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A robust multisurface return-mapping algorithm and its implementation in Abaqus

机译：ABAQUS中强大的多面返回映射算法及其实现

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摘要

The simulation of complex material failure processes requires a precise differentiation of the involved failure mechanisms like fracture or plasticity. This is commonly achieved by using a so-called multisurface failure criterion, where each failure surface is related to a certain failure mechanism. In the case of plasticity, failure surfaces define the elastic domain of the material and any stress state outside of this domain is considered non-admissible and must be returned to the boundary of the elastic domain. So-called return-mapping algorithms are often used and well-studied methods for finding such valid stress states. However, their implementation in numerical simulation tools is often not robust and efficient enough for complex problems that involve sophisticated multisurface definitions. In this work, we present a multisurface return-mapping algorithm and its implementation in the finite element software Abaqus. We found that with additional and enhanced iterative solver methods, the classic Newton-Raphson-based implementation of the algorithm can be improved in order to find solutions to otherwise not returnable stress states. The added computational burden is minimal, as more stress states can be returned without reducing the size of the load increments. The paper focuses on the implementation aspects of such problems and offers the reader a thorough guide and the source code for an Abaqus implementation. We applied the algorithm to simulate the highly orthotropic behavior of wood, allowing us to predict plastic failure of various wooden structures and components.
机译：复杂材料故障过程的模拟需要精确地分化所涉及的失效机制，如裂缝或可塑性。这通常是通过使用所谓的多面故障标准来实现的，其中每个故障表面与某个故障机制有关。在可塑性的情况下，失效表面限定了材料的弹性域，并且该结构域外的任何应力状态被认为是不可允许的，并且必须返回到弹性域的边界。所谓的返回映射算法经常使用和研究良好的方法来查找此类有效应力状态。但是，它们在数值模拟工具中的实现通常不是强大，并且足够有效，以便对涉及复杂的多面积定义的复杂问题。在这项工作中，我们在有限元软件ABAQUS中呈现了多面返回映射算法及其实现。我们发现，通过额外和增强的迭代求解器方法，可以提高算法的经典牛顿 - 拉文申的实现，以便找到否则不可退回的应力状态的解决方案。增加的计算负担是最小的，因为可以返回更多的压力状态而不会降低负载增量的大小。本文重点介绍此类问题的实施方面，并为读者提供了彻底指导和ABAQUS实现的源代码。我们应用了算法来模拟木材的高度正交行为，使我们能够预测各种木结构和部件的塑性失效。

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