DYNAMIC FRACTURE ANALYSIS WITH THE FRAGILE POINTS METHOD

Impact resistant structures in engineering are likely to undergo dynamic fracture when they are subjected to impact or explosion. Restricting the dynamic fracture has been a key method to reinforce structures’ impact resistance. Thus, an accurate prediction on structures’ fracture behavior under dynamic loads is needed. Numerical simulation has been an important tool for the prediction of dynamic fracture. But, finite element method, commonly used in engineering practices, has some difficulties in fracture simulations, such as mesh distortion and inserting crack explicitly. The recently proposed fragile points method (FPM) is a discontinuous Galerkin meshless method which is suitable for fracture simulations. This paper aims on extending the FPM to analyze dynamic fracture problems. On the one hand, taken the weak form meshless methods as references, the FPM uses points and subdomains to discretize the problem domains. The shape function of an FPM subdomain is determined based on the point cloud in its supporting domain, and thus the FPM is not sensitive to mesh distortion. On the other hand, taken the discontinuous Galerkin finite element method as a reference, piece-wise continuous trial functions are used in the FPM, and the interior interface numerical flux correction is introduced in the weak formulations to guarantee the consistency and stabilization of the FPM. Thus, explicit cracks can be easily introduced in the FPM models. This paper starts with the introduction of the core idea and discretization method of FPM. Then the derivation of the equation of motion in weak form for the dynamic FPM is presented. After that the explicit dynamic solution scheme of the FPM is established. Finally some examples are employed to verify the dynamic FPM’s capability regarding the prediction of stress wave propagation and dynamic fracture.