Efficient and Robust Traction Laws for the Modeling of Adhesively Bonded Joints

Gustafson, Peter A.; Waas, Anthony M.

doi:10.2514/6.2008-1847

Cited by 14 publications

(15 citation statements)

References 54 publications

(69 reference statements)

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“…From (A1) and (12), the strain field can be written as: Integration of the strain field yields the longitudinal displacement field…”

Section: Stiffness and Load Contribution Of The Adherends Outside Of mentioning

confidence: 99%

“…With a view to deriving the adaptive shape functions in the lap region, the stress field in the outer center adherend is written directly from equilibrium a11 (x) = P t a (12) wherex is the natural coordinate of this section, defined as:…”

Section: Stiffness and Load Contribution Of The Adherends Outside Of mentioning

confidence: 99%

“…Conventional finite element (FE) models are the current state of the art and are widely available in the literature where work began as early as 1971 ( [1,2] are early references). More 95 recently, promising advances in cohesive zone [3][4][5][6][7][8][9], discrete cohesive zone [10][11][12], fracture mechanics [13], probabilistic prediction [14,15], virtual crack closure technique [16][17][18][19][20][21][22] and other adhesive region models [23][24][25][26] have greatly increased the predictive capability of FE techniques. Cohesive zone models have been incorporated into commercial software including Abaqus R [27] and Genoa R [28], as well as freely available research codes like Tahoe R [29].…”

Section: Introductionmentioning

confidence: 99%

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A bonded joint finite element for a symmetric double lap joint subjected to mechanical and thermal loads

Gustafson

Waas

2009

Numerical Meth Engineering

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SUMMARYA bonded joint finite element (FE) for a symmetric double lap joint is developed that is capable of predicting field quantities in the lap region. The element is a hybrid method and incorporates features of classical analytical and numerical methods. The element stiffness and load vector formulations have unique, load dependent, non-linear shape functions based on an analytical solution. The adaptive shape functions are formulated in terms of the dimensionless mechanical load fraction ( P ) and total load ( tot ) and are capable of predicting the thermal and mechanical load response. The bonded joint element has been implemented as a user element in the Abaqus R commercial FE code. A comparison of the stress predictions for the bonded joint element and a conventional 2D FE model is presented and are found to be in good agreement. Therefore, the element provides a computationally efficient and mesh-independent stress prediction. The single element reproduces the analytical solution with minimal analyst input and can be easily incorporated into early design and sizing studies.

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“…From (A1) and (12), the strain field can be written as: Integration of the strain field yields the longitudinal displacement field…”

Section: Stiffness and Load Contribution Of The Adherends Outside Of mentioning

confidence: 99%

Section: Stiffness and Load Contribution Of The Adherends Outside Of mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A bonded joint finite element for a symmetric double lap joint subjected to mechanical and thermal loads

Gustafson

Waas

2009

Numerical Meth Engineering

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“…Riks method (Riks, 1979) which can follow the equilibrium path after instability. Also, Gustafson and Waas (Gustafson & Waas, 2008) have used a discrete cohesive zone method finite element to evaluate traction law efficiency and robustness in predicting decohesion in a finite element model. They provided a sinusoidal traction law which found to be robust and efficient due to the elimination of the stiffness discontinuities associated with the generalized trapezoidal traction law.…”

Section: Introductionmentioning

confidence: 99%

Finite Element Analysis of Delamination Growth in Composite Materials using LS-DYNA: Formulation and Implementation of New Cohesive Elements

Elmarakbi¹

2011

Advances in Composite Materials - Ecodesign and Analysis

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“…Riks method [18] which can follow the equilibrium path after instability. Also, Gustafson and Waas [19] have used a discrete cohesive zone method finite element to evaluate traction law efficiency and robustness in predicting decohesion in a finite element model. They provided a sinusoidal traction law which found to be robust and efficient due to the elimination of the stiffness discontinuities associated with the generalized trapezoidal traction law.…”

Section: Introductionmentioning

confidence: 99%

Finite element simulation of delamination growth in composite materials using LS-DYNA

Elmarakbi

Fukunaga

2009

Composites Science and Technology

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In this paper, a modified adaptive cohesive element is presented. The new elements are developed and implemented in LS-DYNA, as a user defined material subroutine (UMAT), to stabilize the finite element simulations of delamination propagation in composite laminates under transverse loads. In this model, a pre-softening zone is proposed ahead of the existing softening zone. In this pre-softening zone, the initial stiffness and the interface strength are gradually decreased. The onset displacement corresponding to the onset damage is not changed in the proposed model. In addition, the critical energy release rate of the materials is kept constant. Moreover, the constitutive equation of the new cohesive model is developed to be dependent on the opening velocity of the displacement jump. The traction based model includes a cohesive zone viscosity parameter (g) to vary the degree of rate dependence and to adjust the maximum traction. The numerical simulation results of DCB in Mode-I is presented to illustrate the validity of the new model. It is shown that the proposed model brings stable simulations, overcoming the numerical instability and can be widely used in quasi-static, dynamic and impact problems.

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Efficient and Robust Traction Laws for the Modeling of Adhesively Bonded Joints

Cited by 14 publications

References 54 publications

A bonded joint finite element for a symmetric double lap joint subjected to mechanical and thermal loads

A bonded joint finite element for a symmetric double lap joint subjected to mechanical and thermal loads

Finite Element Analysis of Delamination Growth in Composite Materials using LS-DYNA: Formulation and Implementation of New Cohesive Elements

Finite element simulation of delamination growth in composite materials using LS-DYNA

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