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A plastic crack model for smectic A liquid crystals under longitudinal shear is suggested. The solution of the screw dislocation in smectic A is the key to the correct result that we obtained by overcoming a longstanding puzzle. We further use the dislocation pile-up principle and the singular integral equation method to construct the solution of the crack in the phase. From the solution, we can determine the size of the plastic zone at the crack tip and the crack tip opening (tearing) displacement, which are the parameters relevant to the local stability/instability of materials. Our results may be useful for developing soft-matter mechanics. 相似文献
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Weak solution (or generalized solution) for the boundary-value problems of partial differential equations of elasticity of 3D (three-dimensional) quasicrystals is given, in which the matrix expression is used. In terms of Korn inequality and theory of function space,we prove the uniqueness of the weak solution.This gives an extension of existence theorem of solution for classical elasticity to that of quasicrystals,and develops the weak solution theory of elasticity of 2D quasicrystals given by the second author of the paper and his students. 相似文献
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通过给出准晶弹性偏微分方程组边值问题的矩阵表示去定义弱解,利用Korn不等式和函数空间理论证明了这种弱解的存在性与唯一性,从而把经典弹性理论边值问题解的存在性定理推广到准晶弹性理论上,这种理论为发展极其复杂与困难的准晶弹性的偏微分方程的边值问题的数值解提供了一个基础. 相似文献
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The nature of spin-state phase transition is investigated with [Fe(C4H4N2){Pt(CN)4}] that is a novel 3D Hofmann—like compound. The bistability of this system is obtained by the first-principles calculation. It is demonstrated that thermal expansion is the intrinsic force involved in spin-state transition. Based on these results, we suggest a thermal exciting bistable model of spin-state transition with a temperature dependent crystal-field splitting (CFS). Experimental evidence of spin-state phase transition coincides with our theoretical model. This model approaches something fundamental in the mechanism leading to the transition, and it is important in developing new and practical controllable quantum devices. 相似文献
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Final Governing Equation of Plane Elasticity of Icosahedral Quasicrystals and General Solution Based on Stress Potential Function 总被引:3,自引:0,他引:3 下载免费PDF全文
The stress potential function theory for plane elasticity of icosahedral quasicrystals is developed. By introducing stress functions, huge numbers of basic equations involving elasticity of icosahedral quasicrystals are reduced to a single partial differential equation of the 12th order. The general solution of the equation is expressed by 6 analytic functions of complex variable z = x + iy. 相似文献
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如图1所示,在无限弹性介质中有个椭圆盘状裂纹,裂纹位于... 相似文献
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提出了第一类与第二类二维准晶概念.在笔者已有工作(范天佑. 软物质准晶广义流体动力学方程组[J]. 应用数学和力学, 2016,37(4): 331-344.)的基础上,对可能的7次、9次和14次对称软物质第二类二维准晶广义流体动力学进行了全面讨论,建立了它们的终态控制方程组,为软物质准晶学科的发展提供了一个数学模型,为探讨有关物理问题的时间 空间演化提供了可操作的实际可行的求解体系和分析工具,是对该工作的一个重要发展. 相似文献