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 ...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.展开更多
Microcracks are common in compact bone,but their continued propagation can lead to macroscopic fractures.These microcracks cannot be visualized radiographically,necessitating alternative noninvasive methods to identif...Microcracks are common in compact bone,but their continued propagation can lead to macroscopic fractures.These microcracks cannot be visualized radiographically,necessitating alternative noninvasive methods to identify excessive microcracking and prevent fractures.In this study,terahertz time-domain spectroscopy(THz-TDS)was used to examine bone interiors near cracks resulting from loading in bovine tibia samples.Various loading configurations,such as impact,quasi-static loading,and fatigue loading,known to induce different types of micro-scale damage,were applied.The values of refractive index and absorption coefficient of the bone samples were then determined from the THz-TDS spectra acquired before loading and after fracture.The study revealed that different loading configurations led to varying terahertz optical coefficients associated with various types of bone fractures.Specifically,the refractive index notably increased under fatigue loading but remained relatively stable during quasi-static bending.The absorption coefficient of bone decreased only under fatigue loading.Furthermore,samples were subjected to axial and radial impacts without sustaining damage.Results indicated that in the undamaged state,the change in refractive index was smaller compared to after impact failure,while the change in absorption coefficient remained consistent after failure.Under radial impact loading,changes in refractive index and absorption coefficient were significantly more pronounced than under axial loading.Prior to loading,the measured value of refractive index was 2.72±0.11,and the absorption coefficient was 6.33±0.09 mm^(−1)at 0.5 THz.展开更多
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 spa...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.展开更多
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 dama...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.展开更多
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 ...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.展开更多
基金The project supported by the National Natural Science Foundation of China (19891180-02, 19972004) Major State Research Project (G200007735)
文摘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.
基金supported by the National Natural Science Foundation of China(Grant Nos.11972247 and 12372080).
文摘Microcracks are common in compact bone,but their continued propagation can lead to macroscopic fractures.These microcracks cannot be visualized radiographically,necessitating alternative noninvasive methods to identify excessive microcracking and prevent fractures.In this study,terahertz time-domain spectroscopy(THz-TDS)was used to examine bone interiors near cracks resulting from loading in bovine tibia samples.Various loading configurations,such as impact,quasi-static loading,and fatigue loading,known to induce different types of micro-scale damage,were applied.The values of refractive index and absorption coefficient of the bone samples were then determined from the THz-TDS spectra acquired before loading and after fracture.The study revealed that different loading configurations led to varying terahertz optical coefficients associated with various types of bone fractures.Specifically,the refractive index notably increased under fatigue loading but remained relatively stable during quasi-static bending.The absorption coefficient of bone decreased only under fatigue loading.Furthermore,samples were subjected to axial and radial impacts without sustaining damage.Results indicated that in the undamaged state,the change in refractive index was smaller compared to after impact failure,while the change in absorption coefficient remained consistent after failure.Under radial impact loading,changes in refractive index and absorption coefficient were significantly more pronounced than under axial loading.Prior to loading,the measured value of refractive index was 2.72±0.11,and the absorption coefficient was 6.33±0.09 mm^(−1)at 0.5 THz.
文摘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.
基金The project supported by the National Natural Science Foundation of China (10172084,10232040,10232050,10372012,10302029) and the Special Funds for Major State Research Project (G200077305)
文摘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.
基金supported by the National Natural Science Foundation of China (Grants 11472017, 11002004)
文摘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.
