Elimination of memory from the equations of motion of hereditary viscoelasticity for increased efficiency of numerical integration

TL;DR

This paper introduces a method to eliminate memory effects in the equations of motion for hereditary viscoelasticity, significantly improving computational efficiency by replacing unbounded memory with a finite quadrature.

Contribution

The paper presents a novel approach to remove memory terms in viscoelastic equations using quadrature, applicable to media with known relaxation spectra, including the Strick-Mainardi model.

Findings

Reduces computational effort and storage in viscoelastic simulations.

Applicable to media with separable, completely monotonic relaxation moduli.

Establishes a connection to fractional-order viscoelasticity.

Abstract

A method of eliminating the memory from the equations of motion of linear viscoelasticity is presented. Replacing the unbounded memory by a quadrature over a finite or semi-finite interval leads to considerable reduction of computational effort and storage. The method applies to viscoelastic media with separable completely monotonic relaxation moduli with an explicitly known retardation spectrum. In the seismological Strick-Mainardi model the quadrature is a Gauss-Jacobi quaddrature. The relation to fractional-order viscoelasticity is shown