This work focused on the current state-of-the-art developments in the phase-field method. Soft materials undergo severe embrittlement when exposed to extreme environmental conditions, leading to extensive cracking on the surface of aged materials. The phase-field method provides a robust technique for capturing the propagation of induced cracks in highly brittle, aged materials. However, current phase-field algorithms suffer from the high computational cost associated with the so-called staggered solution scheme, which has proven to be conditionally stable and therefore requires extremely small time increments to advance the crack and avoid convergence issues. In this chapter, we show that the use of a quasi-Newton-based method known as BFGS is more advantageous and efficient compared to the staggered approach in the context of large-deformation mechanics. These results highlight the applicability of the phase-field method as both a robust and efficient method for capturing brittle fracture in materials under extreme conditions.