Steady-state crack growth in rubber-like solids

Kroon, Martin

doi:10.1007/s10704-010-9583-5

Cited by 23 publications

(12 citation statements)

References 57 publications

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“…On the other hand, dynamically propagating cracks tend towards a wedge-like shape, and at very high crack speeds, it appears that cracks propagate as shocks [11,19,25,42]. In the previous study with a Kelvin-type of material [26], no wedge-like crack could be observed, even at the highest crack speed (10 m/s), and the crack front retained a blunted, parabolic shape. However, in the present study with a generalised Maxwell-type of material, the crack tip blunting disappears.…”

Section: Discussion and Concluding Remarksmentioning

confidence: 79%

“…The present work is an attempt to further the theoretical understanding of the fracture process in rubber and the contributions from dissipation in particular. In a previous work by the present author [26], a similar type of steady-state analysis was performed but for a Kelvin-type of material. The use of this type of material is convenient, because no additional internal state variables, associated with viscoelastic relaxation, need to be introduced, and a standard finite element framework can therefore be used.…”

Section: Discussion and Concluding Remarksmentioning

confidence: 99%

“…A derivation of this expression and a proof of the path independence are provided in [26]. We will also consider the energy entity J ff , defined as…”

Section: J -Integral Evaluationmentioning

confidence: 99%

“…Crack speeds in rubber may exceed the shear wave speed of the material, and crack speeds increase with increasing transverse stretch [42]. A few theoretical studies have been done to predict these experimental observations [23,26,36,37,54].…”

mentioning

confidence: 99%

“…The method builds on a previous work by the present author [26], where crack growth was analysed for a Kelvin-type of material (a non-linear spring in parallel with a viscous damper) and under the assumption of plane deformation. In the present study, a generalised Maxwell-type of model is used to describe the material.…”

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confidence: 99%

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Dynamic steady-state analysis of crack propagation in rubber-like solids using an extended finite element method

Kroon

2011

Comput Mech

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In the present study, a computational framework for studying high-speed crack growth in rubber-like solids under conditions of plane stress and steady-state is proposed. Effects of inertia, viscoelasticity and finite strains are included. The main purpose of the study is to examine the contribution of viscoelastic dissipation to the total work of fracture required to propagate a crack in a rubber-like solid. The computational framework builds upon a previous work by the present author (Kroon in Int J Fract 169:49-60, 2011). The model was fully able to predict experimental results in terms of the local surface energy at the crack tip and the total energy release rate at different crack speeds. The predicted distributions of stress and dissipation around the propagating crack tip are presented. The predicted crack tip profiles also agree qualitatively with experimental findings.

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Section: Discussion and Concluding Remarksmentioning

confidence: 79%

Section: Discussion and Concluding Remarksmentioning

confidence: 99%

“…A derivation of this expression and a proof of the path independence are provided in [26]. We will also consider the energy entity J ff , defined as…”

Section: J -Integral Evaluationmentioning

confidence: 99%

mentioning

confidence: 99%

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confidence: 99%

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Dynamic steady-state analysis of crack propagation in rubber-like solids using an extended finite element method

Kroon

2011

Comput Mech

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Finite strain fracture analysis using the extended finite element method with new set of enrichment functions

Rashetnia

Mohammadi

2015

Int. J. Numer. Meth. Engng

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Nonlinear fracture analysis of rubber-like materials is computationally challenging due to a number of complicated numerical problems. The aim of this paper is to study finite strain fracture problems based on appropriate enrichment functions within the extended finite element method. Two-dimensional static and quasi-static crack propagation problems are solved to demonstrate the efficiency of the proposed method. Complex mixed-mode problems under extreme large deformation regimes are solved to evaluate the performance of the proposed extended finite element analysis based on different tip enrichment functions. Finally, it is demonstrated that the logarithmic set of enrichment functions provides the most accurate and efficient solution for finite strain fracture analysis. FINITE STRAIN FRACTURE ANALYSIS BY NEW XFEM ENRICHMENT FUNCTIONS 1317 Dolbow [9,10]; nevertheless, there is still lack of reliable commercial codes on the finite strain XFEM method, and the few available software [1,2] are extremely limited, and can only provide reliable results for very simple linear elastic large strain benchmarks [1]. Moreover, most of the existing commercial codes have serious inaccuracies in predicting the singularity of the stress field at crack tips, as studied by Gigliotti and Kroon [1], because the crack tip singularity enrichment functions are not included in the XFEM formulation. Consequently, the crack tip is forced to lay on the element edges for propagation purposes [1].Many researchers have attempted to use XFEM within the large deformation regime; among them Dolbow and Devan [11], Legrain et al. [12,13], Shen and Lew [14], Mergheim et al. [15], Fagerstrom and Larsson [16], Anahid and Khoei [17], and Khoei et al. [18] have presented various aspects of geometrically nonlinear XFEM analyses. Legrain et al. [12] proposed the first extended finite element stress analysis of the crack tips for plane stress conditions and investigated the importance of the right choice for the singularity enrichment functions. Moreover, they pointed out that due to the blunting process, neglecting the tip enrichments would be more acceptable than using inappropriate functions [12]. In this study, therefore, the goal is set to evaluate different available analytical solutions, to derive appropriate crack tip enrichment functions, and to assess their performance for analysis of a number of complex problems.Developing dedicated enrichment functions for various problems have been the subject of XFEM research in the past decade to improve the accuracy of XFEM for new evolving problems. Sukumar et al. [19] developed the tip enrichment functions from the analytical solution near an interface crack tip in isotropic bimaterials. Asadpour and Mohammadi [20] and Asadpour et al. [21] presented two different sets of orthotropic crack-tip enrichment functions, while Hattori et al. [22] proposed an alternative formulation to derive the orthotropic enrichment functions. Later, Esna Ashari and Mohammadi [23] derived the necessary enrichment functions...

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A multiscale anisotropic polymer network model coupled with phase field fracture

Arunachala,

Abrari Vajari,

Neuner

et al. 2024

Numerical Meth Engineering

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The study of polymers has continued to gain substantial attention due to their expanding range of applications, spanning essential engineering fields to emerging domains like stretchable electronics, soft robotics, and implantable sensors. These materials exhibit remarkable properties, primarily stemming from their intricate polymer chain network, which, in turn, increases the complexity of precisely modeling their behavior. Especially for modeling elastomers and their fracture behavior, accurately accounting for the deformations of the polymer chains is vital for predicting the rupture in highly stretched chains. Despite the importance, many robust multiscale continuum frameworks for modeling elastomer fracture tend to simplify network deformations by assuming uniform behavior among chains in all directions. Recognizing this limitation, our study proposes a multiscale fracture model that accounts for the anisotropic nature of elastomer network responses. At the microscale, damage in the chains is assumed to be driven by both the chain's entropy and the internal energy due to molecular bond distortions. In order to bridge the stretching in the chains to the macroscale deformation, we employ the maximal advance path constraint network model, inherently accommodating anisotropic network responses. As a result, chains oriented differently can be predicted to exhibit varying stretch and, consequently, different damage levels. To drive macroscale fracture based on damages in these chains, we utilize the micromorphic regularization theory, which involves the introduction of dual local‐global damage variables at the macroscale. The macroscale local damage variable is obtained through the homogenization of the chain damage values, resulting in the prediction of an isotropic material response. The macroscale global damage variable is subjected to nonlocal effects and boundary conditions in a thermodynamically consistent phase field continuum formulation. Moreover, the total dissipation in the system is considered to be mainly due to the breaking of the molecular bonds at the microscale. To validate our model, we employ the double‐edge notched tensile test as a benchmark, comparing simulation predictions with existing experimental data. Additionally, to enhance our understanding of the fracturing process, we conduct uniaxial tensile experiments on a square film made up of polydimethylsiloxane (PDMS) rubber embedded with a hole and notches and then compare our simulation predictions with the experimental observations. Furthermore, we visualize the evolution of stretch and damage values in chains oriented along different directions to assess the predictive capacity of the model. The results are also compared with another existing model to evaluate the utility of our model in accurately simulating the fracture behavior of rubber‐like materials.

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Steady-state crack growth in rubber-like solids

Cited by 23 publications

References 57 publications

Dynamic steady-state analysis of crack propagation in rubber-like solids using an extended finite element method

Dynamic steady-state analysis of crack propagation in rubber-like solids using an extended finite element method

Finite strain fracture analysis using the extended finite element method with new set of enrichment functions

A multiscale anisotropic polymer network model coupled with phase field fracture

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