The performance of optical coating systems are frequently limited by the formation of defects and cracks, hence deteriorating the optical properties, film integrity and durability. Typical anti-reflective coating systems consist of inorganic low index and high index thin oxide films (e.g., SiO${}_2$ and ZrO${}_2$) on polymeric substrates that can be subjected to complex strain states induced by environmental effects such as thermal excursions or even by the manufacturing process. Any crack in the multi-layer stack is likely to be problematic in terms of optical performance and visual comfort for the wearer and also in terms of the mechanical durability of the stack. To overcome this limitation, the development of predictive tools is essential to improve the design of coatings systems while complementing experimental analyses. Thus, in this work, we performed numerical simulations by means of phase field fracture models relying on the finite element method and the energy minimization principle. Specifically, we developed and implemented a modelling strategy that can be applied as a readily usable dimensioning tool with a potential to optimize and predict the mechanical behaviour of optical coating systems upon crack initiation and propagation.

光学镀膜系统的性能经常受到缺陷和裂纹形成的限制，从而降低光学性能、薄膜完整性和耐久性。典型的抗反射涂层系统由无机低指数和高指数薄氧化膜（例如，SiO${}_2$ 和氧化锆${}_2$) 在聚合物基材上，这些基材可能会受到环境影响（例如热偏移）甚至制造过程引起的复杂应变状态的影响。多层堆叠中的任何裂纹都可能对佩戴者的光学性能和视觉舒适度以及堆叠的机械耐用性造成问题。为了克服这一限制，预测工具的开发对于改进涂层系统的设计同时补充实验分析至关重要。因此，在这项工作中，我们依靠有限元方法和能量最小化原理，通过相场断裂模型进行数值模拟。具体来说，