基于局部和非局部状态空间能量等效原理的应变局部化数值模拟

发布时间：2018-01-15 21:24

本文关键词：基于局部和非局部状态空间能量等效原理的应变局部化数值模拟　出处：《西南交通大学》2017年硕士论文　论文类型：学位论文

【摘要】：很多土木工程材料在加载至接近破坏时,会出现应变局部化现象。应用经典连续介质理论或一般非局部塑性理论在解决应变局部化问题时,会得到与网格相关的结果,即应变局部化区域(剪切带)的尺寸会随着网格的细化而减小。为了克服网格相关性的缺陷,本文基于一般非局部塑性理论,从状态空间能量等效角度,提出了一种求解应变局部化问题的新方法。在本方法中,应用状态空间理论,对材料体的每一点定义了局部和非局部两个状态空间,利用权函数可以将材料屈服点的内变量从局部状态空间映射到非局部状态空间。通过热力学第一定律,得出了材料体在非局部状态空间中内能的塑性部分和弹性部分与其在局部状态空间中的对应部分相等这一重要结论。基于这个结论,最终导出了应用本方法解决应变局部化问题的一般列式,并给出了有限元算法。然后,通过具体的一维和二维算例,验证了本文方法的可靠性。一维算例为一个有缺陷的拉杆,应用本方法导出了该问题的解析解,并给出了材料特征塑性区域(应变局部化区域)尺寸Lcp与材料内尺度l之间的定量关系,并且通过有限元编程给出了一维及二维算例的数值解,得到了相应的塑性应变分布及荷载-位移曲线。对于一维问题,应用本方法得到的数值结果随着网格的细化稳定地收敛于解析解。一维及二维算例的结果分析表明,应变局部化区域的尺寸与预测值基本相符,并没有随着网格尺寸的细化而变小。这说明本文方法较好地克服了应变局部化模拟中的网格相关性的问题。最后针对具体算例,分析了材料内尺度对应变局部化区域尺寸及荷载-位移曲线的影响,验证了本文得出的两者之间的定量关系。本文提出的方法只要求单元之间的位移场具有C0连续性且无需引入新的参数,比较容易嵌入到现有的有限元程序中。
[Abstract]:Strain localization occurs when many civil engineering materials are loaded to near failure. The classical continuum theory or general non-local plastic theory is used to solve the strain localization problem. The mesh-related results are obtained, that is, the size of the strain localization region (shear band) will decrease with the mesh refinement. In order to overcome the defect of mesh correlation, this paper bases on the general nonlocal plasticity theory. From the point of energy equivalence in state space, a new method to solve the strain localization problem is proposed. In this method, the local and non-local state spaces are defined for each point of the material body by using the state space theory. The internal variables of the yield point of materials can be mapped from the local state space to the non-local state space by using the weight function, and the first law of thermodynamics is adopted. An important conclusion is obtained that the plastic part and elastic part of the material body in the nonlocal state space are equal to their corresponding parts in the local state space. Finally, a general formula for solving the strain localization problem by using this method is derived, and the finite element algorithm is given. Then, a concrete one-dimensional and two-dimensional numerical example is given. The reliability of this method is verified. The one-dimensional example is a drawbar with defects. The analytical solution of the problem is derived by using this method. The quantitative relationship between the size Lcp of the characteristic plastic region (strain localization region) of the material and the internal scale l of the material is given, and the numerical solutions of one-dimensional and two-dimensional examples are given by finite element programming. The corresponding plastic strain distribution and load-displacement curve are obtained. The numerical results obtained by this method converge stably to the analytical solution with the mesh refinement. The results of one-dimensional and two-dimensional numerical examples show that the size of the strain localization region is basically consistent with the predicted value. It shows that the method in this paper can overcome the problem of mesh correlation in strain localization simulation. Finally, a concrete example is given. The influence of material internal scale on strain localization region size and load-displacement curve is analyzed. The proposed method only requires C0 continuity of the displacement field between the elements and does not need to introduce new parameters, so it is easy to embed in the existing finite element program.
【学位授予单位】：西南交通大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：TU501

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