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On large strain viscoelasticity: Continuum formulation and finite element applications to elastomeric structures. (English) Zbl 0920.73064
The paper starts by deriving a mathematical model for the time-dependent highly nonlinear deformation phenomena at finite strains in three-dimensional structures of high-polymeric (viscoelastic) substances. The constitutive equations governing the behaviour of the model are obtained by using the Lagrangian kinematic description within the thermodynamic theory of materials with internal state variables [see the author and J. C. Simo, Int. J. Solids Struct. 33, No. 20-22, 3019-3034 (1996; Zbl 0909.73038)]. In the following two parts the author discusses the time integration of the constitutive response of the model, outlines an update algorithm for the stress tensor and the consistent material tangential moduli, and presents the finite element analysis necessary for the numerical solution of the corresponding boundary value problem. The final part of the paper contains three representative numerical examples (creeping test at large strain, cyclic loading of a rubber block, and pinched thick-walled cylinder) with the intention to demonstrate the qualitative performance and general applicability of the model as well as the effectiveness of the implicit time stepping algorithm.

MSC:
74D10 Nonlinear constitutive equations for materials with memory
74S05 Finite element methods applied to problems in solid mechanics
74D05 Linear constitutive equations for materials with memory
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