Formulations of Viscoelastic Constitutive Laws for Beams in Flexible Multibody Dynamics

It is often necessary to consider material dissipation effects in structural dynamics analysis. A novel three-dimensional viscoelastic beam formulation is proposed. A systematic procedure is proposed to incorporate existing viscoelastic material models into beam theories. The generalized Maxwell model is used to demonstrate the procedure. Starting from a three-dimensional beam theory, classical material viscoelastic constitutive laws are used to develop viscoelastic beam models for flexible multibody dynamics. In contrast with classical beam theories, the proposed beam formulation captures three-dimensional stress and strains distributions based on a novel dimensional reduction method, and models dissipative phenomena at the same time. All cross-sectional deformation modes are considered in the formulation. With the generalized Maxwell model, the formulation is valid for a broad range of frequencies. Because it is based on a three-dimensional formulation, the proposed approach uses a decomposition of the strain tensor into bulk and deviatoric components, thereby eliminating Poisson locking effects. This is particularly important because many highly dissipative materials are also nearly incompressible. Numerical examples are presented to illustrate these characteristics. Because the formulation developed is a beam model, it is computationally efficient and can be used for the simulation of flexible multibody dynamics systems.