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滤环上微局部化模的正则奇点
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作者 周梦 《北京航空航天大学学报》 EI CAS CSCD 北大核心 1998年第1期100-103,共4页
滤环R上的模在微局部化下的性质是许多文献讨论的问题.Essen证明了Zariski滤环R上的模M若具有正则奇点,则它的微局部化QμS(M)作为QμS(R)-模仍具有正则奇点,但QμS(M)作为R-模是否仍具有正则奇点... 滤环R上的模在微局部化下的性质是许多文献讨论的问题.Essen证明了Zariski滤环R上的模M若具有正则奇点,则它的微局部化QμS(M)作为QμS(R)-模仍具有正则奇点,但QμS(M)作为R-模是否仍具有正则奇点则不知道.对这一问题进行了讨论,并证明了若M是有正则奇点的R-模且M上的局部滤是良滤,则QμS(M)作为R-模是具正则奇点的模.在一定条件下解决了该问题. 展开更多
关键词 正则奇点 微局部化 局部
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The Micromechanics of Biological and Biomimetic Staggered Composites 被引量:1
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作者 Sacheen Bekah Reza Rabiei Francois Barthelat 《Journal of Bionic Engineering》 SCIE EI CSCD 2012年第4期446-456,共11页
Natural materials such as bone, tooth and nacre achieve attractive properties through the "staggered structure", which consists of stiff, parallel inclusions of large aspect ratio bonded together by a more ductile a... Natural materials such as bone, tooth and nacre achieve attractive properties through the "staggered structure", which consists of stiff, parallel inclusions of large aspect ratio bonded together by a more ductile and tougher matrix. This seemingly simple structure displays sophisticated micromechanics which lead to unique combinations of stiffness, strength and toughness. In this article we modeled the staggered structure using finite elements and small Representative Volume Elements (RVEs) in order to explore microstructure-property relationships. Larger aspect ratio of inclusions results in greater stiffiless and strength, and also significant amounts of energy dissipation provided the inclusions do not fracture in a brittle fashion. Interestingly the ends of the inclusions (the junctions) behave as crack-like features, generating theoretically infinite stresses in the adjacent inclusions. A fracture mechanics criterion was therefore used to predict the failure of the inclusions, which led to new insights into how the interfaces act as a "'soft wrap" for the inclusions, completely shielding them from excessive stresses. The effect of statistics on the mechanics of the staggered structure was also assessed using larger scale RVEs. Variations in the microstructure did not change the modulus of the material, but slightly decreased the strength and significantly decreased the failure strain. This is explained by strain localization, which can in turn be delayed by incorporating waviness to the inclusions. In addition, we show that the columnar and random arrangements, displaying different deformation mechanisms, lead to similar overall prop- erties. The guidelines presented in this study can be used to optimize the design of staggered synthetic composites to achieve mechanical performances comparable to natural materials. 展开更多
关键词 biological materials biomimetics representative volume element fracture mechanics finite element analysis
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