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

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.