基于非局部塑性理论的剪切带局部化有限元分析

发布时间：2018-04-15 16:38

本文选题：有限元 + 应变局部化　；参考：《西南交通大学》2014年硕士论文

【摘要】：在许多工程材料(如混凝土、岩石和沙土等)的破坏过程中,可以观察到剪切带局部化的现象.伴随剪切带局部化现象发生的同时是材料承载能力的逐渐丧失直致完全破坏。剪切带局部的数值模拟对于分析材料和结构的破坏机理、预测混凝土和岩土结构破坏行为以及正确估计建筑物地基承载能力都具有重要意义。本文分析了古典连续介质力学理论进行剪切带局部化的有限元数值模拟的缺陷,通过一维和二维数值算例验证了古典连续介质力学模型所导致的数值结果的网格相关性,论述了其产生的根本原因是控制微分方程丧失强椭圆性导致弹塑性边值问题不适定,进而导致计算结果的不唯一。从物理的角度分析,基于古典连续介质力学理论的控制微分方程丧失椭圆性的原因是其本构关系模型中没有引入材料内尺度的概念。本文总结分析了已有的用于矫正网格相关性的各种理论和模型,并在此基础上提出了一个非局部塑性模型用于剪切带局部化的有限元分析。所提的模型基于积分形式的非局部塑性理论和代表性体积元(RVE)的概念,在本构关系方程中引入了材料内尺度,通过被积函数的泰勒展开建立了积分形式的非局部模型和其近似等效的微分方程之间的关系。本文导出了耦合的增量塑性一致性方程和增量平衡方程的变分形式,并基于伽辽金近似方法(Galerkin's Method)得出了有限元列式,并提出了用于本构方程积分的非局部有限元和移动边界技术。将本文提出的非局部模型用于一维和二维问题的变形局部化的有限元分析结果表明,本文提出的非局部模型能够得出客观的模拟结果,剪切带的厚度与网格大小无关,而是取决于材料内尺度。当材料内尺度趋近于零时,非局部理论的模拟结果接近于局部理论的结果。本文还提出了将来需要进一步研究的问题。
[Abstract]:In many engineering materials (such as concrete, rock and sand etc.) the destruction process, can be observed in the shear band localization phenomenon. With simultaneous shear band localization phenomenon is the carrying capacity of the material lost gradually until completely destroyed. The numerical simulation for the local shear failure mechanism analysis of material and structure, prediction of failure the soil structure of rock and concrete behavior and correct estimation plays an important role in building foundation bearing capacity. This paper analyzes the classical continuum mechanics theory of finite element simulation of shear band localization numerical grid defects, through correlation of one-dimensional and two-dimensional numerical examples to verify the numerical results of classical continuum mechanics model which, discusses the the basic reason is the loss of strong ellipticity control differential equation leads to the problem of ill posed elastoplastic boundary value, which leads to the results Not only the analysis. From the physical point of view, the reason of loss of control of elliptic differential equation from classical continuum mechanics theory is based on the concept of not introducing constitutive material scale relationship model. This paper summarizes and analyzes the existing correction for various mesh correlation theory and model, and put forward a a non local plasticity model for finite element analysis of shear band localization. The proposed model based on the integral form of the non local plasticity theory and the representative volume element (RVE) concept, in the material constitutive relation equation into the inner scale, the Taylor integrand started to establish the relationship between integral form the non local model and its approximate equivalent differential equations. In this paper, the coupling of the incremental plastic consistency equation and the incremental equilibrium equation of variational form is derived, and based on the Galerkin approximation method (Galer Kin's Method) the finite element formulation, and puts forward the integral constitutive equation for nonlocal finite element and moving boundary technique. The proposed nonlocal model for finite element deformation localization of 1D and 2D problem analysis showed that can non local model proposed in this paper the results of objective. The thickness of the shear band and the mesh size, but depends on the material scale. When the material scale tends to zero, the simulation results are close to the non local theory of local theory results. This paper also put forward the future needs further study.

【学位授予单位】：西南交通大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TU43

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