Precise computation and error control of stress intensity factors and certain integral characteristics in anisotropic inhomogeneous materials
Precise computation and error control of stress intensity factors and certain integral characteristics in anisotropic inhomogeneous materials
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DOI：
10.1007/s10704-013-9859-7
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发表时间：
2013-06
影响因子：
2.5
通讯作者：
M. Steigemann;B. Schramm
中科院分区：
文献类型：
--
作者：
M. Steigemann;B. Schramm
准静态裂纹扩展的数值模拟与应力强度因子或能量释放率等特性的计算密切相关。在这项工作中，提出了如何在线弹性、各向异性和非均匀平面结构中精确计算这些量的想法。应力强度因子和其他局部特征可以根据某些弹性问题的解用泛函来评估。本文使用伽辽金有限元精确计算这些函数值的方法是一种双加权残差法，用于自适应网格细化和后验误差控制。特别是在混合荷载作用下，裂纹面会发生接触。给出了裂纹面相互不侵彻条件的不均匀型的数值实现，以及这种约束对应力强度因子的影响。给出了各向异性和功能梯度材料的数值结果。
The numerical simulation of quasi-static crack propagation is closely related to the computation of characteristics such as stress intensity factors or energy release rates. In this work, ideas are proposed, how such quantities can be calculated precisely in linear elastic, anisotropic and inhomogeneous plane structures. Stress intensity factors and other local characteristics can be evaluated in terms of functionals depending on solutions of certain elasticity problems. The approach used here to calculate these functional values precisely with Galerkin finite elements is a dual-weighted-residual method for adaptive mesh refinement anda posteriorierror control. Especially in structures under mixed-mode loadings contact of crack faces can occur. A numerical realization of mutual non-penetration conditions of inequality type for the crack faces and the effect of such constraints on stress intensity factors is shown. Numerical results are presented for anisotropic and functionally graded materials.