On the passage from nonlinear to linearized viscoelastodynamics

TL;DR

This paper rigorously derives linearized viscoelastodynamics equations from a nonlinear Kelvin-Voigt model, demonstrating convergence of solutions across different scales and solution types, ensuring consistency between nonlinear and linearized theories.

Contribution

It provides a rigorous mathematical derivation and convergence analysis from nonlinear to linearized viscoelastodynamics models, respecting frame indifference.

Findings

Convergence of nonlinear solutions to linearized solutions.

Validation of linearized models across multiple scales.

Mathematical proof of solution consistency.

Abstract

The equations of linearized viscoelastodynamics in Kelvin-Voigt rheology are rigorously derived from a nonlinear model that satisfies the time-dependent frame indifference in the sense of Antman. Besides showing the convergence of corresponding solutions of both systems, we also prove the convergence of time-discrete solutions on various scales and of continuous solutions of nonlinear problems to linearized ones.