IGA: Non-Invasive Coupling with FEM and Regularization of Digital Image Correlation Problems, Volume 2

2Non-invasive Global/Local Hybrid IGA/FEM Coupling

2.1. Introduction

The perspective on the relation between IGA and FEM provided in the previous chapter enables us to fully appreciate the increased per-DOF accuracy attributed to IGA. Indeed, let us recall that IGA allows us to capture a regular solution as accurately as FEM but with fewer DOF because its discretization space is somehow included into the FE C⁰ space. However, this point of view also highlights that IGA, in its standard brute form, does not appear suitable when the solution is no longer regular. For example, this often occurs at the local scale in structural mechanics. In this respect, we may think of the modeling of cracks, local contact, delamination or local heterogeneities, which involves displacement and/or strain discontinuities in the solution. This issue is even more compounded by the tensor product structure of the standard multivariate spline technologies, therefore precluding local mesh refinement and the (boundary fitted) description of geometrical details. As a result, numerous sophisticated methods have been developed over the years to make possible local simulations with IGA. Advanced splines have been defined to address local mesh refinement, for example, locally refined splines (Dokken et al. 2013), hierarchical splines (Hennig et al. 2016; D’Angella and Reali 2020), hierarchical T-splines (Evans et al. 2015; Chen and de Borst 2018). For the representation of geometrical details, one solution, ...