ABSTRACT
A geometrically exact truss-beam formulation is combined with a most simply structured nonlinear material constitutive formulation in this paper on which all subsequent investigations are based. Focus of the paper is then put on working out the embedding of the 1D-stress or 1D-force situation of the truss-element into a 3D continuum mechanical framework based on isotropic hyperelasticity in principal axes directions. This opens up the possibility of introducing several work-conjugate measures of stress and strain, in connection with the classical Saint Venant Kirchhoff model. This results in a multitude of formally possible alternative approaches of formulation of the material constitutive behaviour. It is the dedicated purpose of this paper to clarify the theoretical embedding of the 1D truss element behaviour into the general 3D continuum mechanical framework. Theoretical effects are demonstrated by elementary examples. The well-working of the developed truss model is demonstrated by nonlinear analysis of a three-bar 3D truss structure (Bergan 1985).
