基于能量等效原理的应变局部化分析:I.一维解析解

发布时间：2018-03-30 00:04

本文选题：应变局部化　切入点：非局部塑性　出处：《力学学报》2017年03期

【摘要】：基于热力学第一定律和非局部塑性理论,提出了一种求解应变局部化问题的非局部方法.对材料的每一点定义了局部和非局部两种状态空间,局部状态空间的内变量通过非局部权函数映射到非局部空间,成为非局部内变量.在应变软化过程中,局部状态空间中的塑性变形服从正交流动法则,材料的软化律在非局部状态空间中被引入.通过两个状态空间的塑性应变能耗散率的等效,得到了应变软化过程中明确定义的局部化区域以及其中的塑性应变分布.应用本方法导出了一维应变局部化问题的解析解.解析解表明,应变局部化区域的尺寸只与材料内尺度有关;对于高斯型非局部权函数,局部化区域的尺寸大约是材料内尺度的6倍.一维算例表明,局部化区域的塑性应变分布以及载荷-位移曲线仅与材料参数和结构几何尺寸有关,变形局部化区域的尺寸随着材料内尺度的减小而减小,同时塑性应变也随着材料内尺度的减小变得更加集中.当内尺度趋近于零时,应用本文方法得到的解与采用传统的局部塑性理论得到的解相同.
[Abstract]:Based on the first law of thermodynamics and the theory of nonlocal plasticity, a nonlocal method for solving the strain localization problem is proposed. The local and non-local state spaces are defined for each point of the material. The internal variables of the local state space are mapped to the non-local space by the nonlocal weight function and become non-local internal variables. In the process of strain softening, the plastic deformation in the local state space is governed by the orthogonal flow rule. The softening law of the material is introduced in the nonlocal state space. The localization region and plastic strain distribution in strain softening process are obtained. The analytical solution of one-dimensional strain localization problem is derived by using this method. The size of the strain localization region is only related to the internal scale of the material, and for the Gao Si type nonlocal weight function, the size of the localized region is about 6 times larger than that of the material internal scale. The plastic strain distribution and load-displacement curve in the localized region are only related to the material parameters and the geometric dimensions of the structure. The size of the deformation localization region decreases with the decrease of the internal scale of the material. At the same time, the plastic strain becomes more concentrated with the decrease of the internal scale of the material. When the internal scale approaches 00:00, the solution obtained by using the method in this paper is the same as that obtained by using the traditional local plastic theory.
【作者单位】：西南交通大学土木工程学院桥梁系;交通隧道工程教育部重点实验室;
【基金】：教育部留学回国人员科研启动基金(201250300) 西南交通大学土木工程学院基础研究创新计划基金资助项目
【分类号】：O341

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