Many materials are anisotropic. However, there is no widely accepted measure for characterizing the degree of elastic anisotropy. Here, assuming that the limiting case of extreme anisotropy should possess a positive semidefinite stiffness matrix, we propose three criteria to evaluate measures of anisotropy and show that the existing measures in the literature do not satisfy all of the proposed criteria.We then introduce a new measure of anisotropy based on the maximum strain energy ratio that is universally applicable to all material systems. The proposed measure is helpful for understanding the properties and behaviors of materials. Furthermore, this measure can be easily generalized to situations involving multiple fields and nonlinearity. The J-integral based criterion is widely used in elastic-plastic fracture mechanics. However, it is not rigorously applicable when plastic unloading appears during crack propagation. One difficulty is that the energy density with plastic unloading in the J-integral cannot be defined unambiguously. In this paper, we alternatively start from the analysis on the power balance, and propose a surface-forming energy release rate (ERR), which represents the energy available for separating the crack surfaces during the crack propagation and excludes the loading-mode-dependent plastic dissipation. Therefore the surface-forming ERR based fracture criterion has wider applicability, including elastic-plastic crack propagation problems. Several formulae are derived for calculating the surface-forming ERR, and the definition of the energy density or work density is avoided. For any fracture behaviours, the surface-forming ERR is proven to be path-independent. The physical meanings and applicability of the proposed surface-forming ERR, the local ERR, the traditional global ERR, and J-integral are compared and discussed.
Cell dynamics is of crucial significance for the morphogenesis, self-repair, and other physiological and pathological processes of tissues. Collective cells exhibit greatly different dynamic behaviors from isolated cells. In this lecture, some recent advances in experimental and theoretical researches on collective cell dynamics will be presented, with particular attention paid to the biomechanical mechanisms underlying the morphodynamics of developing embryos and tumors. First, a cell division model is established for the division of interconnecting cells in a biological tissue. Coupled mechanical-chemical mechanisms involved in the multi-phase cell division are taken into account. Second, we explain why spontaneous oscillation of collective cells may occur in such biological tissues as Drosophila amnioserosa during development. It is revealed that the collective cell oscillation in an epithelium-like monolayer results from the dynamic bifurcation induced by feedback between mechanical strains and chemical cues. Further, we investigate, both experimentally and theoretically, the migration of collective cells. We show that migratory cells may behave as a whole either like a viscous solid or fluid, leading to rich patterns with characteristic sizes ranging from several to dozens of cells. On the basis of experimental measurements and theoretical analysis, universal statistical laws are derived for the dynamic features of collective cells.
Metallic glasses (MGs) possess large elastic limit and high strength, but unfortunately they are of limited commercial utility due to their macroscopic brittle nature. Here, we report the recent progress in the improved ductility of MGs via simple structural design. Topics covered include MGs-based chiral nanolattice, and nanoglass (NG) consisting of nanometer-sized glassy grains separated by glass-glass interfaces which can be used to design MGs with unique mechanical properties.
Continuum mechanics predicts that the propagation speed of non-equilibrium information in solids is limited by the longitudinal wave speed, so is crack propagation. However, solids are essentially discrete systems. In this paper, via theoretical analysis and numerical simulations, it is demonstrated in a straightforward way that non- equilibrium disturbance (e.g. force, displacement, energy, and so on) can propagate at a supersonic speed in discrete systems, although the magnitude of the disturbance attenuates very quickly. In dynamic fracture, a cascade of atomic-bond breaking events provides an amplification mechanism to counterbalance the attenuation of the disturbance. Therefore, supersonic crack propagation can be realized in a domino way. Another key factor for supersonic crack propagation is to ensure sufficient energy flowing into the crack tip. Since most energy can only be transferred at a speed limited by the longitudinal wave speed, the conditions for the occurrence of supersonic crack propagation are not easily met in most situations, unless there is high pre-stored energy along the crack path or continuous energy supply from the loading concomitantly moving with the crack tip. A quantitative relation between supersonic crack propagation speed and material properties and parameters is given, which implies that knowing all the classical macroscopic quantities is not enough in determining the supersonic crack propagation speed, and the microstructure does play a role. Moreover, it is interesting to note that fracture toughness affects the crack propagation speed in the subsonic regime, but not in the supersonic regime, because the deformation/stress is uniform in front of a supersonic crack where strength criterion dominates.
Continuous monitoring of blood pressure, an essential measure of health status, typically requires complex, costly, and invasive techniques that can expose patients to risks of complications. Continuous, cuffless, and noninvasive blood pressure monitoring methods that correlate measured pulse wave velocity (PWV) to the blood pressure via the Moens−Korteweg (MK) and Hughes Equations, offer promising alternatives. The MK Equation, however, involves two assumptions that do not hold for human arteries, and the Hughes Equation is empirical, without any theoretical basis. The results presented here establish a relation between the blood pressure P and PWV that does not rely on the Hughes Equation nor on the assumptions used in the MK Equation. This relation degenerates to the MK Equation under extremely low blood pressures, and it accurately captures the results of in vitro experiments using artificial blood vessels at comparatively high pressures. For human arteries, which are well characterized by the Fung hyperelastic model, a simple formula between P and PWV is established within the range of human blood pressures. This formula is validated by literature data as well as by experiments on human subjects, with applicability in the determination of blood pressure from PWV in continuous, cuffless, and noninvasive blood pressure monitoring systems.
划痕会损伤高分子材料表面，影响其功能性与美观性。与直觉想象不同，高分子材料划痕过程伴随着~100°C的剧烈升温。基于线弹性断裂假设的应变能耗散较小，即使完全转化为热量仍然无法描述这一剧烈升温现象。大量研究表明，非晶态脆性PMMA材料的宏观裂纹是由微观韧性银纹演化产生，从银纹微观演化能量角度出发，可以解释刮擦过程的剧烈温升现象。由蒋晗等撰写的关于这一独特现象的复杂宏微观机理的系列论文发表在摩擦学和材料力学领域老牌著名期刊Tribology International和International Journal of Solids and Structures。 Dramatic temperature rise has been observed at the surface facture area during the scratch of brittle poly(methyl methacrylate) (PMMA). However, the strain energy accompanied with the macroscopic linear elastic fracture is inadequate to explain the significant temperature change. To describe this phenomenon, the crazing related energy dissipation mechanism considering the evolution of microscopic crazing is proposed.The frictional heating and macroscopic plastic deformation make their contribution for the temperature rise at relative small scratch load. The energy dissipated by the crazing process plays a dominating role for the scratch-induced fracture. Those findings provide meaningful insight for understanding the mechanism of temperature rise during polymer scratch.