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The present work proposes an extension of the third medium contact method forsolving structural topology optimization problems that involve and exploitself-contact. A new regularization of the void region, which acts as thecontact medium, makes the method suitable for cases with very largedeformations. The proposed contact method is implemented in a second ordertopology optimization framework, which employs a coupled simultaneous solutionof the mechanical, design update, and adjoint problems. All three problems arederived and presented in weak form, and discretized with finite elements ofsuitable order. The capabilities and accuracy of the developed method aredemonstrated in a topology optimization problem for achieving a desirednon-linear force-displacement path.

Internal contact modeling for finite strain topology optimization