Work

Extensions of the constitutive relations to describe the response of compressible nonlinear Kelvin–Voigt solids

Year: 2025

Type: article

Abstract: This paper investigates the propagation of longitudinal waves in some possible models of compressible Kelvin-Voigt viscoelastic solids. With respect to the elastic part two extensions of the classical neo-Hookean material model are proposed: the A-model, which incorporates a logarithmic volumetric function, and the B-model, based on the deviatoric invariants and a power-law volumetric function. For both models, we assume the same dissipative part given by the classical Navier–Stokes constitutive equation. These models are analyzed for their ability to describe a recovery phenomenon, ensuring conditions for monotonicity, boundedness, and uniqueness of solutions. The propagation of longitudinal traveling waves is proved. We show that the equation governing such motions is indeed a special case of the viscous p-system and a weakly nonlinear analysis demonstrates the emergence of Burgers’ equations.

Source: Meccanica

DOI: 10.1007/s11012-025-01947-x

Authors: Julia de Castro Motta, Kumbakonan Rajagopal, Giuseppe Saccomandi

Institutions: University of Salerno, Texas A&M University, Ollscoil na Gaillimhe – University of Galway, University of Perugia, Istituto Nazionale di Fisica Nucleare, Sezione di Perugia

Language: English

Topic: Elasticity and Material Modeling

Subfield: Biomedical Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,990