Adaptive Combined Discrete And Finite Element Method And Its Application On Impact Fracture Analysis Of Automobile Glass

Automobile glass is one of the important components of cars. The researches on its impactfracture mechanism have great significance on pedestrian protection, automotive passive safetyand accident reconstruction. There are some restricted conditions for experimental study whilenumerical study is a better alternative to investigate the impact fracture of automobile glassexcluding some limitations in experimental study. So two kinds of numerical methods, basedon the combined discrete and finite element method, are propose to systematically investigatethe impact fracture procedure of automobile glass. The research significances are summarizedas follows:Firstly, a subregional combined algorithm, four-point combined discrete and finite elementmethod, is proposed to constrain the rotation of a discrete element about its linked point onthe interface and eliminate the potential zero energy mode presented on the interface betweenthe discrete element and the finite element subregions. The impact response of a cantileverglass beam is simulated by using the four-point combined method to investigate the effect ofthe penalty factor α to the simulation results. In addition an averaged stress tensor, which isautomatically symmetrical and invariant by translations, is improved to calculate the averagedstress of the discrete element. The averaged stress tensor contains the contributions denoted bythe connect force, the cohesive traction, the interface force and the contact force between thediscrete elements and the inertia and the external forces acting on the discrete element. Theeffectiveness of the four-point combined method and the averaged stress tensor is validated bycomparing the simulation results of two simple cases in the elastic range with those of the finiteelement method.Secondly, an extrinsic cohesive fracture model is employed to simulate the brittle fractureonly in the discrete element subregion. The effective quantities are the basis of the cohesivefracture model which integrate the effective traction and the effective separation between theneighboring discrete elements. The element-size convergency for the brittle fracture is inves-tigated by a simple specimen with a small pre-crack. The element-size insensitive results areobtained: the size and the distribution of the fracture or cohesive zone with the coarse meshare similar to those with the fine mesh and the coarse mesh can provide a good resolution for the brittle fracture. The impact fracture behaviors of a glass beam and a laminated glass beamare simulated by using the four-point combined method. The effectiveness of the cohesive frac-ture model is validated by comparing the simulation results with those of the impact fractureexperiments of the laminated glass beam.Finally, an adaptive combined discrete and finite element method is proposed to limit thediscrete element subregion in the vicinity of the crack to maximize computational efficiency asmuch as possible. The adaptive combined method may allow for the use of the accurate andefficient finite elements in the lower distorted region and the discrete elements which are au-tomatically generated in the severely deformed finite element region. In this method, a stressequivalence method is proposed to calculate the equivalent area between the discrete elementsin the elastic range. The impact fracture procedures of a glass beam and a laminated glass beamare simulated by using the adaptive combined method. The feasibility of the adaptive combinedmethod is validated by the impact fracture simulation of the glass beam. The comparison ofcalculation time consumption shows that the adaptive combined method has a higher efficiencythan the discrete element method. The effectiveness of the adaptive combined method is vali-dated by comparing the simulation results with the impact experimental results of a laminatedglass and the simulation results achieve good agreements with the experimental results.The proposed combined methods are not only appropriate for analyzing the impact fractureof automobile laminated glass, but also the fracture procedure of some other brittle materials.Based on the proposed combined methods, the corresponding numerical code has been devel-opedinFortran90/95programminglanguagetoenrichthefunctionoftheprogramCDFPwhichis an explicit numerical solver and is inclined to analysis the impact fracture procedure of auto-mobile laminated glass.