Materials and structures in extreme conditions pose new design challenges that require novel methods. We investigate new machine learning and optimization strategies to design structures undergoing complex fracture and plasticity behavior. This involves accelerating simulations to generate more data for structural optimization, and using neural networks to guide the inverse design process. In particular, the acceleration is achieved by creating high-fidelity surrogate models that efficiently handle history-dependency. In addition, a new inverse design method called gradient-free neural topology optimization is proposed.