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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
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