Application of the virtual fields method to mechanical characterization of elastomeric materials

Promma, Nattawit; Raka, Bumedijen; Grédiac, Michel; Toussaint, Evelyne; Cam, Jean‐Benoît Le; Balandraud, Xavier; Hild, François

doi:10.1016/j.ijsolstr.2008.09.025

Cited by 85 publications

(89 citation statements)

References 22 publications

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“…This stress term is expressed by the first Piola-Kirchoff stress and thus the integration domain of the PVW is based on the initial surface area of the specimen S 0 . A similar VFM has been used for static tests on rubbers [14]. The PVW of the nonlinear VFM with one of the virtual fields from Eq.…”

Section: Nonlinear Vfmmentioning

confidence: 99%

The dynamic Virtual Fields Method on rubbers at medium and high strain rates

Yoon

Siviour

2015

EPJ Web of Conferences

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Abstract. Elastomeric materials are widely used for energy absorption applications, often experiencing high strain rate deformations. The mechanical characterization of rubbers at high strain rates presents several experimental difficulties, especially associated with achieving adequate signal to noise ratio and static stress equilibrium, when using a conventional technique such as the split Hopkinson pressure bar. In the present study, these problems are avoided by using the dynamic Virtual Fields Method (VFM) in which acceleration fields, clearly generated by the non-equilibrium state, are utilized as a force measurement with in the frame work of the principle of virtual work equation. In this paper, two dynamic VFM based techniques are used to characterise an EPDM rubber. These are denoted as the linear and nonlinear VFM and are developed for (respectively) medium (drop-weight) and high (gas-gun) strain-rate experiments. The use of the two VFMs combined with high-speed imaging analysed by digital imaging correlation allows the identification of the parameters of a given rubber mechanical model; in this case the Ogden model is used.

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Section: Nonlinear Vfmmentioning

confidence: 99%

The dynamic Virtual Fields Method on rubbers at medium and high strain rates

Yoon

Siviour

2015

EPJ Web of Conferences

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“…Such experiments provide useful tools in mechanical engineering to accurately inspect the behaviour of a material [15]. Furthermore, Promma et al [14] have found that the displacement gradient ∇u associated with such a motion shows a non-constant behaviour in space, which implies that the motion is sufficiently complex for our needs. We use the two areas of interest in Figure 1 as our images f 1 and f 2 and solve the extended optical flow problem.…”

Section: Experimental Evaluationmentioning

confidence: 99%

Lagrangian Strain Tensor Computation with Higher Order Variational Models

Hewer¹,

Weickert²,

Seibert³

et al. 2013

Procedings of the British Machine Vision Conference 2013

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The reliable estimation of the Lagrangian stress tensor from an image sequence is a challenging problem in mechanical engineering. Since this tensor involves first order motion derivatives, it appears tempting to estimate the optical flow field with a highly accurate variational model and compute its derivatives afterwards. In this paper we explain why this idea is inappropriate due to lower order smoothness assumptions and the ill-posedness of differentiation. As a remedy, we propose a variational framework that performs higher order regularisation of the optical flow field and directly computes the Lagrangian stress tensor from the image measurements. Due to its recursive structure, this framework is very generic. It can incorporate smoothness assumptions of arbitrary high order and allows to compute derivatives of any desired order in a stable way. With a biaxial tensile experiment with an elastomer we demonstrate that our novel approach gives substantially better results for the Lagrangian stress tensor than computing derivatives of the optical flow field. Moreover, it also outperforms a frequently used commercial software that marks the state-of-the-art for Lagrangian stress tensor computation.

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“…The Virtual Fields Method (VFM) is an approach dedicated to the identification of material parameters from full-field measurements [11][12][13]18]. The principle may be summarized in two steps:…”

Section: Inverse Approachmentioning

confidence: 99%

“…The choice of virtual fields was largely discussed in the literature [11][12][13]18], but only when the VFM is applied in infinitesimal deformation conditions. No rule has been established for finite deformations.…”

Section: Inverse Approachmentioning

confidence: 99%

Inverse methods for characterizing the anisotropic hyperelastic behaviour of arteries in vitro

Avril

Badel

Genovese

2010

EPJ Web of Conferences

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Abstract. In this paper, we present a bi-axial characterization of in vitro human arteries. From the full-field experimental data obtained in inflation/extension tests, an inverse approach, called the virtual fields method (VFM), is used for deriving the material parameters of the tested arterial segment. The obtained results are promising and the approach can effectively provide relevant values for the anisotropic hyperelastic properties of the tested sample.

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Application of the virtual fields method to mechanical characterization of elastomeric materials

Cited by 85 publications

References 22 publications

The dynamic Virtual Fields Method on rubbers at medium and high strain rates

The dynamic Virtual Fields Method on rubbers at medium and high strain rates

Lagrangian Strain Tensor Computation with Higher Order Variational Models

Inverse methods for characterizing the anisotropic hyperelastic behaviour of arteries in vitro

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