Computations of the dynamic fracture of quasi-brittle plane and shell structures by the extended finite element method.

摘要

Finite element methods for the simulation of dynamic fracture in plane and thin shell structures and their application to quasi-brittle fracture problems are presented. The method is based on the extended finite element method (XFEM) and is incorperated within an explicit time integration scheme. The method is implemented using 4-node quadrilateral plane and Belytschko-Lin-Tsay shell elements, which have high computational efficiency because of their use of a one-point integration scheme. Discontinuities in the translational and angular velocity fields are introduced to model cracks by XFEM based on the Hansbo and Hansbo approach; the element which contains the crack is replaced by two superposed elements with additional phantom nodes. Though this discontinuity representation scheme uses the same linear combination of enrichment functions as the conventional XFEM, it allows for considerable simplifications in fractured plane and thin shell elements formalisms, and furthermore is applicable to arbitrary large deformations. Also, the method provides consistent history variables because it retains the original quadrature points even for the integration of the discontinuous integrands of cracked elements.; When modeling fracture, the method employs a cohesive law with a fracture criterion. The development of a fracture criterion that is computationally efficient and is easily applied, in terms of available data, poses a significant difficulty. Fracture criteria for quasi-brittle materials are usually expressed in terms of the critical maximum principal tensile strain. However, in low order finite element models solved by explicit time integration, the maximum principal tensile strain tends to be quite noisy, so that crack paths computed by direct application of such criteria tend to be erratic and do not conform to experimentally observed crack paths. To circumvent these difficulties, a nonlocal form of a strain-based fracture criterion is developed. The nonlocal form is obtained by a kernel-weighted average over a sector in front of the crack tip.; The methodology is applied to the simulation of several experiments involving dynamic fracture and nonlinearities. They demonstrate that the method is able to reproduce the observed failure modes in the experiments quite well and they support the use of the developed methods for general applications of dynamic fracture.