Transient analysis of trusses considering nonlinear elastic and viscoelastic material models

Abstract

The use of simple bar elements in nonlinear structural finite element formulations has the academic advantage of uncoupling element technology issues from the structural phenomena to be observed. In this work, we present a finite element setting for the formulation of different nonlinear material models applied to the transient analysis of trusses. While nonlinear elasticity is considered by studying a Hooke-like linear relationship between different pairs of nonlinear measures of stress and strain, hyperelasticity is formulated using Ogden’s model. Viscoelasticity is introduced using a generalized Kelvin rheological model to account for strain rate effects. The finite kinematics is set in a corotational total Lagrangian description where the virtual work is described using the Second Piola-Kirchhoff and the Green Lagrange measures. Although the derivation is omitted, the consistent tangent moduli are given for all these cases. Numerical problems involving simultaneously different truss models are studied and made available as benchmarks since little comparative data is found in literature.