On why mesh untangling may not be required

Generating tangle-free high-quality hexahedral meshes is an ongoing challenge. Tangled meshes, i.e., meshes containing negative Jacobian elements, are unsuitable for finite element (FE) simulations as they lead to erroneous results. Consequently, many untangling methods have been proposed; however, untangling is not always achievable.The present paper addresses this challenge by allowing tangled meshes for FE analysis with the use of the isoparametric tangled finite element method (i-TFEM). The proposed method efficiently handles complex configurations of tangled elements, making it suitable for real-world scenarios. By introducing minor modifications to standard FEM, i-TFEM offers an easy implementation and reduces to standard FEM for non-tangled meshes. Numerical experiments, involving both linear and nonlinear elasticity, demonstrate the accuracy, convergence characteristics, and applicability of the method to real-world tangled meshes. The results emphasize the importance of reevaluating mesh quality indicators for tangled meshes.