A Topology Optimisation Framework Incorporating Fracture and Contact

  • Ciceri, Mirko (Imperial College London)
  • Hewson, Robert (Imperial College London)
  • Santer, Matthew (Imperial College London)

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The application of topology optimisation to real-world structures is particularly challenging when large deformations are involved. Traditional approaches are generally restricted to linear elastic behaviour, whereas nonlinear effects such as fracture and internal contact between structural members frequently occur in practice. By explicitly modelling these effects during optimisation, nonlinear mechanisms can be anticipated and prevented or controlled and exploited broadening the design domain. This opens the possibility of tailoring post-failure load redistribution, enhancing energy dissipation, or introducing controlled failure modes. In this way, topology optimisation evolves from a tool primarily aimed at generating stiff, lightweight structures into a comprehensive framework for designing robust, multifunctional systems capable of maintaining or adapting performance even under extreme loading conditions. Building on this perspective, the presented topology optimisation framework exploits a novel variational formulation that incorporates third medium contact and phase field fracture in a fully differentiable manner, enabling efficient sensitivity analysis. The framework is then applied to numerical examples, demonstrating that the explicit inclusion of fracture behaviour and internal contact in the optimisation formulation enables new functional design outcomes, with structures capable of maintaining functionality after the initiation of partial failure.