Dimensionally reduced nonlinear solids with general loads and constitutive laws: Theory and finite element formulation for rod-like bodies

Abstract

Dimensionally reduced solids are formulated by linking the kinematics of a slender, rod-like body and a true, geometrically exact, rod. This link is enforced in such a way that the solid, where volumetric and surface loads can be applied, becomes slave of the rod, where the mechanical equilibrium is enforced. The model poses no limitations on the size of the deformations and displacements in either body and it can be used for quasistatic or dynamic analyses. A general finite-element approximation of the ensemble is described in detail, and shown to require only modifications at the assembly level for its implementation, resulting in large computational savings. These dimensionally reduced models are especially useful for problems such as fluid/solid interaction and contact where the surface forces among neighboring bodies need to be calculated accurately. By accounting for the internal energy in the slave solid instead of the rod, the proposed formulation allows also to model — without any additional ingredients — the mechanics of rods with complex material constitutive laws. Numerical examples illustrate the use of the new models in situations with complex loading and constitutive behavior.