Deformation gradient averaging regularization for third medium contact
This work addresses a domain-specific issue in computational mechanics, particularly for topology optimization, by providing an incremental improvement to existing regularization methods for third medium contact.
The paper tackles the problem of enforcing contact constraints in finite strain settings using the third medium contact method by proposing a regularization technique based on element-wise deformation gradient averaging and a linear elastic term, which improves robustness and enables the use of first-order finite elements without extra degrees of freedom.
The third medium contact method has recently come into popularity as an alternative to traditional contact methods in contexts where search for contact boundaries is problematic, i.e. topology optimization. To enforce the contact constraints, it relies on a fictitious compliant material occupying the void space. In finite strain setting, this necessitates regularization techniques to improve the behavior of the third medium material. A number of existing models rely on penalization of locally computed second gradients of displacements, either through direct calculation on second-order elements or through additional degrees of freedom. Here we propose an alternative approach using element-wise deformation gradient averaging to effectively penalize spatial variations of the deformation gradient, together with a linear elastic term enforcing constant third medium stiffness. Our approach enables the use of first-order finite element formulations without any additional degrees of freedom and is therefore easy to implement. We demonstrate the robustness of the proposed method on several well-established benchmarks.