Constitutive modeling of cortical bone considering anisotropic inelasticity and damage evolution

Abstract

Researchers have conducted finite element (FE) analyses with human models to predict injuries due to traffic accidents or falling. In most of their analyses, cortical bone was simply modeled as a general isotropic elastoplastic material. In this study, a constitutive model of cortical bone considering anisotropic inelasticity and damage evolution was developed to predict injuries more accurately. The new model can satisfactorily represent mechanical properties of cortical bone including anisotropy of elastic modulus and yield stress with strain-rate dependency, and asymmetric stress-strain curves in tension and compression. Simultaneously the included damage-evolution equation enables to predict failure stress and strain with rate dependency in bone fracture simulations. The proposed model was verified using experimental data obtained from the literature. We applied the proposed model to a simple cylindrical FE model of the human femur, and performed simulations under loading conditions such as tension, compression, and torsion. The results showed some tendency of characteristic fracture patterns such as transverse fracture in tensile loading, oblique fracture in compression, and spiral fracture in torsion. The proposed constitutive model would have the potential for better injury prediction in the future.Key words : Cortical bone, Constitutive modeling, Anisotropy, Damage evolution, Fracture, Rate dependency IntroductionIn recent years, many researchers have conducted finite element (FE) analyses with human models to predict injuries due to traffic accident or falling (Tanaka et al., 2004;Watanabe et al., 2011). However, compared with the reproduction accuracy of the shapes of bones, the material model used in such analyses is simplified because mechanical properties of biomaterials have not been fully explained and satisfactory constitutive models do not exist. In most FE analyses, the option of isotropic elastoplastic material built in general-purpose FE-analysis software is selected as the mechanical property for cortical bone.Many researchers studied the actual mechanical properties of cortical bone. For example, Reilly and Burstein (1975) and Yoon and Katz (1976) conducted experiments that found transverse isotropy in elastic modulus of the femur. Moreover, at the point of strength and damage, anisotropy is observed along the circumferential and radial directions; hence, cortical bone could be considered as an orthotropic material (Currey, 2002). McElhaney (1966), Wood (1971), andCarter andHayes (1977) researched strain-rate dependency in the stress-strain curve of cortical bone; they found that the stiffness and brittleness were proportional to the strain rate. In addition, the strength of cortical bone decreases in the order of compressive, tensile, and torsional loading (Yamada, 1970). As explained previously, the mechanical properties of cortical bone considerably depend on the loading direction, differences in strain rates, and loading patterns such as tension and compression (Cowin et al., 19...

Biomechanical analysis of tension-compression asymmetry, anisotropy and heterogeneity of bone reconstruction in response to periprosthetic fracture repair

“…It is seen (Fig. 2) the good correlation between the experimental and simulation results [19]. Stress-strain diagrams of embalmed human femur under uniaxial compression were obtained for six different strain rates of 1500, 300, 1, 0.1, 0.01 and 0.001 -1 s [20].…”

“…Comparison between the experimental and simulation results has been given in Fig. 3 [19]. Experimental data discussed above demonstrate tension/compression asymmetry of bone, but, unfortunately, they were obtained by different authors and at different laboratories and conditions.…”

“…For this purpose, such experiments, as uniaxial tension, uniaxial compression and pure torsion were conducted. Figure 4 shows the stress-strain diagrams of femur influenced by type of loading, as well as, the correlation between the experimental and simulation results [19].…”

“…Comparison of experimental data for cortical bone in compression [20] with simulation results [19] Comparison of experimental data for cortical bone in tension, compression and torsion [21] with simulation results[19] …”

Patient-Specific Bone Multiscale Modelling, Fracture Simulation and Risk Analysis—A Survey

“…Bone exhibited experimental transversely isotropic material symmetry in some works [233,253,254]. Recent works modelled bone as a transversally isotropic material [220,255].…”