On the effectiveness of convolutive type variational principles in the numerical solution of viscoelastic problems

Carini, Angelo; Levi, Francesca; Genna, Francesco

doi:10.2140/jomms.2023.18.319

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On the effectiveness of convolutive type variational principles in the numerical solution of viscoelastic problems

Angelo Carini, Francesca Levi and Francesco Genna

Vol. 18 (2023), No. 3, 319–354

DOI: 10.2140/jomms.2023.18.319

Abstract

With reference to the nonaging linear viscoelastic problem, three convolutive type variational formulations existing in the literature are critically reviewed: the Gurtin formulation, the split Gurtin formulation and the Huet formulation. The formulations are used for the numerical solution of the hereditary viscoelastic problem through spatial and temporal discretizations considering both a finite time range and using a step-by-step method of time marching. Several numerical examples are included and numerical results are compared with the aim of investigating the effectiveness of the variational formulations in the numerical solution of the viscoelastic problem.

Dedicated to the memory of Professor Morton Gurtin

Keywords

viscoelasticity, convolutive variational principles

Milestones

Received: 1 August 2022

Accepted: 11 August 2022

Published: 5 May 2023

Authors

Angelo Carini
Department of Civil, Environmental, Architectural Engineering and Mathematics University of Brescia Brescia Italy

Francesca Levi
Department of Civil, Environmental, Architectural Engineering and Mathematics University of Brescia Brescia Italy

Francesco Genna
Department of Civil, Environmental, Architectural Engineering and Mathematics University of Brescia Brescia Italy

Vol. 18, No. 3, 2023

Angelo Carini, Francesca Levi and Francesco Genna

Abstract

Keywords

Milestones

Authors