Local uncovering of unresolved physics in structural mechanics: seamless choice of modelling resolution using a CutFEM level-set approach
In this paper, we present a robust and efficient unfitted concurrent multiscale method for continuum-continuum coupling, based on the Cut Finite Element Method (CutFEM). The computational domain is defined using approximate signed distance functions over a fixed background mesh and is decomposed into microscale and macroscale regions using a novel zooming technique. The zoom interface is represented by a signed distance function intersecting the computational mesh arbitrarily. The mesh inside the zoomed region is hierarchically refined to resolve the microstructure. In the examples considered, the microstructure may contain voids and hard inclusions, and its geometry is defined implicitly by a signed distance function interpolated over the refined mesh. Our zooming technique allows the zoom interface to intersect the microstructure interface in an arbitrary fashion, enabling greater flexibility and accuracy in the modelling of complex geometries. The micro and macro regions are coupled using Nitsche's method, ensuring stability and accuracy in the solution. Ghost penalty terms are utilised to ensure the stability of cut elements along the zoom interface and the microstructure interface. To demonstrate the effectiveness of our framework, we apply it for modelling several heterogeneous structures with both linear elasticity and plasticity constitutive behaviours. The results show that our framework is robust and efficient, producing accurate and reliable solutions for such problems. Our proposed method provides a highly versatile and effective approach to multiscale modeling of structures with complex microstructures, and has the potential to be extended to problems requiring seamless moving of zooming region(s) during the simulation, such as damage growth and fracture propagation.