Restrictive Conditions on the Elastic Potential for a Compressible Anisotropic Hyperelastic Solid.
Abstract
The elastic potential of an anisotropic compressible hyperelastic solid was considered to depend upon entropy and the 6 components of strain, and to possess an absolute minimum corresponding to some stress-free natural state. The mathematical requirements for such a minimum introduce a set of restrictive inequalities which the strain and entropy derivatives must satisfy for the unstrained natural state. It is shown that the same set of inequalities must hold for any deformation within the range of variables. For the most general case of anisotropy, the set of restrictions involves 56 inequalities contained within 6 sub-sets. In the case of an isotropic hyperelastic solid there are only 4 independent restrictive conditions. The isotropic restrictions were also transformed to strain invariant representations; the forms of the resulting restrictive conditions are more complicated than in the case of the strain component representation. However, the 4 restrictive conditions associated with the unstrained state of an isotropic hyperelastic solid are extremely simple and allow easy determination of the compatibility of any assumed strain energy function. Such a compatibility decreases the probability that any predicted deformational response will violate the physical reality of the material. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1970
- Accession Number
- AD0864409
Entities
People
- John N. Majerus