On the Replicability of the Empirical Constant Stiffness Force-Crush Model using a Mechanics of Materials Approach

The subject theoretical study was undertaken with the purpose of determining the replicability, using a mechanics of materials approach, of the energy absorbed term associated with the B stiffness coefficient of the empirical constant stiffness force-crush model. For the non-restitutive case, it is shown that this term can be derived exactly using a plane rectangular bilinear element formulation with appropriately prescribed nodal displacements and a constitutive formulation based on the linear isotropic model but with the enforcement of zero values for both the shear modulus and the Poisson's ratio. The analytical closed-form solution for the non-restitutive plane stress model with two translational degrees of freedom per node coupled with a fully developed linear elastic formulation is also derived. An example is included to show the implementation of these models.