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Non-linear boundary element formulation with tangent operator to analyse crack propagation in quasi-brittle materials

机译：非线性边界元的切线算子公式，用于分析准脆性材料中的裂纹扩展

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摘要

This work deals with analysis of cracked structures using BEM. Two formulations to analyse the crack growth process in quasi-brittle materials are discussed. They are based on the dual formulation of BEM where two different integral equations are employed along the opposite sides of the crack surface. The first presented formulation uses the concept of constant operator, in which the corrections of the nonlinear process are made only by applying appropriate tractions along the crack surfaces. The second presented BEM formulation to analyse crack growth problems is an implicit technique based on the use of a consistent tangent operator. This formulation is accurate, stable and always requires much less iterations to reach the equilibrium within a given load increment in comparison with the classical approach. Comparison examples of classical problem of crack growth are shown to illustrate the performance of the two formulations.
机译：这项工作涉及使用BEM分析裂纹结构。讨论了两种分析准脆性材料中裂纹扩展过程的公式。它们基于BEM的对偶公式，其中沿裂纹表面的相对侧使用了两个不同的积分方程。首先提出的公式使用常数算子的概念，其中仅通过沿裂纹表面施加适当的牵引力来校正非线性过程。第二种提出的用于分析裂纹扩展问题的BEM公式是一种基于使用一致切线算符的隐式技术。与传统方法相比，该公式准确，稳定，并且在给定的载荷增量内始终需要较少的迭代来达到平衡。给出了裂纹扩展经典问题的比较示例，以说明两种配方的性能。

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