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 引用本文: 吴建营. 固体结构损伤破坏统一相场理论、算法和应用[J]. 力学学报, 2021, 53(2): 301-329.
Wu Jianying. ON THE UNIFIED PHASE-FIELD THEORY FOR DAMAGE AND FAILURE IN SOLIDS AND STRUCTURES: THEORETICAL AND NUMERICAL ASPECTS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(2): 301-329.
 Citation: Wu Jianying. ON THE UNIFIED PHASE-FIELD THEORY FOR DAMAGE AND FAILURE IN SOLIDS AND STRUCTURES: THEORETICAL AND NUMERICAL ASPECTS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2021, 53(2): 301-329.

## ON THE UNIFIED PHASE-FIELD THEORY FOR DAMAGE AND FAILURE IN SOLIDS AND STRUCTURES: THEORETICAL AND NUMERICAL ASPECTS

• 摘要: 固体开裂引起的损伤和断裂是工程材料和结构最为普遍的破坏形式. 为了防止这种破坏, 结构设计首先必须了解裂缝在固体内如何萌生、扩展、分叉、汇聚甚至破碎; 更重要的是, 还需要准确量化这些裂缝演化过程对于结构完整性和安全性降低的不利影响. 针对上述固体结构损伤破坏问题, 本工作系统地介绍了笔者提出的统一相场理论、算法及其应用. 作为一种裂缝正则化变分方法, 统一相场理论将基于强度的裂缝起裂准则、基于能量的裂缝扩展准则以及满足变分原理的裂缝路径判据纳入同一框架内. 不仅常用的脆性断裂相场模型是该理论的特例, 还自然地给出了一类同时适用于脆性断裂和准脆性破坏的相场正则化内聚裂缝模型即 PF-CZM. 该模型非常便于通过有限元等方法加以数值实现; 为了求解有限元空间离散后得到的非线性方程组, 还介绍了几种常用的数值算法, 其中整体BFGS拟牛顿迭代算法的计算效率最高. 静力、动力和多场耦合条件下若干二维和三维代表性算例表明: 相场正则化内聚裂缝模型 PF-CZM能够高精度地再现复杂裂缝演化导致的脆性和准脆性固体损伤破坏; 特别是, 所有情况下, 模型的数值结果不依赖于裂缝尺度参数和有限元网格. 因此, 该模型具有相当好的预测能力, 有望在工程结构的损伤破坏分析方面发挥重要作用. 最后建议了若干值得进一步开展的研究课题.

Abstract: Cracking-induced damage and fracture are the most commonly encountered failure modes of engineering materials and structures. In order to prevent such failure, it is a prerequisite in structural designs to understand how cracks nucleate, propagate, branch, coalesces and even fragmentation, etc., in solids, and more importantly, to quantify their adverse effects to the loss of integrity and even catastrophic collapse of structures. Aiming to provide a feasible approach in the modeling of damage and quasi-brittle failure in solids, this work presents systematically the theoretical and numerical aspects of the unified phase-field theory proposed recently by the author, with applications to a couple of representative benchmark problems. Being a variational approach for regularized cracks, this theory incorporates intrinsically the strength-based nucleation and energy-based propagation criteria, as well as the energy minimization-oriented path following criterion, in a standalone framework. Not only several popular phase-field models for brittle fracture can be recovered as particular examples, but also a novel model——the phase-field regularized cohesive zone model (or shortly, PF-CZM)——that applies to both brittle fracture and quasi-brittle failure, emerges naturally. This model can be numerically implemented in context of the coupled finite element method. In order to solve efficiently the discretized governing equations, several numerical algorithms are discussed, with the monolithic BFGS quasi-newton method being the most efficient one. Representative two- and three-dimensional numerical examples reveal that the PF-CZM is capable of reproducing complex fracture configurations in both brittle and quasi-brittle solids under quasi-static, dynamic and multi-physical environments. Remarkably, in all cases objective numerical predictions are achieved independent of the incorporated length scale and mesh discretization. Therefore, the PF-CZM can be used as a numerically predictive approach for the modeling of damage and failure in engineering structures. Finally, some research topics deserving further studies are suggested.

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