Large deformation axial element for implicit constitutive relations

This work documents the formulation of an axial element that could handle implicit constitutive relations. This formulation uses nodal displacements, member forces, and reaction forces as primary unknowns. For some assumed values of these primary unknowns satisfying the nodal equilibrium equations, the computed stretch and stress in the members need not be in agreement with the constitutive relation. Hence, these primary unknowns are found such that the error in the constitutive relation for the members are minimized subjected to the constraint that the nodal equilibrium equations hold. Axial element developed using this concept is used to analyze a few trusses. The results of this formulation are in agreement with the results obtained from ABAQUS ® when stress is an explicit function of the stretch ratio. Also, some statically determinate as well as indeterminate trusses are solved for an implicit constitutive relation and the reasonableness of the obtained results established.