Morphogenesis of Floating Bone Segments: A Legacy of Serial Tensile Cross-Strut Microdamage in Trabecular Disconnection “Crumple Zones”?

Trabecular bone disconnection “hotspots” of real termini (ReTm) previously mapped as loci of weakness in the female aging spine and hip may be a source of free-floating cancellous segments found in the medullary space using a bespoke, thick slice histological method for identifying ReTm. A factor in their origin is apparently microdamage proliferation (differentiated by en bloc silver staining) with occasional callus moderation. Validation of similar “floating segments” (FS) in the ex-breeder rat suggested a pilot model for a potentially common phenomenon. Following marrow elution and density fractionation of the isolated floating segments from the whole proximal rat femora, scanning electron microscopy (SEM) and elemental microanalysis (EDS) was performed. The eluent contained numbers of vertically truncated, laterally branched floating segments (acute severance of sequential tensile cross-struts, causing chronic compression overload of axial-struts, with ii) inadequate stabilising callus, facilitating ReTm stacking into predetermined, substructural “crumple zones” of force containment, spheroidal attrition and particulate dissociation. As a catabolic outcome of altered tensile and hormonal influence, FS number may add a novel variable to cancellous bone kinetics particularly in women of relevance to fracture predisposition.

CLOSED TRANS-SCALE STATISTICAL MICRODAMAGE MECHANICS

Damage and failure due to distributed microcracks or microvoids are on the challenging frontiers of solid mechanics. This appeals strongly to tools not yet fully developed in continuum damage mechanics, in particular to irreversible statistical thermodynamics and a unified macroscopic equations of mechanics and kinetic equations of microstructural transformations. This review provides the state of the art in statistical microdamage mechanics. (1) It clarifies on what level of approximation continuum damage mechanics works. Particularly,D-level approximation with dynamic function of damage appears to be a proper closed trans-scale formulation of the problem. (2) It provides physical foundation of evolution law in damage mechanics. Essentially, the damage-dependent feature of the macroscopic evolution law is due to the movement of microdamage front, resulting from microdamage growth. (3) It is found that intrinsic Deborah numberD *, a ratio of nucleation rate over growth rate of microdamage, is a proper indication of critical damage in damage mechanics, based on the idea of damage localization. (4) It clearly distinguishes the non-equilibrium damage evolution from equilibrium phase transition, like percolation.

Osteoporosis affects both post-yield microdamage accumulation and plasticity degradation in vertebra of ovariectomized rats

Estrogen withdrawal in postmenopausal women increases bone loss and bone fragility in the vertebra. Bone loss with osteoporosis not only reduces bone mineral density (BMD), but actually alters bone quality, which can be comprehensively represented by bone post-yield behaviors. This study aimed to provide some information as to how osteoporosis induced by estrogen depletion could influence the evolution of post-yield microdamage accumulation and plastic deformation in vertebral bodies. This study also tried to reveal the part of the mechanisms of how estrogen deficiency-induced osteoporosis would increase the bone fracture risk. A rat bilateral ovariectomy (OVX) model was used to induce osteoporosis. Progressive cyclic compression loading was developed for vertebra testing to elucidate the post-yield behaviors. BMD, bone volume fraction, stiffness degradation, and plastic deformation evolution were compared among rats raised for 5 weeks (ovx5w and sham5w groups) and 35 weeks (ovx35w and sham35w groups) after sham surgery and OVX. The results showed that a higher bone loss in vertebral bodies corresponded to lower stiffness and higher plastic deformation. Thus, osteoporosis could increase the vertebral fracture risk probably through microdamage accumulation and plastic deforming degradation.

The effect of low fluoride concentrations on microdamage accumulation in mouse tibias under impact loading

Microdamage accumulation in bone is one of the mechanisms for energy dissipation during the fracture process. Changes in the ultrastructure and composition of bone constituents due to aging or diseases could affect microdamage accumulation. Low concentration （1 mM） of sodium fluoride （NaF） has been used in this study to investigate the effect of ultrastructural changes on microdamage accumu- lation in mouse tibias following free-fall impact loadings. Twenty-two tibias were divided randomly into control and NaF-treated groups. Free-fall impact loading was conducted twice on each tibia to produce microdamage. The elas- tic modulus of NaF-treated tibias decreased significantly after the impact loadings, while there was no significant difference in the modulus of untreated samples between pre- and post-damage loadings. Microdamage morphology analysis showed that less and shorter microcracks existed in NaF-treated tibias compared with control bones. Meanwhile, more and longer microcracks were observed in tensile regions in untreated samples compared with that in compressive regions, whereas no significant difference was observed between tensile and compressive regions in NaF-treated bones. The results of this study indicate that more energy is required to generate microcracks in NaF-treated bone than in normal bone. A low concentration of fluoride treatment may increase the toughness of bone under impact loading.

SPALLATION ANALYSIS WITH A CLOSED TRANS-SCALE FORMULATION OF DAMAGE EVOLUTION

A closed,trans-scale formulation of damage evolution based on the statistical mi- crodamage mechanics is summarized in this paper.The dynamic function of damage bridges the mesoscopic and macroscopic evolution of damage.The spallation in an aluminium plate is studied with this formulation.It is found that the damage evolution is governed by several dimensionless parameters, i.e.,imposed Deborah numbers De~* and De,Mach number M and damage number S.In particular, the most critical mode of the macroscopic damage evolution,i.e.,the damage localization,is deter- mined by Deborah number De~*.Deborah number De~* reflects the coupling and competition between the macroscopic loading and the microdamage growth.Therefore,our results reveal the multi-scale nature of spallation.In fact,the damage localization results from the nonlinearity of the microdamage growth.In addition,the dependence of the damage rate on imposed Deborah numbers De~* and De, Mach number M and damage number S is discussed.

Fatigue behavior of cortical bone:a review

Fatigue is a common cause of bone failure.As the main load-bearing tissue,cortical bone carries a considerable share of load in the whole bone.Under cyclic loading condition,microdamage may generates and accumulates in cortical bone,which further triggers the fracture of bone.It is crucial to explore the fatigue properties of cortical bone and the influential factors for both clinical diagnosis and establishment of models that can predict fatigue failure of human cortical bone.In this review,the fatigue behavior of cortical bone was investigated.Through the complex hierarchical structure and self-repairing process,the risk of catastrophic fracture is reduced.Based on these understandings,the multiple influential factors of cortical bone fatigue properties were analyzed,which were considered to be a combination of internal and external factors.The internal factors include material properties of bone composition(i.e.,mineral,organic material,and water)and bone structure.External factors refer to loading condition such as frequency,amplitude and direction of load.Besides,age,disease,radiation exposure and other factors affect the fatigue behavior of bone by altering one or more factors mentioned above.