A viscoelastic viscoplastic constitutive model including mechanical degradation: Uniaxial transient finite element formulation at finite strains and application to space truss structures

Abstract

This article presents a one-dimensional finite element formulation for the transient analysis of geometrically nonlinear trusses associated to viscoelastic viscoplastic materials including mechanical degradation. The proposed formulation aims at problems involving inertial loads and high strain rate deformations, and accounts for velocities, accelerations and rate-dependent effects. The kinematic description adopts an updated Lagrangian approach, whereas the dynamic equilibrium equations are solved using the Newmark algorithm coupled to an incremental-iterative Newton–Raphson procedure. The viscoelastic and viscoplastic behaviors are accounted for the generalized Kelvin–Voigt and Perzyna models, and material degradation is considered using Continuum Damage Mechanics. The evolution equations are integrated using an implicit scheme, including derivation of the analytical tangent stiffness and algorithmic material tangent operator. Numerical examples illustrate application of the proposed formulation to the analysis of polymeric truss structures undergoing snap-through.