本文關(guān)鍵詞： 應(yīng)變梯度 內(nèi)部特征長(zhǎng)度 尺寸效應(yīng) 網(wǎng)格依賴性 損傷局部化　出處：《長(zhǎng)沙理工大學(xué)》2015年碩士論文　論文類型：學(xué)位論文

【摘要】：材料的破壞是力學(xué)發(fā)展的世紀(jì)難題,梯度理論是解決材料破壞機(jī)理的必要途徑。由于物體的均勻性假設(shè)不能精確滿足,經(jīng)典連續(xù)介質(zhì)理論在描述物體微觀結(jié)構(gòu)特性起主導(dǎo)作用的破壞過程時(shí)會(huì)出現(xiàn)如“描述材料的應(yīng)變/損傷局部化”,“描述材料的尺寸效應(yīng)”,“數(shù)值模擬時(shí)的網(wǎng)格病態(tài)依賴性”等疑難。為了合理描述物體的力學(xué)行為,我們?cè)诒緲?gòu)方程中引入了應(yīng)變梯度、內(nèi)部特征長(zhǎng)度向量和損傷,發(fā)展新的應(yīng)變梯度彈性理論及其損傷理論。本文通過應(yīng)變和應(yīng)變梯度的比值定義一個(gè)材料內(nèi)部特征長(zhǎng)度向量;假設(shè)應(yīng)變能密度是由應(yīng)變張量和應(yīng)變梯度張量決定。依據(jù)上述定義和假設(shè),由應(yīng)變能密度在初始狀態(tài)的泰勒展開式推導(dǎo)出一種修正的梯度彈性理論(Modified Gradient Elasticity,MGE理論)。由于引入了應(yīng)變梯度項(xiàng),模型可以描述出現(xiàn)較大應(yīng)變梯度時(shí)材料的強(qiáng)度和變形行為;在材料內(nèi)部特征長(zhǎng)度向量為零時(shí),可退化成經(jīng)典彈性理論�；谔摴υ砗妥兎衷�,建立了相應(yīng)的小變形、準(zhǔn)靜態(tài)荷載情況下梯度彈性問題的有限元格式,編制MGE理論的有限元程序,數(shù)值算例驗(yàn)證了所編程序的正確性和MGE理論在內(nèi)部特征長(zhǎng)度向量為零時(shí)退化為經(jīng)典彈性理論的結(jié)論。然后,利用MGE有限元程序?qū)﹄p材料剪切層問題、雙材料拉伸邊界層問題、裂紋尖端奇異性進(jìn)行了數(shù)值模擬。結(jié)果顯示:雙材料剪切和拉伸邊界層的厚度由內(nèi)部特征長(zhǎng)度決定;MGE理論能模擬邊界層的尺寸效應(yīng)并消除網(wǎng)格病態(tài)依賴性;消除了裂尖應(yīng)變場(chǎng)的奇異性。最后,在MGE理論本構(gòu)方程中引入損傷變量,建立了MGE損傷模型,模擬了土樣單軸壓縮的損傷局部化現(xiàn)象。結(jié)果顯示:MGE損傷理論能消除數(shù)值結(jié)果的網(wǎng)格病態(tài)依賴性;能模擬巖土材料損傷局部化帶的萌生、發(fā)展直到破壞的整個(gè)過程;損傷局部化剪切帶的寬度與內(nèi)部特征長(zhǎng)度有關(guān)。
[Abstract]:The failure of materials is a difficult problem in the development of mechanics in the century. Gradient theory is the necessary way to solve the failure mechanism of materials. Classical continuum theory can be used to describe the failure process in which the microstructural characteristics of an object play a leading role, such as "describing strain / damage localization of material", "describing material size effect", "meshing morbid dependence" in numerical simulation. In order to reasonably describe the mechanical behavior of an object, The strain gradient, internal characteristic length vector and damage are introduced into the constitutive equation. A new strain gradient elastic theory and its damage theory are developed. In this paper, a material internal characteristic length vector is defined by the ratio of strain to strain gradient. It is assumed that the strain energy density is determined by strain Zhang Liang and strain gradient Zhang Liang. Based on the Taylor expansion of strain energy density in the initial state, a modified gradient Gradient elasticity theory is derived. With the introduction of the strain gradient term, the model can describe the strength and deformation behavior of the material with large strain gradient. When the characteristic length vector of material is 00:00, it can degenerate into classical elastic theory. Based on virtual work principle and variational principle, the finite element scheme of gradient elastic problem under small deformation and quasi-static load is established. The finite element program of MGE theory is compiled. Numerical examples verify the correctness of the program and the conclusion that the MGE theory degenerates into the classical elastic theory at 00:00 in the interior characteristic length vector. Then, the MGE finite element program is used to solve the problem of shearing layer in the bimaterial. Bimaterial stretching boundary layer problem, The numerical simulation of crack tip singularity shows that the thickness of the bimaterial shear and tensile boundary layer is determined by the internal characteristic length. The MGE theory can simulate the size effect of the boundary layer and eliminate the pathological dependence of the meshes. The singularity of the crack tip strain field is eliminated. Finally, the damage variable is introduced into the constitutive equation of MGE theory, and the MGE damage model is established. The damage localization of soil samples under uniaxial compression is simulated. The results show that the damage theory can eliminate the mesh-morbid dependence of numerical results, simulate the initiation and development of damage localization zones of geotechnical materials until the whole process of failure. The width of the damage localized shear band is related to the internal characteristic length.
【學(xué)位授予單位】：長(zhǎng)沙理工大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2015
【分類號(hào)】：TB301

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