Topology optimization (TO) is a mathematical approach to mechanical and multiphysics design with the objective of maximizing structural performance under physical and manufacturing constraints. However, applying conventional TO to the design of metamaterials remains challenging due to the existence of implicit physical constraints, combinatorial constraints, and nonlinear physical constraints. Thus, we proposed a user-friendly TO computing framework for general nonlinear metamaterial design. Our contributions included proposing and implementing the TO computing framework and benchmarking its performance. The framework shows advantages in tackling the following difficulties. 1). Implicit Physical Constraints—the manufacturable structure should not have spatially isolated components, but classical methods never explicitly formulated it. Thus, we use the deep image prior (DIP) technique to reparameterize the optimization variables, which is expected to bias toward spatially smooth structures; 2). Combinatorial Constraints—we designed a generalized straight-through technique and its equivalent reformulation to deal with the combinatorial constraint; 3). Nonlinear Physical Constraints—SOTA methods can not handle nonlinear physical constraints. Our TO computing framework successfully solved various design problems including multi-story buildings and supporting bridges with SOTA compliance (i.e., the objective function in TO) and guaranteed feasibility.