2023/09/28 by Souhayl Sadik, Arash Yavari, Sadik, Souhayl +1 · 3 citations
Biochemistry, Genetics and Molecular Biology · Engineering · #Cellular Mechanics and Interactions #Elasticity and Material Modeling #Elasticity and Wave Propagation #FOS: Physical sciences #Materials Science (cond-mat.mtrl-sci)
paper · pdf · doi:10.48550/arxiv.2309.16555
openalex publication_date 2023/09/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we revisit the mathematical foundations of nonlinear viscoelasticity. We study the underlying geometry of viscoelastic deformations, and in particular, the intermediate configuration. Starting from the multiplicative decomposition of deformation gradient into elastic and viscous parts F=\Fe\Fv , we point out that \Fv can be either a material tensor (\Fe is a two-point tensor) or a two-point tensor (\Fe is a spatial tensor). We show that based on physical grounds the second choice is unacceptable. It is assumed that the free energy density is the sum of an equilibrium and a non-equilibrium part. The symmetry transformations and their action on the total, elastic, and viscous deformation gradients are carefully discussed. Following a two-potential approach the governing equations of nonlinear viscoelasticity are derived using the Lagrange-d'Alembert principle. We discuss the constitutive and kinetic equations for compressible and incompressible isotropic, transversely isotropic, orthotropic, and monoclinic viscoelastic solids. We finally semi-analytically study creep and relaxation in three examples of universal deformations.