Numerical integration in G/XFEM analysis of 2-D fracture mechanics problems for physically nonlinear material and cohesive crack propagation

PurposeThe aim of this paper is to present a novel data transfer technique to simulate, by G/XFEM, a cohesive crack propagation coupled with a smeared damage model. The efficiency of this technique is evaluated in terms of processing time, number of Newton–Raphson iterations and accuracy of structural response.Design/methodology/approachThe cohesive crack is represented by the G/XFEM enrichment strategy. The elements crossed by the crack are divided into triangular cells. The smeared crack model is used to describe the material behavior. In the nonlinear solution of the problem, state variables associated with the original numerical integration points need to be transferred to new points created with the triangular subdivision. A nonlocal strategy is tailored to transfer the scalar and tensor variables of the constitutive model. The performance of this technique is numerically evaluated.FindingsWhen compared with standard Gauss quadrature integration scheme, the proposed strategy may deliver a slightly superior computational efficiency in terms of processing time. The weighting function parameter used in the nonlocal transfer strategy plays an important role. The equilibrium state in the interactive-incremental solution process is not severely penalized and is readily recovered. The advantages of such proposed technique tend to be even more pronounced in more complex and finer meshes.Originality/valueThis work presents a novel data transfer technique based on the ideas of the nonlocal formulation of the state variables and specially tailored to the simulation of cohesive crack propagation in materials governed by the smeared crack constitutive model.

Hybrid Equilibrium Finite Element Formulation for Cohesive Crack Propagation

Equilibrium elements have been developed in hybrid formulation with independent equilibrated stress fields on each element. Traction equilibrium condition, at sides between adjacent elements and at sides of free boundary, is enforced by use of independent displacement laws at each side, assumed as Lagrangian parameters. The displacement degrees of freedom belongs to the element side, where an extrinsic interface can be embedded. The embedded interface is defined by the same stress fields of the hybrid equilibrium element and it does not require any additional degrees of freedom. The extrinsic interface is developed in the consistent thermodynamic framework of damage mechanics with internal variable and produces a bilinear response in a traction separation diagram. The proposed extrinsic interface can be modelled on every single element side or can be modelled only on a set of predefined element sides.

Vector form Intrinsic Finite Element Based Approach to Simulate Crack Propagation

This paper presents a new approach to simulate the propagation of elastic and cohesive cracks under mode-I loading based on the vector form intrinsic finite element method. The proposed approach can handle crack propagation without requiring global stiffness matrices and extra weak stiffness elements. The structure is simulated by mass particles whose motions are governed by the Newton's second law. Elastic and cohesive crack propagation are simulated by proposed VFIFE-J-integral and VFIFE-FCM methods, respectively. The VFIFE-J-integral method is based on vector form intrinsic finite element (VFIFE) and J-integral methods to calculate the stress intensity factors at the crack tips, and the VFIFE-FCM method combines VFIFE and fictitious crack models (FCM). When the stress state at the crack tip meets the fracture criterion, the mass particle at the crack tip is separated into two particles. The crack then extends in the plate until the plate splits into two parts. The proposed VFIFE-J-integral method was validated by elastic crack simulation of a notched plate, and the VFIFE-FCM method by cohesive crack propagation of a three point bending beam. As assembly of the global stiffness matrix is avoided and each mass particle motion is calculated independently, the proposed method is easy and efficient. Numerical comparisons demonstrate that the present results predicted by the VFIFE method are in agreement with previous analytical, numerical and experimental works.