The influence of yield surface shape and damage in the depth-dependent response of bone tissue to nanoindentation using spherical and Berkovich indenters

Prevention and treatment of osteoporosis rely on understanding of the micromechanical behaviour of bone and its influence on fracture toughness and cell-mediated adaptation processes. Postyield properties may be assessed by nonlinear finite element simulations of nanoindentation using elastoplastic and damage models. This computational study aims at determining the influence of yield surface shape and damage on the depth-dependent response of bone to nanoindentation using spherical and conical tips. Yield surface shape and damage were shown to have a major impact on the indentation curves. Their influence on indentation modulus, hardness, their ratio as well as the elastic-to-total work ratio is well described by multilinear regressions for both tip shapes. For conical tips, indentation depth was not statistically significant (p<0.0001). For spherical tips, damage was not a significant parameter (p<0.0001). The gained knowledge can be used for developing an inverse method for identification of postelastic properties of bone from nanoindentation.

A generalized anisotropic quadric yield criterion and its application to bone tissue at multiple length scales

Nonlinear computational analysis of materials showing elasto-plasticity or damage relies on knowledge of their yield behavior and strengths under complex stress states. In this work, a generalized anisotropic quadric yield criterion is proposed that is homogeneous of degree one and takes a convex quadric shape with a smooth transition from ellipsoidal to cylindrical or conical surfaces. If in the case of material identification, the shape of the yield function is not known a priori, a minimization using the quadric criterion will result in the optimal shape among the convex quadrics. The convexity limits of the criterion and the transition points between the different shapes are identified. Several special cases of the criterion for distinct material symmetries such as isotropy, cubic symmetry, fabric-based orthotropy and general orthotropy are presented and discussed. The generality of the formulation is demonstrated by showing its degeneration to several classical yield surfaces like the von Mises, Drucker–Prager, Tsai–Wu, Liu, generalized Hill and classical Hill criteria under appropriate conditions. Applicability of the formulation for micromechanical analyses was shown by transformation of a criterion for porous cohesive-frictional materials by Maghous et al. In order to demonstrate the advantages of the generalized formulation, bone is chosen as an example material, since it features yield envelopes with different shapes depending on the considered length scale. A fabric- and density-based quadric criterion for the description of homogenized material behavior of trabecular bone is identified from uniaxial, multiaxial and torsional experimental data. Also, a fabric- and density-based Tsai–Wu yield criterion for homogenized trabecular bone from in silico data is converted to an equivalent quadric criterion by introduction of a transformation of the interaction parameters. Finally, a quadric yield criterion for lamellar bone at the microscale is identified from a nanoindentation study reported in the literature, thus demonstrating the applicability of the generalized formulation to the description of the yield envelope of bone at multiple length scales.

Computational and experimental methodology for site-matched investigations of the influence of mineral mass fraction and collagen orientation on the axial indentation modulus of lamellar bone

Relationships between mineralization, collagen orientation and indentation modulus were investigated in bone structural units from the mid-shaft of human femora using a site-matched design. Mineral mass fraction, collagen fibril angle and indentation moduli were measured in registered anatomical sites using backscattered electron imaging, polarized light microscopy and nano-indentation, respectively. Theoretical indentation moduli were calculated with a homogenization model from the quantified mineral densities and mean collagen fibril orientations. The average indentation moduli predicted based on local mineralization and collagen fibers arrangement were not significantly different from the average measured experimentally with nanoindentation (p=0.9). Surprisingly, no substantial correlation of the measured indentation moduli with tissue mineralization and/or collagen fiber arrangement was found. Nano-porosity, micro-damage, collagen cross-links, non-collagenous proteins or other parameters affect the indentation measurements. Additional testing/simulation methods need to be considered to properly understand the variability of indentation moduli, beyond the mineralization and collagen arrangement in bone structural units.

Loss of bone strength in HLA-B27 transgenic rats is characterized by a high bone turnover and is mainly osteoclast-driven

Objective Although osteopenia is frequent in spondyloarthritis (SpA), the underlying cellular mechanisms and association with other symptoms are poorly understood. This study aimed to characterize bone loss during disease progression, determine cellular alterations, and assess the contribution of inflammatory bowel disease (IBD) to bone loss in HLA-B27 transgenic rats. Methods Bones of 2-, 6-, and 12-month-old non-transgenic, disease-free HLA-B7 and disease-associated HLA-B27 transgenic rats were examined using peripheral quantitative computed tomography, μCT, and nanoindentation. Cellular characteristics were determined by histomorphometry and ex vivo cultures. The impact of IBD was determined using [21-3 x 283-2]F1 rats, which develop arthritis and spondylitis, but not IBD. Results HLA-B27 transgenic rats continuously lost bone mass with increasing age and had impaired bone material properties, leading to a 3-fold decrease in bone strength at 12 months of age. Bone turnover was increased in HLA-B27 transgenic rats, as evidenced by a 3-fold increase in bone formation and a 6-fold increase in bone resorption parameters. Enhanced osteoclastic markers were associated with a larger number of precursors in the bone marrow and a stronger osteoclastogenic response to RANKL or TNFα. Further, IBD-free [21-3 x 283-2]F1 rats also displayed decreased total and trabecular bone density. Conclusions HLA-B27 transgenic rats lose an increasing amount of bone density and strength with progressing age, which is primarily mediated via increased bone remodeling in favor of bone resorption. Moreover, IBD and bone loss seem to be independent features of SpA in HLA-B27 transgenic rats.