Finite viscoelasticity plays a major role in defining the behavior of polymeric material systems which exhibit finite strains. An extension of small strain linear viscoelasticity to finite strains is directly accomplished when the generalized Maxwell model is chosen as the underlying analogous viscoelastic material structure. The rheological elements in parallel preserve the linear structure of the formulation even at finite strains. This formulation is based upon the Mooney-Rivlin strain-energy function and the second Piola-Kirchhoff stress tensor. The internal variables are approximated by a recursive expression. The efficient solution of the hereditary integral is crucial for the incremental numerical implementation. The viscoelastic solution is for the incremental nominal stress tensor which is equal to the product of the formulated fourth-order elasticity tensor and the incremental deformation gradient. For the special case of a finite elastic material, the formulation appropriately reduces to yield the elastic value of the incremental nominal stress tensor.
Finite viscoelasticity Polymeric material systems Generalized Maxwell model Mooney-Rivlin strain-energy function Second Piola-Kirchhoff stress tensor Incremental nominal stress tensor Incremental deformation gradient
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