We present a new computational framework for brittle fracture simulation, building on a novel four-field mixed finite element formulation for elasticity that independently approximates stresses, logarithmic stretches, rotations vectors, and displacements. Each field is associated with sets of equations, i.e. conservation of linear momentum, conservation of angular momentum, constitutive equation, and consistency equation between displacements and deformation. The stresses are approximated in $H(\text{div})$ space, and the remaining three fields in $L^2$ space. Such formulation results in a very sparse system of equations that is easy to parallelise, enabling highly scalable and robust solvers. To enhance computational efficiency, we employ a hybridisation technique that significantly reduces the size of the global stiffness matrix. In the hybridisation technique, the stress field is approximated using a broken space; in other words, stresses are in $L^2$ space. Meanwhile, the continuity of divergence of stress is enforced by introducing degrees of freedom in the interface between elements. The crack is simply propagated by eliminating the interface degrees of freedom associated with an element that meets the energetic fracture criterion, resulting in a robust and scalable approach that can handle large-scale fracture problems. Using multiple numerical examples, we validate the formulation and implementation. Subsequently, the scalability of the formulation is demonstrated through a nuclear industry problem involving contact and fracture modelling under prolonged exposure to radiation.