The phase-field approach to fracture modeling entails diffuse approximation of the fracture process via an auxiliary crack phase-field variable and hence offers itself as a suitable candidate for the development of a unified framework capable of dealing with both crack nucleation as well as propagation; see [1, Chapter 4] and the references therein for instance. However, there still remain several open questions, particularly with regards to robustness of the numerical solution procedure employed for incremental solution of the coupled system of equations at each load step. Within the context of the commonly adopted staggered solution scheme, the degree of coupling between the displacement and damage fields varies strongly as cracks evolve, thereby adversely impacting regularity of the underlying, highly nonlinear displacement sub-problem. Extensive numerical studies highlight the critical nature of this issue in finite strain problems as the displacement stiffness matrix tends to lose its positive definiteness during brutal crack propagation, thus leading to non-convergence of the standard Newton-Raphson scheme for this sub-problem. In this work, we propose two different nonlinear solvers tailor-made for the problem at hand. The first one entails a modification of the standard Newton-Raphson method by means of a coercion procedure and a line search algorithm to ensure convergence for a certain class of hyperelastic materials. The second one, based on the trust-region method [2], caters to the class of slightly incompressible hyperelastic materials involving a volumetric-isochoric split of the strain energy function. The current capabilities, computational cost, and limitations of the proposed nonlinear solvers are depicted by means of appropriate numerical examples. REFERENCES [1] Kumar P., Enhanced Computational Homogenization and Phase-Field Fracture Approaches for Polymer Nano-Composites, PhD Thesis, Friedrich-Alexander-Universität Erlangen-Nürnberg, 2024. [2] Conn A. R., Gould N. I. M., Toint P. L., Trust Region Methods, Society for Industrial and Applied Mathematics, 2000.