A finite element constitutive update scheme for anisotropic, viscoelastic solids exhibiting non-linearity of the Schapery type

This study presents a new scheme for performing integration point constitutive updates for anisotropic, small strain, non-linear viscoelasticity, within the context of implicit, non-linear "nite element structural analysis. While the basic scheme has been presented earlier by the authors for linear viscoelasticity, the present work illustrates the generality of the underlying fundamentals by extending to Schaperyʹs non-linear model. The method features a judicious choice of state variables, a stable backward Euler integration step, and a consistent tangent operator. Its greatest strength lies in ready incorporation into existing FEM codes. Numerical examples involving homogeneous stress states such as uniaxial extension and simple shear, and non-uniform stress states such as a beam under tip load, were carried out by incorporating the present scheme into a general purpose FEM package. Excellent agreement with analytical results is observed