https://scholars.lib.ntu.edu.tw/handle/123456789/168347
標題: | 彈塑性之閔氏時空群論與模式識別實驗 | 作者: | 洪宏基 | 關鍵字: | Plasticity;differential dynamic system;Minkowski spacetime;Lorentz group;Poincar$\acute{\mbox{e}}$ group;causal group;conformal group;generalized Hamiltonian system;塑性;微分動態系統;閔氏時空;Lorentz 群;Poincar$\acute{\mbox{e}}$ 群;因果群;共形群;廣義哈米爾頓系統 | 公開日期: | 1998 | 出版社: | 臺北市:國立臺灣大學土木工程學系暨研究所 | 摘要: | 本計畫利用閔氏時空群論研究彈塑性組成模式。 在前一系列有關固體材料的力學行為研究中 [2-6],我們 將固體材料的力學性質演化視為一種帶塑性不可逆開關的微分動態系統, 並發展固態系統彈塑性行為的現代非線性動態系統分析方法,論證闡明 固態系統在外加載重下的行為特質。根據這些思想, 本研究 [1] 承繼非線性動態系統的分析方法,深入分析幾種固態系統模式 的力學行為,及其內在對稱性與時空結構。 報告 [1]中特別對彈性完全塑性模式、雙線性模式、 等向硬軟化模式、混合硬軟化模式及雙內時走動模式給與非常詳細的分析。 我們引進閔氏時空結構,推導在閔氏時空上的各種作用群的 彈塑性動態系統。從而發展固態系統彈塑性行為的 閔氏時空上作用群的研究方法。在此, 我們嘗試以內部對稱性來刻劃組成模式的層級組織架構,並 滿足閔氏時空的因果關係。其作用群包括 Lorentz 群、Poincar$\acute{\mbox{e}}$ 群、因果群、共形群。 我們進一步探討Lorentzian 系統與廣義哈米爾頓系統的關係,引進 Lie-Poisson 括號及 Poisson 括號,作為耗散動態系統,因此開啟廣義哈米爾頓系統的研究方法。 本報告[1]在實驗方面使用國立台灣大學工學院固體力學聯合實驗室的MTS809 軸扭試驗機 ,配合實心圓棒及中空薄壁試桿 進行鋁6061 的單軸及軸扭雙軸循環棘齒行為實驗,對於不同條件下的棘齒 行為有完整的觀察及詳盡的描述,特別是環向應變在循環負載下亦有棘齒 行為的發生。 The project employed a group-theoretical approach to investigate constitutive models of elastoplasticity. In a series of researches [2-6], we have been viewing the evolution of mechanical properties of a solid material as a differential dynamic system with an on-off switch for plasticity mechanism, examining phenomenological characteristics of behavior of the system subjected to external loading. Continuing this line of thought, the project [1] investigated theoretically the mechanical behavior from the viewpoint of dynamic systems induced by group actions on Minkowski spacetime, and experimentally studied a few related topics of cyclic plasticity of solid materials, in particular the aluminum alloy Al-6061. The emphases were placed on the global analyses of internal symmetries in the constitutive models. The models analyzed are perfect elastoplasticity, bilinear elastoplasticity, isotropic-hardening, mixed-hardening, and kinematic hardening with two intrinsic times. It is amazing that the inclusion of action groups on Minkowski spacetime in the frame of dynamic systems of plasticity is very natural. With the new concept of ``space' and ``time' in plasticity a core connection between the causality in Minkowski spacetime, the time arrow direction and the irreversibility of plasticity was built up. Internal symmetry groups classify the models of elastoplasticity and simultaneously fulfill the requirement of causality. The groups under study included Lorentz group, Poincar$\acute{\mbox{e}}$ group, causal group, and conformal group. We further developed a generalized Hamiltonian dynamic-system-theoretic technique to construct elastoplastic models. Generalized Hamiltonians of constitutive models were formulated through brackets, for example, a perfect elastoplastic model through the Lie-Poisson bracket and a non-normality flow model through the Poisson bracket. It is found that the yield function just plays a role of the Hamiltonian function, and the plastic potential can be used to determine the non-canonical metric. The axial-torsional test equipment MTS809 of the NTU College of Engineering was used to study the cyclic and ratchetting behavior of solid bar and tubular specimens of Al-6061. The ratchetting effect was observed in various loading conditions, in particular, in hoop strain under cyclic axial-torsional loading[1]. |
URI: | http://ntur.lib.ntu.edu.tw//handle/246246/2662 | 其他識別: | 872211E002035 | Rights: | 國立臺灣大學土木工程學系暨研究所 |
顯示於: | 土木工程學系 |
檔案 | 描述 | 大小 | 格式 | |
---|---|---|---|---|
872211E002035.pdf | 22.41 kB | Adobe PDF | 檢視/開啟 |
在 IR 系統中的文件,除了特別指名其著作權條款之外,均受到著作權保護,並且保留所有的權利。