This study proposes a novel phase-field fracture model based on unified phase field theory, aiming to overcome current limitations in simulating material complex fracture behaviors. Through this model, analytical solutions for two-dimensional bars subjected to tensile or compressive stresses are provided, enabling the coupling of multiple failure criteria and further proficient simulation of mode-I, mode-II, and mixed mode-I/II fractures, effectively addressing challenges faced in modelling materials with different or complex failure modes under various loading conditions. Furthermore, to account for the strong anisotropic failure behavior of materials, a novel directional-dependent structural tensor is proposed. The tensor correlates fracture energy with crack surface orientation, facilitating precise characterization of material damage evolution with multiple potential crack orientations. This tensor ensures the consistency of phase-field fracture evolution with predefined fracture patterns. The effectiveness of the proposed model is validated through case studies, emphasizing its robustness and superior predictive capability in capturing fracture behavior under various conditions. This research provides a more accurate and universally applicable approach for simulating material failure, particularly for complex or multiple failure mode material failure simulations.

中文翻译：

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固体断裂中的各向异性损伤演化：一种具有多个失效准则和方向相关结构张量的新型相场方法


本研究提出了一种基于统一相场理论的新型相场断裂模型，旨在克服当前模拟材料复杂断裂行为的局限性。通过该模型，提供了承受拉应力或压应力的二维棒材的解析解，能够耦合多个失效准则，并进一步熟练地模拟 I 型、II 型和 I/II 型混合断裂，有效解决在各种负载条件下对具有不同或复杂失效模式的材料进行建模所面临的挑战。此外，为了解释材料的强各向异性失效行为，提出了一种新型的方向相关结构张量。张量将断裂能与裂纹表面方向相关联，有助于精确表征具有多个潜在裂纹方向的材料损伤演化。该张量确保了相场断裂演化与预定义断裂模式的一致性。通过案例研究验证了所提出模型的有效性，强调了其在各种条件下捕捉断裂行为的鲁棒性和卓越的预测能力。这项研究为模拟材料失效提供了一种更准确且普遍适用的方法，特别是对于复杂或多失效模式的材料失效模拟。