CAE-Companion-2018-2019

Modeling of Materials & Connections WISSEN CAE

Material Models and Failure Criteria of Glass for Crash Simulation – X-FEM

Introduction High quality simulation of safety glass, used for making windshields in automotive industry, is still a challenging topic for commercial crash solvers. Holistic modelling of the behavior of glass becomes more important due to its influence on structural behavior in several load cases, like for static and dynamic roof crush, as well as for highly dynamic impacts and pedestrian protection enhancement. The main requirement of the automotive industry is to use the same model and the same mesh for all load cases. Nowaday exist many material models as well as many failure criteria. The common approach for fracture modelling is to apply shell-element deletion, or setting its stiffness, at the integration point, to zero, when the failure criteria is reached. This approach works well, but has a major disadvantage: It is highly mesh sensitive! Local refinement, like adaptive meshing, will lead to local- ization of plasticity and at the end to failure in the refined area. Adaptive meshing is a suitable method for stamping simulation where the final deformed shape is known. It is not recommended in crash applications. To overcome this drawback, ALTAIR has developed further the extended Finite Element Method (X-FEM) [2] and imple- mented it in the RADIOSS crash solver [1]. Theory X-FEM is a numerical method for geometries containing discontinuities and singularities without the need of building a conforming mesh. This numerical method was developed for modelling large (displacement) as well as slight (strain) discontinuities within a standard finite element framework. It is based on the Partition of Unity Method [3]. X-FEMwill be applied for the simulation of crack initiation and propagation without the need of re-meshing [4]. With X-FEM, cracks are represented as surfaces of discontinuous displace- ments continuously propagating through finite elements (see figure 1). Dynamic crack propagation is an application domain for which X-FEM is particularly suitable because the most prevalent method for treating crack growth (see figure 3), where re-meshing, is not suitable for a solution of this problem (see fig. 2).

Figure 1: Schematic visualization of the discontinuity in a finite element continuum

Figure 2: Modelling of discontinuous displacement field: Re-meshing vs. X-FEM

Figure 3: Modelling of crack propagation with X-FEM

Application for simulating the windshield behaviour in crash The X-FEMmethod is designed as a module and can be add- ed to the existing failure criteria, like Forming Limit Diagram (FLD), Johnson-Cook, tabulated failure-strain-vs-triaxiality and others. For the usage of any application, it is highly rec- ommended to validate the material and failure model first, before activating the X-FEMextension. The typical safety glass consists of: Glass – Polyvinylbutyral (PVB) foil – Glass It is obligatory for the FEMmethod, to be able to represent the correct behaviour of a windshield, to mimic independent cracks within one shell-element, depending on the state of stress and strain, in the individual layer (see figure 4).

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