the former case while the principal invariant approach seems preferable for the torsion problem.