Crack Propagation in Finite Elastodynamics

Tarantino, Angelo Marcello

doi:10.1177/1081286505036421

Cited by 25 publications

(32 citation statements)

References 29 publications

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“…Analytic static (Knowles and Sternberg, 1983) and dynamic (Tarantino, 2005) analyses for a class of nonlinear elastic constitutive laws focussed on the large deformation asymptotic region, i.e. well beyond the small displacement-gradients region, and found a 1= ffiffi ffi r p displacement-gradients singularity, similar to that of LEFM.…”

Section: Resultsmentioning

confidence: 94%

“…It is important to note that the weakly nonlinear 1=r displacement-gradients singularity derived in this paper differs from available finite deformation near-tip solutions (Knowles and Sternberg, 1983;Geubelle, 1995;Tarantino, 2005). Analytic static (Knowles and Sternberg, 1983) and dynamic (Tarantino, 2005) analyses for a class of nonlinear elastic constitutive laws focussed on the large deformation asymptotic region, i.e.…”

Section: Resultsmentioning

confidence: 97%

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The 1/r singularity in weakly nonlinear fracture mechanics

Bouchbinder

Livne

Fineberg

2009

Journal of the Mechanics and Physics of Solids

101

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Material failure by crack propagation essentially involves a concentration of large displacement-gradients near a crack's tip, even at scales where no irreversible deformation and energy dissipation occurs. This physical situation provides the motivation for a systematic gradient expansion of general nonlinear elastic constitutive laws that goes beyond the first order displacement-gradient expansion that is the basis for linear elastic fracture mechanics (LEFM). A weakly nonlinear fracture mechanics theory was recently developed by considering displacement-gradients up to second order. The theory predicts that, at scales within a dynamic lengthscale $\ell$ from a crack's tip, significant $\log{r}$ displacements and $1/r$ displacement-gradient contributions arise. Whereas in LEFM the $1/r$ singularity generates an unbalanced force and must be discarded, we show that this singularity not only exists but is {\em necessary} in the weakly nonlinear theory. The theory generates no spurious forces and is consistent with the notion of the autonomy of the near-tip nonlinear region. The J-integral in the weakly nonlinear theory is also shown to be path-independent, taking the same value as the linear elastic J-integral. Thus, the weakly nonlinear theory retains the key tenets of fracture mechanics, while providing excellent quantitative agreement with measurements near the tip of single propagating cracks. As $\ell$ is consistent with lengthscales that appear in crack tip instabilities, we suggest that this theory may serve as a promising starting point for resolving open questions in fracture dynamics.Comment: 12 pages, 2 figure

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Section: Resultsmentioning

confidence: 94%

Section: Resultsmentioning

confidence: 97%

The 1/r singularity in weakly nonlinear fracture mechanics

Bouchbinder

Livne

Fineberg

2009

Journal of the Mechanics and Physics of Solids

101

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“…However, analyses for the crack tip field based on finite strain elastodynamics are still limited. The existing solutions are only on plane stress cracks with incompressible neo-Hookean [25], or compressible neo-Hookean and Mooney-Rivlin material models [94,95]. Efforts are needed to extend the elastodynamic crack tip solutions to a wider class of material models (e.g.…”

Section: Summary and Discussionmentioning

confidence: 99%

Crack tip fields in soft elastic solids subjected to large quasi-static deformation — A review

Long

Hui

2015

Extreme Mechanics Letters

127

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We review analytical solutions for the asymptotic deformation and stress fields near the tip of a crack in soft elastic solids. These solutions are based on finite strain elastostatics and hyperelastic material models, and exhibit significantly different characteristics than the classical crack tip field solutions in linear elastic fracture mechanics. Specifically, we summarize some available finite strain crack tip solutions for two dimensional cracks, namely that plane strain, plane stress, and anti-plane shear cracks in a certain class of homogeneous materials. Interface cracks between soft elastic solids and a rigid substrate are also discussed. We focus on incompressible material models with various degrees of strain stiffening effect such as generalized neo-Hookean model, exponentially hardening model and Gent model. We also explored the physical implications of the crack tip fields, and highlighted pitfalls in the applications of these solutions, particularly the J-integral and the distribution of true stress in the deformed configuration which have not been discussed in the literature.

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“…Among components of the tensor W, the rotation α around the X axis and β around the Z axis are recognizable. Using (62), the deformation gradient (25) can be rewritten in the following approximated form: 22…”

Section: Qn Hmentioning

confidence: 99%

Finite Anticlastic Bending of Hyperelastic Solids and Beams

Lanzoni

Tarantino

2017

J Elast

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This paper deals with the equilibrium problem in nonlinear elasticity of hyperelastic solids under anticlastic bending. A three-dimensional kinematic model, where the longitudinal bending is accompanied by the transversal deformation of cross sections, is formulated. Following a semi-inverse approach, the displacement field prescribed by the above kinematic model contains three unknown parameters. A Lagrangian analysis is performed and the compressible Mooney-Rivlin law is assumed for the stored energy function. Once evaluated the Piola-Kirchhoff stresses, the free parameters of the kinematic model are determined by using the equilibrium equations and the boundary conditions. An Eulerian analysis is then accomplished to evaluating stretches and stresses in the deformed configuration. Cauchy stress distributions are investigated and it is shown how, for wide ranges of constitutive parameters, the obtained solution is quite accurate. The whole formulation proposed for the finite anticlastic bending of hyperelastic solids is linearized by introducing the hypothesis of smallness of the displacement and strain fields. With this linearization procedure, the classical solution for the infinitesimal bending of beams is fully recovered.

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Crack Propagation in Finite Elastodynamics

Cited by 25 publications

References 29 publications

The 1/r singularity in weakly nonlinear fracture mechanics

The 1/r singularity in weakly nonlinear fracture mechanics

Crack tip fields in soft elastic solids subjected to large quasi-static deformation — A review

Finite Anticlastic Bending of Hyperelastic Solids and Beams

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