Modeling of failure in composites by X-FEM and level sets within a multiscale framework

Hettich, Thomas; Hund, Andrea; Ramm, Ekkehard

doi:10.1016/j.cma.2007.07.017

Cited by 114 publications

(53 citation statements)

References 32 publications

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“…XFEM has been applied to bimaterial problems by Sukumar et al [100], Hettich et al [54] and Huynh and Belytschko [56]. In the latter, both the crack and the interface were described by level sets.…”

Section: Dynamic Fracture and Other Topicsmentioning

confidence: 99%

The extended/generalized finite element method: An overview of the method and its applications

Fries

Belytschko

2010

Numerical Meth Engineering

1,176

695

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Abstract.The extended and generalized finite element methods are reviewed with an emphasis on their applications to problems in material science: (1) fracture (2) dislocations (3) grain boundaries and (4) phases interfaces. These methods facilitate the modeling of complicated geometries and the evolution of such geometries, particularly when combined with level set methods, as for example in the simulation growing cracks or moving phase interfaces. The state of the art for these problems is described along with the history of developments.

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Section: Dynamic Fracture and Other Topicsmentioning

confidence: 99%

The extended/generalized finite element method: An overview of the method and its applications

Fries

Belytschko

2010

Numerical Meth Engineering

1,176

695

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“…Recently, computational homogenisation techniques have also been applied to determine constitutive relations for predefined interfaces [8,9] as well as for cohesive cracks [10]. Variational multiscale methods are nowadays also used to simulate microstructural effects on cohesive cracks [11]. An alternative homogenisation scheme for modelling cohesive cracks in piezoelectric materials was proposed in [12].…”

Section: Introductionmentioning

confidence: 99%

“…Note that in this expression, matrix-vector notation is used instead of tensor notation. In combination with equation (11), this equation yields the nonlinear system of equations that governs microscale equilibrium…”

mentioning

confidence: 99%

Computational homogenization for adhesive and cohesive failure in quasi‐brittle solids

Verhoosel

Remmers

Gutiérrez

et al. 2010

Numerical Meth Engineering

122

111

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SUMMARYA computational multiscale framework is proposed that incorporates microstructural behaviour in a macroscale discrete fracture model. Homogenisation procedures are derived for both adhesive and cohesive failure on the macroscale and are implemented in an FE 2 -setting. The most important feature of the homogenisation procedure is that it implicitly defines a traction-opening relation for the macroscale fracture model. The representativeness of the micro models is studied using a onedimensional example, which shows that in the softening regime the proposed multiscale scheme behaves different from a bulk homogenisation scheme. These results are also observed in a numerical simulation for a micro model with a periodic microstructure. Numerical simulations further demonstrate the applicability of the method.

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“…The reader is invited to consult the works (Radtke et al, 2011(Radtke et al, , 2010a(Radtke et al, , 2010bHettich et al, 2008;Chudoba et al, 2009;Oliver et al, 2008) where field enrichments are imposed inside the 2D domain in order to model the fiber-matrix coupling. These enrichments are based on general known behavior of fiber-matrix connections.…”

Section: Latin American Journal Of Solids and Structures 12 (2015) 58mentioning

confidence: 99%

Fiber-matrix Contact Stress Analysis for Elastic 2D Composite Solids

Paccola

Sampaio

Coda

2015

Lat. Am. j. solids struct.

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This paper presents a finite element formulation for the analysis of two dimensional reinforced elastic solids developing both small and large deformations without increasing the number of degrees of freedom. Fibers are spread inside the domain without the necessity of node coincidence. Contact stress analysis is carried out for both straight and curved elements via two different strategies. The first employs consistent differential relations and the second adopts a simple average calculation. The development of all equations is described along the paper. Numerical examples are employed to demonstrate the behavior of the proposed methodology and to compare the contact stress results for both calculations.

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Modeling of failure in composites by X-FEM and level sets within a multiscale framework

Cited by 114 publications

References 32 publications

The extended/generalized finite element method: An overview of the method and its applications

The extended/generalized finite element method: An overview of the method and its applications

Computational homogenization for adhesive and cohesive failure in quasi‐brittle solids

Fiber-matrix Contact Stress Analysis for Elastic 2D Composite Solids

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