Homogenisation method to capture the non-linear behaviour of intervertebral discs in multi-body systems

The present contribution is motivated by the desire to compute physiological loads on the intervertebral discs (IVD) of a human lumbar spine during activities like standing, bending and falling. Following this, a mechanical multi-body system (MBS) is utilised to capture the overall mechanical behaviour of a human, whereas an inhomogeneous, anisotropic, multi-phasic finite-element model (FEM) is applied to resolve the resulting field quantities inside an IVD. In order to couple the FEM of the IVD with the numerically diverse MBS, a homogenisation procedure has to be applied such that field quantities can be converted into discrete quantities. In particular, the MBS captures the mechanical behaviour of an IVD using a bushing element, which provides discrete force-displacement and moment-rotation relations. The goal of this contribution is to present a homogenisation method for the IVD as well as a possibility to include the homogenised results in the MBS without the need for embedded FE computations in the MBS. Instead, certain deformation modes of the IVD are pre-computed and represented using a non-linear constitutive equations. This task becomes even more challenging, as the resulting discrete DOF of a motion segment appear in a coupled fashion due to the structure of the IVD, i. e., a rotation in the sagittal plane triggers a resulting moment and a resulting force. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)