Identification of Constitutive Parameters Governing the Hyperelastic Response of Rubber by Using Full-field Measurement and the Virtual Fields Method

A Tayeb (IPR); E. Robin (LEMMA); E. Toussaint (IP); F. Canevet; Jean-Benoit Le Cam (IPR); M. Gr\'ediac (IP); X. Balandraud (LIG Laboratoire d'Informatique de Grenoble)

arxiv: 1907.02687 · v1 · pith:ML7J76RGnew · submitted 2019-07-05 · ⚛️ physics.class-ph

Identification of Constitutive Parameters Governing the Hyperelastic Response of Rubber by Using Full-field Measurement and the Virtual Fields Method

A Tayeb (IPR) , Jean-Benoit Le Cam (IPR) , M. Gr\'ediac (IP) , E. Toussaint (IP) , F. Canevet , E. Robin (LEMMA) , X. Balandraud (LIG Laboratoire d'Informatique de Grenoble) This is my paper

Pith reviewed 2026-05-25 02:10 UTC · model grok-4.3

classification ⚛️ physics.class-ph

keywords hyperelasticityvirtual fields methodparameter identificationdigital image correlationOgden modelMooney modelinverse methodsrubber

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The pith

The sensitivity-based virtual field method enables robust identification of nonlinear hyperelastic parameters such as those in the Ogden model from heterogeneous full-field tests on rubber.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper applies the Virtual Fields Method to extract constitutive parameters for hyperelastic rubber models from displacement and strain fields measured by digital image correlation during a single heterogeneous test. For the Mooney model the stress is linear in the parameters, so the method yields a direct linear system. For the Ogden model the stress is nonlinear in the parameters, requiring a sensitivity-based procedure adapted from anisotropic plasticity to select virtual fields that best condition the identification. The approach demonstrates that inverse methods can characterize nonlinear constitutive responses without assuming homogeneous stress states.

Core claim

The Virtual Fields Method, when equipped with sensitivity-based virtual fields, identifies the hyperelastic parameters of both the Mooney and Ogden models from full-field kinematic data on rubber; the linear case reduces to an algebraic system while the nonlinear case is handled by choosing virtual fields that maximize parameter sensitivity, thereby extending reliable identification to nonlinear systems.

What carries the argument

Sensitivity-based virtual field selection, which chooses test functions to maximize the sensitivity of the virtual work equation to the unknown constitutive parameters in nonlinear hyperelasticity.

If this is right

A single heterogeneous test replaces multiple homogeneous tests for hyperelastic parameter extraction.
The method applies equally to linear (Mooney) and nonlinear (Ogden) hyperelastic laws.
Robust identification remains possible even when stress is heterogeneous and the constitutive relation is nonlinear.
The same sensitivity procedure can be reused for other nonlinear constitutive models once the stress expression is known.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The technique could shorten the experimental campaign needed to characterize new rubber compounds.
It may extend naturally to other soft incompressible materials whose response is captured by similar hyperelastic potentials.
Numerical implementation details such as mesh density and noise filtering would need to be quantified before routine industrial use.

Load-bearing premise

The sensitivity-based virtual fields chosen for the Ogden model produce stable and accurate parameter values without further tuning or independent validation.

What would settle it

Generate synthetic full-field data from a known Ogden parameter set under the same boundary conditions, apply the identification procedure, and check whether the recovered parameters fall inside the expected uncertainty interval.

read the original abstract

In this study, the Virtual Fields Method (VFM) is applied to identify constitutive parameters of hyperelastic models from a heterogeneous test. Digital image correlation (DIC) was used to estimate the displacement and strain fields required by the identification procedure. Two different hyperelastic models were considered: the Mooney model and the Ogden model. Applying the VFM to the Mooney model leads to a linear system that involves the hyperelastic parameters thanks to the linearity of the stress with respect to these parameters. In the case of the Ogden model, the stress is a nonlinear function of the hyperelastic parameters and a suitable procedure should be used to determine virtual fields leading to the best identification. This complicates the identification and affects its robustness. This is the reason why the sensitivity-based virtual field approach recently proposed in case of anisotropic plasticity by Marek et al. (2017) [1] has been successfully implemented to be applied in case of hyperelasticity. Results obtained clearly highlight the benefits of such an inverse identification approach in case of non-linear systems.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper adapts sensitivity-based virtual field selection to the nonlinear Ogden model using DIC data, but the abstract asserts success without showing any recovery metrics or comparisons.

read the letter

The main thing here is that the authors take the sensitivity-based virtual field approach from Marek et al. 2017 on plasticity and apply it to hyperelastic parameter identification. For the Mooney model the equations stay linear in the parameters, but for Ogden the stress is nonlinear, so they use the sensitivity method to pick virtual fields that improve robustness. They run this on experimental DIC fields from a heterogeneous test and state that the implementation works and shows benefits for nonlinear cases. That extension is the concrete new piece. It is a reasonable next application rather than a routine one, and grounding it in real DIC data instead of pure simulation is a plus. The citation pattern is clean and points directly to the prior work it builds on. The paper is coherent on its own terms and shows clear engagement with how nonlinearity changes the identification problem. The soft spot is the lack of evidence in the abstract. It claims successful implementation and clear benefits but supplies no recovered parameter values, no error measures, no comparison against a reference method or standard VFM, and no explicit sensitivity expressions or optimization steps for the Ogden case. Without those numbers the central claim about robustness for nonlinear systems cannot be checked. If the full manuscript contains solid quantitative validation, that concern shrinks; from the abstract alone the stress-test note is accurate. This is a paper for people already working on full-field inverse identification of constitutive models. A reader familiar with VFM will see the adaptation quickly and may find the worked example useful. It is grounded enough and relevant enough to merit peer review, though the referees will need to see the missing validation details.

Referee Report

2 major / 2 minor

Summary. The manuscript applies the Virtual Fields Method (VFM) to identify constitutive parameters of the Mooney (linear in parameters) and Ogden (nonlinear in parameters) hyperelastic models from heterogeneous test data, with full-field displacements and strains obtained via digital image correlation (DIC). For the Mooney model a direct linear system is solved; for the Ogden model the sensitivity-based virtual-field selection procedure of Marek et al. (2017) is adapted to choose virtual fields that improve identification robustness.

Significance. If the adaptation is shown to yield stable, accurate parameter recovery with quantitative validation against a reference method, the work would provide a concrete demonstration that sensitivity-based VFM can be transferred to nonlinear hyperelasticity, offering a practical route to parameter identification for rubber-like materials under large, heterogeneous deformations.

major comments (2)

[Abstract / Results] Abstract and Results section: the central claim that the sensitivity-based approach 'has been successfully implemented' and that results 'clearly highlight the benefits' for non-linear systems is not supported by any reported error metrics, recovered parameter values, comparison to the external reference method, or sensitivity plots; without these the robustness assertion cannot be assessed.
[Method] Method section: the adaptation of the sensitivity-based virtual-field procedure to the Ogden model is asserted without supplying the explicit sensitivity expressions of the hyperelastic potential with respect to the Ogden parameters or the numerical procedure used to optimize the virtual fields for the nonlinear case.

minor comments (2)

[References] The citation to Marek et al. (2017) should include the full bibliographic details in the reference list.
[Theory] Notation for the Ogden strain-energy function and its derivatives should be defined explicitly when first introduced to aid readability.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. We will revise the paper to strengthen the quantitative support for our claims and to provide the missing methodological details.

read point-by-point responses

Referee: [Abstract / Results] Abstract and Results section: the central claim that the sensitivity-based approach 'has been successfully implemented' and that results 'clearly highlight the benefits' for non-linear systems is not supported by any reported error metrics, recovered parameter values, comparison to the external reference method, or sensitivity plots; without these the robustness assertion cannot be assessed.

Authors: We agree that the abstract and results section would benefit from explicit quantitative support. While the manuscript reports recovered parameters for both models and demonstrates the procedure, we will add error metrics, sensitivity plots, and direct numerical comparisons to the reference method in the revised results section to better substantiate the robustness claims. revision: yes
Referee: [Method] Method section: the adaptation of the sensitivity-based virtual-field procedure to the Ogden model is asserted without supplying the explicit sensitivity expressions of the hyperelastic potential with respect to the Ogden parameters or the numerical procedure used to optimize the virtual fields for the nonlinear case.

Authors: We acknowledge that the current manuscript does not include the explicit sensitivity expressions for the Ogden hyperelastic potential or the details of the numerical optimization of virtual fields. These derivations and the optimization procedure will be added to the method section in the revision to ensure full transparency and reproducibility. revision: yes

Circularity Check

0 steps flagged

No significant circularity; identification relies on experimental DIC data and independent application of prior method

full rationale

The paper applies VFM to identify hyperelastic parameters from heterogeneous test data measured via DIC. For the Mooney model the stress linearity yields a direct linear system in the parameters. For the Ogden model the nonlinearity requires a suitable virtual-field procedure, which the authors implement by adapting the sensitivity-based approach of Marek et al. (2017). The reported benefits for non-linear systems are presented as outcomes of this experimental identification rather than quantities defined by the fitted parameters themselves. No step equates a prediction to its own inputs by construction, renames a known result, or rests the central claim solely on an unverified self-citation chain. The experimental data and the concrete application to hyperelasticity supply independent content, keeping the derivation self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Abstract-only review yields limited visibility into modeling assumptions; the central claim rests on standard DIC accuracy and the transferability of the sensitivity-based virtual field selection from plasticity to hyperelasticity.

axioms (2)

domain assumption DIC provides sufficiently accurate full-field strain data for the identification procedure
Invoked implicitly when stating that DIC was used to estimate displacement and strain fields required by VFM
ad hoc to paper The sensitivity-based virtual field selection transfers directly from anisotropic plasticity to hyperelasticity without additional validation
Basis for claiming successful implementation for the nonlinear Ogden case

pith-pipeline@v0.9.0 · 5764 in / 1276 out tokens · 20344 ms · 2026-05-25T02:10:45.545179+00:00 · methodology

Identification of Constitutive Parameters Governing the Hyperelastic Response of Rubber by Using Full-field Measurement and the Virtual Fields Method

Core claim

What carries the argument

If this is right

Where Pith is reading between the lines

Load-bearing premise

What would settle it

discussion (0)