2024/05/27 by Arash Yavari, Alain Goriely, Yavari, Arash +1 · 2 citations
Engineering · #Dynamics and Control of Mechanical Systems #Elasticity and Material Modeling #Elasticity and Wave Propagation #FOS: Physical sciences #Materials Science (cond-mat.mtrl-sci)
paper · pdf · doi:10.48550/arxiv.2405.17362
openalex publication_date 2024/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For a given material, controllable deformations are those deformations that can be maintained in the absence of body forces and by applying only boundary tractions. For a given class of materials, universal deformations are those deformations that are controllable for any material within the class. In this paper, we characterize the universal deformations in compressible isotropic implicit elasticity defined by solids whose constitutive equations, in terms of the Cauchy stress \boldsymbolσ and the left Cauchy-Green strain b, have the implicit form \boldsymbolf(\boldsymbolσ,b)=0. We prove that universal deformations are homogeneous. However, an important observation is that, unlike Cauchy (and Green) elasticity, not every homogeneous deformation is permissible for a given implicit-elastic solid. In other words, the set of universal deformations is material-dependent, yet it remains a subset of homogeneous deformations.