Isogeometric analysis of shear bands

Berger-Vergiat, Luc; McAuliffe, Colin; Waisman, Haim

doi:10.1007/s00466-014-1002-8

Cited by 13 publications

(14 citation statements)

References 41 publications

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“…The velocity and temperature fields are discretized with bilinear C 0 continuous functions and the stress and equivalent plastic strain are bilinear C −1 continuous. Details on the numerical implementation can be found in McAuliffe and Waisman [22,69] and Berger-Vergiat et al [21]. Fig.…”

Section: Benchmark Example: 45 • Shear Band Under Uniform Tensionmentioning

confidence: 98%

“…Other regularization techniques reported in the literature include strain gradient theories [10][11][12], which have been used in the context of shear bands in [13][14][15] and nonlocal methods [16][17][18]. Mesh alignment is another form of sensitivity that can be improved using mesh-free formulations [19,20] or Isogeometric analysis [21].…”

Section: Background On Shear Bandsmentioning

confidence: 99%

“…The perturbation method is applied to the governing equations resulting in the fourth-order characteristic equation R(ω) presented in (21). The reader may refer to Appendix B for the full derivation of the characteristic equation.…”

Section: Linear Perturbation Analysis Of the 1d Shear Band Problemmentioning

confidence: 99%

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Onset of shear band localization by a local generalized eigenvalue analysis

Arriaga

McAuliffe

Waisman

2015

Computer Methods in Applied Mechanics and Engineering

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Shear bands are material instabilities associated with highly localized intense plastic deformation zones which can form in materials undergoing high strain rates. Determining the onset of shear band localization is a difficult task and past work reported in the literature attempt to detect this instability by computing the eigenvalues of the acoustic tensor or by studying the linear stability of the perturbed governing equations. However, both methods have their limitations and are not suited for general rate dependent materials in multidimensions.In this work we propose a novel approach to determine the onset of shear band localization and alleviate the limitations of the above mentioned methods.Owing to the implicit mixed finite elements discretization employed in this work, we propose to cast the instability analysis as a generalized eigenvalue problem by employing a particular decomposition of the element Jacobian matrix. We show that this approach is attractive, as it is applicable to general rate dependent multidimensional cases where no special simplifying assumptions ought to be made.To verify the accuracy of the proposed eigenvalue analysis, we first extend an analytical criterion by applying linear perturbation techniques to the continuous PDE model, considering an elastoplastic material with thermal diffusion and a nonlinear Taylor-Quinney coefficient. While this extension is novel on its own, it requires strenuous derivations and is not easily extended to general multidimension applications. Hence, herein it is only used for verification purposes in 1D.Numerical results on one-dimensional problems show that the eigenvalue analysis exactly recovers the instability point predicted by the analytical criterion with non-linear Taylor-Quinney coefficient. In addition, the proposed generalized eigenvalue analysis is applied on two-dimensional problems where propagation of the instability can be easily determined.

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Section: Benchmark Example: 45 • Shear Band Under Uniform Tensionmentioning

confidence: 98%

Section: Background On Shear Bandsmentioning

confidence: 99%

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Onset of shear band localization by a local generalized eigenvalue analysis

Arriaga

McAuliffe

Waisman

2015

Computer Methods in Applied Mechanics and Engineering

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“…[1,33,53] and nonlocal methods [7,23,45]. Mesh alignment is another form of sensitivity that can be improved using mesh-free formulations [35,36] or Isogeometric analysis [16].…”

Section: Introductionmentioning

confidence: 99%

Instability analysis of shear bands using the instantaneous growth-rate method

Arriaga

McAuliffe

Waisman

2016

International Journal of Impact Engineering

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a b s t r a c tShear banding, as an unstable process of localization, is a common precursor to fracture in materials under high strain rate loadings, making the detection of the instability point after which localization will occur of significant importance. Stability analysis based on the perturbation method or the acoustic tensor have been employed. However, these methodologies are limited to certain class of problems and are difficult to generalize.In this work we propose an alternative for identifying the instability point by employing the concept of generalized stability analysis. In this framework, a stability measure is obtained by computing the instantaneous growth rate of the vector tangent to the solution. Such an approach is more appropriate for non-orthogonal problems and is easier to generalize to difficult dynamic fracture problems.Under conditions where the local instability triggers the non-homogeneous solution growth, i.e. problems that are homogeneous until the appearance of local instability, the generalized stability analysis and the modal stability analysis will closely match. Therefore, the non-homogeneous growth can be approximated by the Rayleigh Quotient of the vector tangent to the solution, which is easier to compute.We show that for a particular class of problems that respect the aforementioned conditions, in 1D and 2D examples, both quantities successfully find the instability point predicted analytically and validated experimentally in past literature results. This methodology is general and can be applied to a wide array of dynamic fracture problems, for which instability that leads to localization is important.

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“…In general, the numerical simulation of such coupled systems is complex due to different time-scales associated with thermal and mechanical fields [42]. For solving these equations two numerical integration schemes namely monolithic [43,44,45] and operator splitting [46,47] techniques can be employed. In the operator splitting technique Eq.…”

Section: Governing Thermomechanical Equationsmentioning

confidence: 99%

A non-ordinary state-based peridynamics formulation for thermoplastic fracture

Amani

Öterkuş

Areias

et al. 2016

International Journal of Impact Engineering

153

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In this study, a three-dimensional (3D) non-ordinary state-based peridynamics (NOSB-PD) formulation for thermomechanical brittle and ductile fracture is presented. The Johnson-Cook (JC) constitutive and damage model is used to taken into account plastic hardening, thermal softening and fracture. The formulation is validated by considering two benchmark examples: 1) The Taylor-bar impact and 2) the Kalthoff-Winkler tests. The results show good agreements between the numerical simulations and the experimental results.

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Isogeometric analysis of shear bands

Cited by 13 publications

References 41 publications

Onset of shear band localization by a local generalized eigenvalue analysis

Onset of shear band localization by a local generalized eigenvalue analysis

Instability analysis of shear bands using the instantaneous growth-rate method

A non-ordinary state-based peridynamics formulation for thermoplastic fracture

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