No abstract

This study presents an effective and robust time integration procedure for general anisotropic, thermal rheologically simple viscoelasticity, that is suitable for implementation in a broad spectrum of general purpose nonlinear ®nite element programs. It features a judicious choice of state variables which record the extent of inelastic¯ow (creep), a stable backward Euler integration step, and a consistent tangent operator. Numerical examples involving homogeneous stress states such as uniaxial tension 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.

SUMMARYThis 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 Schapery's 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.