Four-point combined DE/FE algorithm for brittle fracture analysis of laminated glass

AbstractA four-point combined DE/FE algorithm is proposed to constrain the rotation of a discrete element about its linked point and analyze the cracks propagation of laminated glass. In this approach, four linked points on a discrete element are combined with four nodes of the corresponding surface of a finite element. The penalty method is implemented to calculate the interface force between the two subdomains, the finite element (FE) and the discrete element (DE) subdomains. The sequential procedure of brittle fracture is described by an extrinsic cohesive fracture model only in the DE subdomain. An averaged stress tensor for granular media, which is automatically symmetrical and invariant by translations, is used to an accurate calculation of the averaged stress of the DE. Two simple cases in the elastic range are given to certify the effectiveness of the combined algorithm and the averaged stress tensor by comparing with the finite element method and the mesh-size dependency of the combined algorithm and the cohesive model is also investigated. Finally, the impact fracture behavior of a laminated glass beam is simulated, and the cracks propagation is compared with experimental results showing that the theory in this work can be used to predict some fracture characteristics of laminated glass

A ghost particle-based coupling approach for the combined finite-discrete element method

The combined finite-discrete element method takes the advantages of both the finite element (FE) method and the discrete element (DE) method, but a coupling approach is required for effective combination of the two methods. In this paper, a novel coupling approach is proposed by means of ghost particles. The entire domain is decomposed into a FE- A nd a DE-subdomain, and ghost particles are constructed inside the interface FE domain to connect with the DE domain in a consistent interaction manner as the DE method. A novel one-step back strategy is proposed to overcome the incompatibility of degree of freedoms between FE nodes and DE particles from a numerical sense. The coupling approach is very simple to implement and its effectiveness is validated by numerical examples

Single-Impact Failure of Multi-Layered Automotive Coatings: A Finite Element-Based Study

Automotive coatings are a multi-layered polymer composite structure whose impact resistance is closely related to the appearance and safety of a vehicle. Since experimental methods are of high cost and poor repeatability, in our work, a finite element model is developed for the single-impact failure of automotive coatings. In this model, a multi-mechanism damage model and a large deformation cohesive zone model are employed to account for the polymer-ply and interlaminar failures of the coating, and some rate-dependent material models are adopted to capture the effect of impact velocity. The simulated results indicate that the proposed model can reproduce the failure patterns of automotive coatings well. In addition, the impact failure mechanisms of the coating are revealed. Numerical findings show that both brittle and ductile failures are found in the coating and there are three stages for the propagation of the delamination crack. Finally, we numerically investigate the effects of primer mechanical properties, i.e., Young’s modulus, yield strength, and re-hardening modulus, on the impact resistance of automotive coatings. Our work is helpful to the design of coating, which can improve the impact resistance of automotive coatings

Experimental study on mechanical property and stone-chip resistance of automotive coatings

The damage of automotive coatings caused by stone impact is a problem that has attracted great attention from automotive companies and users. In this work, experiments were conducted to investigate the dynamic tensile properties and stone-chip resistance of automotive coatings. Four kinds of paint films and three typical coatings (single-layer electrocoat coating, single-layer primer coating, and multilayered coating) were used. Under dynamic tensile load using split Hopkinson tension bar (SHTB), the engineering stress-strain curves of the paint films at medium and high strain rates (from 50 to 600 s ^−1 ) were obtained. Results indicated that the mechanical properties of the paint films exhibited strong nonlinearity and strain-rate correlation. A modified anti-impact tester was used to complete repeatable single impact tests. The effects of some key parameters, i.e., impact velocity, impact angle, and paint film thickness, on the stone-chip resistance of coatings were systematically investigated. The influence of contact type under high-speed impact conditions was investigated as well. The surface morphologies of the coatings after impact were examined by scanning electron microscopy (SEM), and the failure mechanism of the coatings under normal/oblique impact was discussed. In all experiments, the paint films showed brittle fracture behavior

Effects of Interlaminar Failure on the Scratch Damage of Automotive Coatings: Cohesive Zone Modeling

Interlaminar failure caused by scratches is a common damage mode in automotive coatings and is considered the potential trigger for irreversible destruction, i.e., plowing. This work strives to numerically investigate the mechanisms responsible for the complex scratch behavior of an automotive coating system, considering the interfacial failure. A finite element model is developed by incorporating a large deformation cohesive zone model for scratch-induced debonding simulation, where the mass scaling technique is utilized to minimize computational burden while ensuring accuracy. The delamination phenomenon of the automotive coating is reproduced, and its effects on scratch damage behavior are analyzed. Accordingly, it is revealed that the interlaminar delamination would produce significant stress redistribution, which leads to brittle and ductile damage of the coating and consequently affects the formation of plowing. Eventually, parametric studies on the effects of interfacial properties are performed. They demonstrate that the shear strength and shear fracture energy dominate scratch-induced delamination

A Lagrangian coupling approach for the combination of finite-discrete element method

In this paper, an effective approach to couple finite elements (FEs) with discrete elements (DEs) is presented. The proposed approach conforms to displacement compatibility condition at the interface between FEs and DEs, and this constraint is enforced by the Lagrange multiplier method. The coupling system is solved by the Gauss-Seidel iteration strategy and the incompatibility of degrees of freedom between FEs and DEs can be effectively addressed. Two numerical examples are employed for validation and the effectiveness of the proposed approach is also demonstrated via comparison with other numerical methods

An explicit Lagrange constraint method for finite element analysis of frictionless 3D contact/impact problems

An effective contact algorithm is essential for modeling complicated contact/impact problems. Unlike the penalty method, the Lagrange multiplier method can generate more precise results while not adversely affecting stability; however, its formulation in explicit contact treatment is singular. In order to overcome this deficiency, a new Lagrange constraint method with different constraints under initial impact and persistent contact is proposed. In this method, the coupled contact system equilibrium equations with non-diagonal coefficient matrix are uncoupled via Gauss-seidel iteration strategy. Particularly, this implicit contact treatment can be compatible with explicit time integration scheme. To reduce oscillations, the displacement constraint is imposed under initial impact, while the combined constraints of velocity, acceleration and displacement are enforced under persistent contact. Numerical example validates this method

Impact Fracture and Fragmentation of Glass via the 3D Combined Finite-Discrete Element Method

A driving technical concern for the automobile industry is their assurance that developed windshield products meet Federal safety standards. Besides conducting innumerable glass breakage experiments, product developers also have the option of utilizing numerical approaches that can provide further insight into glass impact breakage, fracture, and fragmentation. The combined finite-discrete element method (FDEM) is one such tool and was used in this study to investigate 3D impact glass fracture processes. To enable this analysis, a generalized traction-separation model, which defines the constitutive relationship between the traction and separation in FDEM cohesive zone models, was introduced. The mechanical responses of a laminated glass and a glass plate under impact were then analyzed. For laminated glass, an impact fracture process was investigated and results were compared against corresponding experiments. Correspondingly, two glass plate impact fracture patterns, i.e., concentric fractures and radial fractures, were simulated. The results show that for both cases, FDEM simulated fracture processes and fracture patterns are in good agreement with the experimental observations. The work demonstrates that FDEM is an effective tool for modeling of fracture and fragmentation in glass