To efficiently predict the crack propagation in thin-walled structures, a global–local approach for phase field modeling using large-deformation solid shell finite elements considering the enhanced assumed strain (EAS) and the assumed natural strain (ANS) methods for the alleviation of locking effects is developed in this work. Aiming at tackling the poor convergence performance of standard Newton schemes, a quasi-Newton (QN) scheme is proposed for the solution of coupled governing equations stemming from the enhanced assumed strain shell formulation in a monolithic manner. The excellent convergence performance of this QN monolithic scheme for the multi-field shell formulation is demonstrated through several paradigmatic boundary value problems, including single edge notched tension and shear, fracture of cylindrical structure under mixed loading and fatigue induced crack growth. Compared with the popular alternating minimization (AM) or staggered solution scheme, it is also found that the QN monolithic solution scheme for the phase field modeling using enhanced strain shell formulation is very efficient without the loss of robustness, and significant computational gains are observed in all the numerical examples. In addition, to further reduce the computational cost in fracture modeling of large-scale thin-walled structures, a specific global–local phase field approach for solid shell elements in the 3D setting is proposed, in which the full displacement-phase field problem is considered at the local level, while addressing only the elastic problem at the global level. Its capability is demonstrated by the modeling of a cylindrical structure subjected to both static and fatigue cyclic loading conditions, which can be appealing to industrial applications.

为了有效地预测薄壁结构中的裂纹扩展，使用大变形实体壳有限元的全局-局部相场建模方法考虑了增强假设应变 (EAS) 和假设自然应变 (ANS) 方法来缓解在这项工作中开发了锁定效果。针对标准牛顿方案收敛性能差的问题，提出了一种拟牛顿（QN）方案，用于以整体方式求解源自增强假设应变壳公式的耦合控制方程。这种用于多场壳公式的 QN 整体方案的出色收敛性能通过几个典型的边值问题得到证明，包括单边缺口拉伸和剪切，混合载荷下圆柱结构的断裂和疲劳诱发的裂纹扩展[J]. 与流行的交替最小化 (AM) 或交错求解方案相比，还发现使用增强应变壳公式进行相场建模的 QN 整体求解方案非常有效，且不损失鲁棒性，并且在所有的数值例子。此外，为了进一步降低大型薄壁结构断裂建模的计算成本，提出了一种特定的 3D 设置中实体壳单元的全局-局部相场方法，其中全位移相场问题为在地方层面考虑，而仅在全球层面解决弹性问题。