各向异性地质材料在压缩与围压条件下断裂的相场建模
Phase-Field Modeling of Fracture under Compression and Confinement in Anisotropic Geomaterials
AI总结：
本文提出一种适用于强各向异性地质材料的相场断裂模型，通过引入各向异性断裂功、有效损伤响应和正则化裂纹法向场，准确预测压缩与围压条件下的裂纹扩展模式，并在层状试样和页岩实验中验证了其有效性。
摘要：
强各向异性地质材料在压缩载荷下会发生断裂。本文应用相场断裂模型来研究这一断裂过程。虽然相场断裂模型具有若干优点，但当应力状态复杂且包含可导致裂纹面接触的压缩时，它们会给出不符合物理的预测。\n在考虑裂纹面上压缩牵引力的相场模型基础上，本文将模型扩展到各向异性断裂。关键特征包括：（1）均匀化的各向异性弹性响应和强各向异性的断裂功模型；（2）一种有效的损伤响应，该响应一致地考虑裂纹面上的压缩牵引力，并由各向异性弹性响应推导得出；（3）一种正则化的裂纹法向场，克服了各向同性设置中的缺陷，并能在跨裂纹面方向以及沿裂纹面横向方向上实现正确的裂纹响应。\n为检验该模型，我们首先将预测结果与具有空间非均匀性的完全解析层状试样中的相场断裂演化计算结果进行比较，并表明该模型能够捕捉裂纹扩展的整体模式。然后，我们将模型应用于先前报道的页岩实验室试样在压缩与围压条件下断裂演化的实验观测，发现该模型能在广泛的加载条件下很好地预测所观测到的裂纹模式。我们进一步应用该模型预测压缩与围压条件下翼型裂纹的扩展。有效的裂纹响应模型使我们能够将初始裂纹简单地视为计算域内的非奇异损伤区，从而便于进行简单且通用的计算。
英文摘要：
Strongly anisotropic geomaterials undergo fracture under compressive loading. This paper applies a phase-field fracture model to study this fracture process. While phase-field fracture models have several advantages, they provide unphysical predictions when the stress state is complex and includes compression that can cause crack faces to contact. Building on a phase-field model that accounts for compressive traction across the crack face, this paper extends the model to anisotropic fracture. The key features include: (1) a homogenized anisotropic elastic response and strongly-anisotropic model for the work to fracture; (2) an effective damage response that accounts consistently for compressive traction across the crack face, that is derived from the anisotropic elastic response; (3) a regularized crack normal field that overcomes the shortcomings of the isotropic setting, and enables the correct crack response, both across and transverse to the crack face. To test the model, we first compare the predictions to phase-field fracture evolution calculations in a fully-resolved layered specimen with spatial inhomogeneity, and show that it captures the overall patterns of crack growth. We then apply the model to previously-reported experimental observations of fracture evolution in laboratory specimens of shales under compression with confinement, and find that it predicts well the observed crack patterns in a broad range of loading conditions. We further apply the model to predict the growth of wing cracks under compression and confinement. The effective crack response model enables us to treat the initial crack simply as a non-singular damaged zone within the computational domain, thereby allowing for easy and general computations.
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