To overcome mesh-dependency of finite element simulations observed when continuum damage mechanics models are used, a variety of different methods have been proposed. As an alternative to rather established approaches like phase field fracture or gradient damage formulations, this talk presents a framework based on rank-one convexification. One of the main advantages is that the semi-convexified potential is directly linked to the homogenization of microstructures which evolve in their composition into weakly and strongly damaged phases. Another benefit is that no specification of length scale parameters is required, however, still enabling mesh independency of numerical calculations. Furthermore, no additional primary variables associated with the damage need to be computed from partial differential equations. Starting from [1], a novel reconvexification approach [4] will be presented, where the individual micro-phases are allowed to evolve themselves, thus enabling the description of strain-softening as basis for the simulation of fracture. Although full three-dimensional rank-one convexification algorithms have been shown to work properly [2], their efficiency is limited rendering the solution of practically relevant boundary value problems difficult. To overcome this, a novel algorithm leveraging hierarchical sequences [3, Definition 5.14] to approximate and establish an upper bound for the rank-one convex envelope will be presented. This method aligns with the rank-one convex envelope for materials achieving energetic optimality at each laminar level and facilitates concurrent numerical relaxation within large strain models, ensuring compatibility of the implied microstructure. Numerical examples will be provided showing that the proposed framework is indeed able to reasonably simulate engineering problems including damage. [1] Balzani, Ortiz (2012). International journal for numerical methods in engineering, 92(6):551-570. [2] Balzani, Köhler, Neumeier, Peter, Peterseim (2023). Computational Mechanics, 73: 27-47. [3] Dacorogna (2007). Direct methods in the calculus of variations. Springer Science & Business Media. [4] Köhler, Balzani (2023). Journal of the Mechanics and Physics of Solids, 173:105199, 2023.