Modeling complex crack problems using the three-node triangular element fitted to numerical manifold method with continuous nodal stress

Abstract

A three-node triangular element fitted to numerical manifold method with continuous nodal stress, called Trig3-CNS (NMM) element, was recently proposed for linear elastic continuous problems and linear elastic simple crack problems. The Trig3-CNS (NMM) element can be considered as a development of both the Trig3-CNS element and the numerical manifold method (NMM). Inheriting all the advantages of Trig3-CNS element, calculations using Trig3-CNS (NMM) element can obtain higher accuracy than Trig3 element without extra degrees of freedom (DOFs) and yield continuous nodal stress without stress smoothing. Inheriting all the advantages of NMM, Trig3-CNS (NMM) element can conveniently treat crack problems without deploying conforming mathematical mesh. In this paper, complex problems such as a crucifix crack and a star-shaped crack with many branches are studied to exhibit the advantageous features of the Trig3-CNS (NMM) element. Numerical results show that the Trig3-CNS (NMM) element is prominent in modeling complex crack problems.