Triangular element partition method with consideration of crack tip

In fracture simulation,how to model the pre-existing cracks and simulate their propagation without remeshing is an important topic.The newly developed triangular element partition method(TEPM)provides an efficient approach to this problem.It firstly meshes the cracked body regardless of the geometry integrity of the interesting object with triangular elements.After the meshing procedure is completed,some elements are intersected by cracks.For the element intersected by a crack,the TEPM takes the element partition technique to incorporate the discontinuity into the numerical model without any interpolation enrichment.By this approach,the TEPM can simulate fracture without mesh modification.In the TEPM,all the cracked elements are treated as the usual partitioned elements in which the crack runs through.The virtual node pairs(the intersection points of crack faces and elements)at the opposite faces of the crack move independently.Their displacements are respectively determined by their neighbor real nodes(nodes formatted in the original mesh scheme)at the same side of the crack.However,among these cracked elements,the element containing a crack tip,referred to as the crack tip element thereafter,behaves differently from those cut through by the crack.Its influence on the singular field at the vicinity of the fracture tip becomes increasingly significant with the element size increasing.In the crack tip element,the virtual node pair at the crack tip move consistently before fracture occurs while the virtual node pair separate and each virtual node moves independently after the fracture propagates.Accordingly,the crack tip element is automatically transformed into the usual partitioned element.In the present paper,the crack tip element is introduced into the TEPM to account for the effect of the crack tip.Validation examples indicate that the present method is almost free from the element size effect.It can reach the same precision as the conventional finite element method under the same meshing scheme.But the TEPM is much more efficient and convenient than the conventional finite element method because the TEPM avoids the troubles that the conventional finite element method suffers,e.g.,the meshing problem of cracked body,modification of mesh scheme,etc.Though the extended finite element method can also avoid these troubles,it introduces extra degrees of freedom due to node interpolation enrichment.Due to the simplicity of the present TEPM,it is believed that its perspective should be highly inspiring.