各向异性脆性材料中的裂纹扩展：从相场模型到形状优化方法
Crack propagation in anisotropic brittle materials: from a phase-field model to a shape optimization approach
AI总结：
本文提出基于黎曼形状空间优化的裂纹扩展新方法，通过连续形状导数实现网格无关结果，并用相场模型数值评估各向异性脆性材料中的裂纹路径。
摘要：
相场方法基于能量最小化原理，这是一种用于模拟扩散裂纹的几何方法，通常结合基于Griffith准则的不可逆性进行实现。该方法需要一个长度尺度参数来平滑尖锐的不连续性，该参数影响弥散带并导致网格敏感的断裂扩展结果。最近，提出了一种基于黎曼形状空间优化的新方法，其中裂纹路径通过形状优化技术实现。该方法需要形状导数，该导数以连续意义推导，并用于基于梯度的算法以最小化系统能量。由于形状导数的连续推导，该方法产生与网格无关的结果。本文介绍了基于形状优化的新方法，随后使用相场模型的数值计算评估了各向异性脆性材料中预测的裂纹路径。
英文摘要：
The phase-field method is based on the energy minimization principle which is a geometric method for modeling diffusive cracks that are popularly implemented with irreversibility based on Griffith's criterion. This method requires a length-scale parameter that smooths the sharp discontinuity, which influences the diffuse band and results in mesh-sensitive fracture propagation results. Recently, a novel approach based on the optimization on Riemannian shape spaces has been proposed, where the crack path is realized by techniques from shape optimization. This approach requires the shape derivative, which is derived in a continuous sense and used for a gradient-based algorithm to minimize the energy of the system. Due to the continuous derivation of the shape derivative, this approach yields mesh-independent results. In this paper, the novel approach based on shape optimization is presented, followed by an assessment of the predicted crack path in anisotropic brittle material using numerical calculations from a phase-field model.
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