A shear-lag model is used to study the mechanical properties of bone-like hierarchical materials. The relationship between the overall effective modulus and the number of hierarchy level is obtained. The result is com...A shear-lag model is used to study the mechanical properties of bone-like hierarchical materials. The relationship between the overall effective modulus and the number of hierarchy level is obtained. The result is compared with that based on the tension-shear chain model and finite element simulation, respectively. It is shown that all three models can be used to describe the mechanical behavior of the hierarchical material when the number of hierarchy levels is small. By increasing the number of hierarchy level, the shear-lag result is consistent with the finite element result. However the tension-shear chain model leads to an opposite trend. The transition point position depends on the fraction of hard phase, aspect ratio and modulus ratio of hard phase to soft phase. Further discussion is performed on the flaw tolerance size and strength of hierarchical materials based on the shear-lag analysis.展开更多
Owing to its viscoelastic nature, axon exhibits a stress rate-dependent me- chanical behavior. An extended tension-shear chain model with Kelvin-Voigt viscoelas- ticity is developed to illustrate the micromechanical b...Owing to its viscoelastic nature, axon exhibits a stress rate-dependent me- chanical behavior. An extended tension-shear chain model with Kelvin-Voigt viscoelas- ticity is developed to illustrate the micromechanical behavior of the axon under dynamic torsional conditions. Theoretical closed-form expressions are derived to predict the de- formation, stress transfer, and failure mechanism between microtubule （MT） and tau protein while the axon is sheared dynamically. The results obtained from the present an- alytical solutions demonstrate how the MT-tau interface length, spacing between the tau proteins, and loading rate affect the mechanical properties of axon. Moreover, it is found that the MTs are more prone to rupture due to the contributions from the viscoelastic effects. Under the torsional force, the MTs are so long that the stress concentrates at the loaded end where axonal MTs will break. This MT-tau protein dynamics model can help to understand the underlying pathology and molecular mechanisms of axonal injury. Additionally, the emphasis of this paper is on the micromechanical behavior of axon, whereas this theoretical model can be equally applicable to other soft or hard tissues, owning the similar fibrous structure.展开更多
基金Project supported by the National Natural Science Foundation of China(Nos.10432050,10428207 and 10672163)the Chinese Academy of Sciences through Grant KJCX-YW-M04.
文摘A shear-lag model is used to study the mechanical properties of bone-like hierarchical materials. The relationship between the overall effective modulus and the number of hierarchy level is obtained. The result is compared with that based on the tension-shear chain model and finite element simulation, respectively. It is shown that all three models can be used to describe the mechanical behavior of the hierarchical material when the number of hierarchy levels is small. By increasing the number of hierarchy level, the shear-lag result is consistent with the finite element result. However the tension-shear chain model leads to an opposite trend. The transition point position depends on the fraction of hard phase, aspect ratio and modulus ratio of hard phase to soft phase. Further discussion is performed on the flaw tolerance size and strength of hierarchical materials based on the shear-lag analysis.
基金Project supported by the National Natural Science Foundation of China(No.11032005)the Major Project of Department of Science and Technology of Guizhou Province(No.2014-6024)the Academician Workstation of Department of Science and Technology of Guizhou Province(No.2015-4004)
文摘Owing to its viscoelastic nature, axon exhibits a stress rate-dependent me- chanical behavior. An extended tension-shear chain model with Kelvin-Voigt viscoelas- ticity is developed to illustrate the micromechanical behavior of the axon under dynamic torsional conditions. Theoretical closed-form expressions are derived to predict the de- formation, stress transfer, and failure mechanism between microtubule （MT） and tau protein while the axon is sheared dynamically. The results obtained from the present an- alytical solutions demonstrate how the MT-tau interface length, spacing between the tau proteins, and loading rate affect the mechanical properties of axon. Moreover, it is found that the MTs are more prone to rupture due to the contributions from the viscoelastic effects. Under the torsional force, the MTs are so long that the stress concentrates at the loaded end where axonal MTs will break. This MT-tau protein dynamics model can help to understand the underlying pathology and molecular mechanisms of axonal injury. Additionally, the emphasis of this paper is on the micromechanical behavior of axon, whereas this theoretical model can be equally applicable to other soft or hard tissues, owning the similar fibrous structure.
