Nonlinear analysis of hyperelastoplastic truss-like structures

Abstract

In this paper, a uniaxial model for elastoplastic materials under large strain regime is applied to a finite element formulation in order to analyze highly flexible truss-like structures. The bars are axially loaded and do not buckle. The finite displacements are exactly described via geometrically nonlinear analysis and the geometry is modeled with a truss bar finite element of linear order. To define the material response, a uniaxial hyperelastoplastic framework is developed. Details of the return mapping algorithm and the consistent tangent operator are also provided. The usual isotropic von Mises yield criterion and associative flow rule are employed. Different models to describe the elastic response and hardening behavior are selected: the Saint Venant–Kirchhoff elastic model, the neo-Hookean hyperelastic model, the Swift isotropic hardening law, a general polynomial isotropic hardening model, and the Armstrong–Frederick kinematic hardening rule. In the context of the adopted constitutive models, the expressions employed to determine stresses and strains are provided. The present formulation is tested in six problems involving truss-like structures under finite displacements and finite elastoplastic strains: three plane and three complex space trusses. The constitutive data of some real and general materials are employed. The first problem is used only to illustrate the material elastoplastic behavior in a large strain range. The other numerical examples are employed to show the influence of the constitutive model on the truss behavior. The present numerical results show that the formulation can be used to analyze general truss-like structures in the context of finite uniaxial elastoplasticity.