Viscoelastic crack analysis by the boundary integral equation method

Sládek, J.; Sumec, Jozef; Sládek, V.

doi:10.1007/bf00532553

Cited by 9 publications

(4 citation statements)

References 11 publications

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“…However, numerical approaches in this scientific field are relatively limited (Syngellakis 2002). In the context of BEM models applied into the viscoelastic fracture mechanics problems, it is worth mentioning (Sladek et al 1984). In this work, a numerical approach based on the Laplace transform is presented to determine the crack opening displacements into a penny shaped crack.…”

Section: Introductionmentioning

confidence: 99%

A BEM formulation applied in the mechanical material modelling of viscoelastic cracked structures

Oliveira

Leonel

2016

Int J Adv Struct Eng

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The present study aims at performing a mechanical analysis of 2D viscoelastic cracked structural materials using the Boundary Element Method (BEM). The mesh dimensionality reduction provided by the BEM and its accuracy in representing high gradient fields make this numerical method robust to solve fracture mechanics problems. Viscoelastic models address phenomena that provide changes on the mechanical material properties along time. Well-established viscoelastic models such as Maxwell, Kelvin-Voigt and Boltzmann are used in this study. The numerical viscoelastic scheme, which is based on algebraic BEM equations, utilizes the Euler method for time derivative evaluation. Therefore, the unknown variables at the structural boundary and its variations along time are determined through an ordinary linear system of equations. Moreover, time-dependent boundary conditions may be considered, which represent loading phases. The dual BEM formulation is adopted for modelling the mechanical structural behaviour of cracks bodies. Three examples are considered to illustrate the robustness of the adopted formulation. The results achieved by the BEM are in good agreement with reported data and numerical stability is observed.

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Section: Introductionmentioning

confidence: 99%

A BEM formulation applied in the mechanical material modelling of viscoelastic cracked structures

Oliveira

Leonel

2016

Int J Adv Struct Eng

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“…The first and most commonly applied approach uses the correspondence principle to establish an associated elastic problem solved in the Laplace transform domain. Then, the solution in time domain is recovered by a numerical inversion [1,2,3,4,5,6]. The second approach works directly in the time domain, however, it requires a time dependent fundamental solution [7,8,9].…”

Section: Introductionmentioning

confidence: 99%

A simple and efficient BEM implementation of quasistatic linear visco-elasticity

Panagiotopoulos

Mantič

Roubíček

2014

International Journal of Solids and Structures

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a b s t r a c tA simple yet efficient procedure to solve quasistatic problems of special linear visco-elastic solids at small strains with equal rheological response in all tensorial components, utilizing boundary element method (BEM), is introduced. This procedure is based on the implicit discretisation in time (the so-called Rothe method) combined with a simple ''algebraic'' transformation of variables, leading to a numerically stable procedure (proved explicitly by discrete energy estimates), which can be easily implemented in a BEM code to solve initial-boundary value visco-elastic problems by using the Kelvin elastostatic fundamental solution only. It is worth mentioning that no inverse Laplace transform is required here. The formulation is straightforward for both 2D and 3D problems involving unilateral frictionless contact. Although the focus is to the simplest Kelvin-Voigt rheology, a generalization to Maxwell, Boltzmann, Jeffreys, and Burgers rheologies is proposed, discussed, and implemented in the BEM code too. A few 2D and 3D initial-boundary value problems, one of them with unilateral frictionless contact, are solved numerically.

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“…On the other hand, BEM has been shown to be a reliable tool for performing LVFM analyses. An early such threedimensional formulation [24], based on the Laplace transform approach, predicted the crack opening displacement of a penny-shaped crack in a viscoelastic material characterised by a threeparameter Kelvin model. Two-dimensional stress and displacement fields were later analysed in the neighbourhood of a crack filled with failed, so-called craze material [25].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Viscoelastic Fracture Mechanics Using Boundary Elements

Syngellakis

2010

KEM

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The boundary element methodology is applied to the fracture mechanics of non-linear viscoelastic solids. The adopted non-linear model is based on the ‘free volume’ concept, which is introduced into the relaxation moduli entering the linear viscoelastic relations through a time shift depending on the volumetric strain. Nonlinearity generates an irreducible domain integral into the original boundary integral equation governing the behaviour of linear viscoelastic solids. This necessitates the evaluation of domain strains, which relies on a non-standard differentiation of an integral with a strong kernel singularity. A time domain formulation based on constant shape functions over boundary elements and domain cells is computer-implemented through a numerical integration algorithm. The effectiveness of the developed numerical tool is demonstrated through the analysis of a plate with a central crack. The predicted stress field around the crack tip is compared with respective results obtained by the finite element method.

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Viscoelastic crack analysis by the boundary integral equation method

Cited by 9 publications

References 11 publications

A BEM formulation applied in the mechanical material modelling of viscoelastic cracked structures

A BEM formulation applied in the mechanical material modelling of viscoelastic cracked structures

A simple and efficient BEM implementation of quasistatic linear visco-elasticity

Nonlinear Viscoelastic Fracture Mechanics Using Boundary Elements

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