On compressible materials capable of sustaining axisymmetric shear deformations. I: Anti-plane shear of isotropic hyperelastic materials
As is well-known, an anti-plane shear deformation is not controllable in every compressible or incompressible, homogeneous and isotropic elastic material. However, Knowles has presented the necessary and sufficient conditions on the strain energy function to determine whether a specified hyperelastic material with a monotone shear stress response function can sustain general, nonaxisymmetric, anti-plane shear deformations. For compressible materials, two conditions are required. In the present work, the authors introduce, under a weaker condition on the shear response function, a single necessary and sufficient condition on the strain energy density function, providing that the material may support axisymmetric, anti-plane shear deformations. They illustrate with several examples the simplicity of the result. They further prove that while Knowless conditions suffice for general anti-plane shear deformations, they are not necessary for a hyperelastic material to sustain axisymmetric, anti-plane shear deformation. This work is quite interesting and may find several readers in finite elasticity theory.
scientific article; zbMATH DE number 797095