P. Letallec et al., 3-DIMENSIONAL INCOMPRESSIBLE VISCOELASTICITY IN LARGE STRAINS - FORMULATION AND NUMERICAL APPROXIMATION, Computer methods in applied mechanics and engineering, 109(3-4), 1993, pp. 233-258
This paper considers viscoelastic incompressible solids in large defor
mations. A three-dimensional thermodynamical model is first proposed.
It leads to a nonlinear variational problem which is approximated in s
pace by mixed finite elements and in time by a first order implicit sc
heme. This approximation is analyzed on the corresponding linearized p
roblem. Finally, an elimination strategy is described which reduces ea
ch step of the discrete problem to the solution of a standard hyperela
stic problem to be solved by Newton's method.