Calibration of a constitutive model for the post-yield behaviour of cortical bone

An experimental and computational investigation of the post-yield behaviour of trabecular bone during vertebral device subsidence

“…The present study has shown that a continuum based pressure dependent DP plasticity formulation is also inadequate in capturing the inelastic trabecular behaviour although previously implemented for trabecular bone (Bessho et al 2007;Derikx et al 2011). Kelly and McGarry (2012) and the present study have demonstrated that continuum based plasticity formulations such as the DP and Mohr-Coulomb formulations that that have linear yield surfaces in the q-p plane are inappropriate for modelling trabecular bone, although they have been shown to capture the inelastic behaviour of cortical bone (Feerick and McGarry 2012;Mullins et al 2009). Plasticity formulations such as 22 the modified super-ellipsoid yield criterion (Bayraktar et al 2004a), the Tsai-Wu plasticity formulation (Fenech and Keaveny 1999;Keaveny et al 1999) and a cellular solid criterion (Fenech and Keaveny 1999) have also been proposed to describe the multiaxial yielding of trabecular bone.…”

Experimental and numerical characterisation of the elasto-plastic properties of bovine trabecular bone and a trabecular bone analogue

“…The DP and MC models have been successfully calibrated for cortical bone (Mercer et al, 2006;Tai et al, 2006;Mullins et al, 2009). Using the MC model for cortical bone Tai et al trabeculae and is not reflective of the macroscale inelastic behaviour of the porous trabecular bone structure.…”

“…The DP criterion was introduced by Drucker and Prager (1951) and was traditionally used to model soils. Both the DP and MC models have previously been calibrated for cortical bone (Mercer et al, 2006;Tai et al, 2006;Mullins et al, 2009), where a high friction angle results in an increased von Mises yield stress with increasing pressure as shown in Fig. 3(B).…”

“…Several studies have considered von Mises plasticity which neglects pressure dependent yield (Lotz et al, 1991;Keyak and Rossi, 2000;Keyak, 2001;Mullins et al, 2009;Adam and Swain, 2011). Additionally, several studies have focused on the Drucker-Prager (DP) (Mercer et al, 2006;Bessho et al, 2007;Mullins et al, 2009;Carnelli et al, 2010;Adam and Swain, 2011;Carnelli et al, 2011) and MohrCoulomb (MC) (Tai et al, 2006;Wang et al, 2008) constitutive formulations. Through the definition of a friction angle the DP and MC models allow for an increasing yield stress for increasing pressure.…”

“…Through the definition of a friction angle the DP and MC models allow for an increasing yield stress for increasing pressure. Comparing the von Mises and DP models for the simulation of cortical bone nanoindentation, Mullins et al (2009) suggested that a pressure dependent yield criterion should be used when modelling the post yield behaviour of cortical bone due to frictional mechanisms. Cortical and trabecular bone have different micro architecture and therefore the plasticity mechanisms of both materials may be very different.…”