The Multi-Axial Failure Response of Porcine Trabecular Skull Bone Estimated Using Microstructural Simulations

The development of a multi-axial failure criterion for trabecular skull bone has many clinical and biological implications. This failure criterion would allow for modeling of bone under daily loading scenarios that typically are multi-axial in nature. Some yield criteria have been developed to evaluate the failure of trabecular bone, but there is a little consensus among them. To help gain deeper understanding of multi-axial failure response of trabecular skull bone, we developed 30 microstructural finite element models of porous porcine skull bone and subjected them to multi-axial displacement loading simulations that spanned three-dimensional (3D) stress and strain space. High-resolution microcomputed tomography (microCT) scans of porcine trabecular bone were obtained and used to develop the meshes used for finite element simulations. In total, 376 unique multi-axial loading cases were simulated for each of the 30 microstructure models. Then, results from the total of 11,280 simulations (approximately 135,360 central processing unit-hours) were used to develop a mathematical expression, which describes the average three-dimensional yield surface in strain space. Our results indicate that the yield strain of porcine trabecular bone under multi-axial loading is nearly isotropic and despite a spread of yielding points between the 30 different microstructures, no significant relationship between the yield strain and bone volume fraction is observed. The proposed yield equation has simple format and it can be implemented into a macroscopic model for the prediction of failure of whole bones.

A Reformulation of a Multi-Axial Failure Criterion for the Concrete

The research of a failure criterion for concrete under multi-axial stresses is a very important task because of the numerous civil engineering applications. Nowadays several concrete failure tests are available in literature and various criteria have been proposed. A multi-axial failure criterion for the concrete founded on a simple physical basis, has been proposed by one of the authors. In this paper a sharper foundation of this criterion is given. The hardened cement paste (hcp), the binder of all the aggregate particles, is responsible of the concrete strength. Consequently, a preliminary average evaluation of the stresses, occurring, when the concrete is loaded, into the various phases components, and particularly in the hcp, is necessary to analyse the failure. To that end, the paper revolves around the analysis of the thermal behaviour of the concrete at its early stage of setting. It is shown that the heat production during the cement hydration process, is responsible to produce clearances among the various particles and the surrounding hcp that, in turn, the consequent statically determined structure of the concrete. Validation of this result comes out by analysing the elastic moduli and the thermal expansion coefficients. The micro-macro failure condition of Como & Luciano thus receives a sounder physical basis.

The biomechanical effect of changes in cancellous bone density on synthetic femur behaviour

Biomechanical researchers increasingly use commercially available and experimentally validated synthetic femurs to mimic human femurs. However, the choice of cancellous bone density for these artificial femurs appears to be done arbitrarily. The aim of the work reported in this paper was to examine the effect of synthetic cancellous bone density on the mechanical behaviour of synthetic femurs. Thirty left, large, fourth-generation composite femurs were mounted onto an Instron material testing system. The femurs were divided evenly into five groups each containing six femurs, each group representing a different synthetic cancellous bone density: 0.08, 0.16, 0.24, 0.32, and 0.48 g/cm3. Femurs were tested non-destructively to obtain axial, lateral, and torsional stiffness, followed by destructive tests to measure axial failure load, displacement, and energy. Experimental results yielded the following ranges and the coefficient of determination for a linear regression ( R2) with cancellous bone density: axial stiffness (range 2116.5–2530.6 N/mm; R2 = 0.94), lateral stiffness (range 204.3–227.8 N/mm; R2 = 0.08), torsional stiffness (range 259.9–281.5 N/mm; R2 = 0.91), failure load (range 5527.6–11 109.3 N; R2 = 0.92), failure displacement (range 2.97–6.49 mm; R2 = 0.85), and failure energy (range 8.79–42.81 J; R2 = 0.91). These synthetic femurs showed no density effect on lateral stiffness and only a moderate influence on axial and torsional stiffness; however, there was a strong density effect on axial failure load, displacement, and energy. Because these synthetic femurs have previously been experimentally validated against human femurs, these trends may be generalized to the clinical situation. This is the first study in the literature to perform such an assessment.