Abstract We present a computational framework for applying the phase-field approach to brittle fracture efficiently to complex shell structures. The momentum and phase-field equations are solved in a staggered scheme using isogeometric Kirchhoff–Love shell analysis for the structural part and isogeometric second- and fourth-order phase-field formulations for the brittle fracture part. For the application to complex multipatch structures, we propose penalty formulations for imposing all the required interface constraints, i.e., displacement ( C 0 ) and rotational ( C 1 ) continuity for the structure as well as C 0 and C 1 continuity for the phase field, where the latter is required only in the case of the fourth-order phase-field model. All involved penalty terms are scaled with the corresponding problem parameters to ensure a consistent scaling of the penalty contributions to the global system of equations. As a consequence, all coupling terms are controlled by one global penalty parameter, which can be set to 1 0 3 independent of the problem parameters. Furthermore, we present a multistep predictor–corrector algorithm for adaptive local refinement with LR NURBS, which can accurately predict and refine the region around the crack even in cases where fracture fully develops in a single load step, such that rather coarse initial meshes can be used, which is essential especially for the application to large structures. Finally, we investigate and compare the numerical efficiency of loosely vs. strongly staggered solution schemes and of the second- vs. fourth-order phase-field models.

中文翻译：

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多面体壳结构中相场脆性断裂的高效等几何计算框架

摘要 我们提出了一种计算框架，用于将相场方法有效地应用于复杂壳结构的脆性断裂。动量和相场方程以交错方案求解，结构部分使用等几何 Kirchhoff-Love 壳分析，脆性断裂部分使用等几何二阶和四阶相场公式。对于复杂多面体结构的应用，我们提出了用于施加所有必需的界面约束的惩罚公式，即结构的位移 (C 0 ) 和旋转 ( C 1 ) 连续性以及相场的 C 0 和 C 1 连续性，其中仅在四阶相场模型的情况下才需要后者。所有涉及的惩罚项都使用相应的问题参数进行缩放，以确保对全局方程组的惩罚贡献的缩放比例一致。因此，所有耦合项都由一个全局惩罚参数控制，该参数可以设置为 1 0 3 独立于问题参数。此外，我们提出了一种使用 LR NURBS 进行自适应局部细化的多步预测器-校正器算法，即使在单个载荷步中裂缝完全发展的情况下，它也可以准确地预测和细化裂纹周围的区域，这样就可以得到相当粗糙的初始网格使用，这对于大型结构的应用尤其重要。最后，我们研究并比较了松散与强交错解方案以及第二与强交错解方案的数值效率。