Identification of constitutive parameters from full thermal and kinematic fields: application to hyperelasticity

Jean-Benoit Le Cam (IPR); S. Charl\`es (IPR)

arxiv: 1907.02692 · v1 · pith:XXX6GECWnew · submitted 2019-07-05 · ⚛️ physics.class-ph

Identification of constitutive parameters from full thermal and kinematic fields: application to hyperelasticity

S. Charl\`es (IPR) , Jean-Benoit Le Cam (IPR) This is my paper

Pith reviewed 2026-05-25 02:03 UTC · model grok-4.3

classification ⚛️ physics.class-ph

keywords inverse identificationhyperelasticityheat source reconstructionfull field measurementsthermomechanical couplinglarge deformationrubberconstitutive parameters

0 comments

The pith

Matching heat sources reconstructed from temperature and from kinematics identifies hyperelastic parameters at the local scale without boundary conditions.

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

The paper presents a new inverse method that reconstructs the internal heat source in two independent ways from full-field measurements. One reconstruction uses the measured temperature field together with known thermophysical parameters. The other uses the measured deformation field together with a thermo-hyperelastic constitutive model whose parameters are the unknowns. Equating the two reconstructions at each material point yields the parameters directly, without reference to specimen boundaries or applied loads. This matters for testing soft materials under large heterogeneous deformation where boundary data are difficult to control or measure.

Core claim

The identification procedure reconstructs the heat source field once from the temperature measurement and once from the kinematic measurement via the thermo-hyperelastic model; setting the two fields equal at every point determines the model parameters locally and without boundary conditions.

What carries the argument

Dual reconstruction of the volumetric heat source field, one thermal and one kinematic, whose equality supplies the constitutive parameters.

Load-bearing premise

The assumed thermo-hyperelastic model correctly predicts the heat generated by any given deformation.

What would settle it

For a material with independently known hyperelastic parameters, the two independently reconstructed heat-source fields fail to coincide after parameter optimization.

read the original abstract

In this paper, a new inverse identification method is developed from full kinematic and thermal field measurements. It consists in reconstructing the heat source from two approaches, a first one that requires the measurement of the temperature field and the value of the thermophysical parameters, and a second one based on the measurement of the kinematics field and a thermo-hyperelastic model that contains the parameters to be identified. The identification does not require any boundary conditions since it is carried out at the local scale. In the present work, the method is applied to the identification of hyperelastic parameters from a heterogeneous heat source field. Due to large deformation undergone by the rubber specimen tested, a motion compensation technique is developed to plot the kinematic and thermal fields at the same points before reconstructing the heat source.

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 outlines a local heat-source equating procedure for hyperelastic parameter identification that skips boundary conditions, but the abstract supplies no results or checks so the method's reliability stays unproven.

read the letter

The main takeaway is that the authors have outlined a method to identify hyperelastic parameters locally by reconstructing the heat source field in two independent ways and setting them equal. One reconstruction uses the measured temperature field plus known thermophysical properties. The other uses the measured kinematic field plugged into a thermo-hyperelastic model whose parameters are the unknowns. Because everything happens pointwise, no boundary conditions enter the identification. They also describe a motion compensation step to handle the large strains in the rubber specimen so the fields line up. This local matching without boundary conditions is the concrete new element. It could simplify experiments where global conditions are hard to control or measure. The motion compensation part shows they thought through the practical side of applying this to real large-deformation tests. The weak point is the reliance on the thermo-hyperelastic model being accurate. The identification only recovers the right parameters if that model correctly predicts how deformation produces heat in the material. The abstract gives the logic but no numerical results, no comparison to known parameter values, and no sensitivity checks. So the stress-test concern is fair: we cannot yet tell whether the method delivers usable parameters or just reproduces the model's assumptions. If the full paper has those checks, that would change the picture, but based on the description here it is the load-bearing assumption. The paper is aimed at people doing experimental work on hyperelastic materials, especially those interested in full-field measurements and inverse problems. Someone in that area might pick up the local heat-source idea for their own setups. It is not going to change how everyone does materials testing, but it is a targeted improvement. It is worth sending to peer review. The idea is specific enough and the motivation is solid, even if the write-up needs the actual data and validation to stand on its own. A referee could ask for the missing validation steps and see if the numbers check out.

Referee Report

1 major / 1 minor

Summary. The paper develops an inverse identification procedure for hyperelastic constitutive parameters that reconstructs the internal heat source field in two independent ways: (i) from measured temperature fields together with known thermophysical constants, and (ii) from measured kinematic fields inserted into a thermo-hyperelastic constitutive model whose parameters are the unknowns. The two reconstructed source fields are set equal at each material point; the resulting local equations are solved for the unknown parameters. The approach is demonstrated on a rubber specimen undergoing large heterogeneous deformation, for which a motion-compensation scheme is introduced to register the thermal and kinematic fields.

Significance. If the central modeling assumption holds, the method supplies a boundary-condition-free, local-scale route to hyperelastic parameter identification that exploits the coupling between large-strain kinematics and heat generation. Such a capability would be valuable for experimental characterization of soft materials where global force-displacement data are insufficient.

major comments (1)

[Abstract (second reconstruction approach)] The identification procedure is predicated on the thermo-hyperelastic constitutive relation correctly predicting the deformation-induced heat source for the tested rubber. No independent validation, sensitivity study, or comparison against a known hyperelastic model (e.g., via separate isothermal tests) is described; without such evidence the equality of the two heat-source reconstructions cannot be guaranteed to yield the true parameters.

minor comments (1)

[Abstract] The motion-compensation technique is mentioned but its algorithmic details, interpolation scheme, and residual registration error are not quantified; these should be reported to allow assessment of field-alignment uncertainty.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their constructive review. The major comment identifies a key modeling assumption in the identification procedure, which we address point by point below.

read point-by-point responses

Referee: [Abstract (second reconstruction approach)] The identification procedure is predicated on the thermo-hyperelastic constitutive relation correctly predicting the deformation-induced heat source for the tested rubber. No independent validation, sensitivity study, or comparison against a known hyperelastic model (e.g., via separate isothermal tests) is described; without such evidence the equality of the two heat-source reconstructions cannot be guaranteed to yield the true parameters.

Authors: We agree that the procedure assumes the chosen thermo-hyperelastic constitutive relation correctly predicts the deformation-induced heat source. The identification solves for parameters that enforce local equality between the model-based reconstruction (from kinematics) and the independent thermal reconstruction (from temperature fields and known thermophysical properties). The manuscript demonstrates the method on heterogeneous large-deformation data from a rubber specimen but does not report separate isothermal validation tests or sensitivity studies to confirm the heat-source prediction in isolation. The local matching itself constitutes an internal consistency condition under the model assumption. We will revise the manuscript to state this assumption explicitly in the abstract and discussion sections and to outline possible validation routes, such as comparison of identified parameters with those from standard global tests. revision: yes

Circularity Check

0 steps flagged

No significant circularity in the identification chain

full rationale

The method reconstructs the heterogeneous heat source independently from the measured temperature field (using separately measured thermophysical constants) and from the measured kinematic field (via the thermo-hyperelastic constitutive relation whose parameters are the unknowns). Equating the two reconstructed fields then solves for the parameters. This is a standard inverse identification procedure whose central step is the modeling assumption that the chosen constitutive relation correctly links deformation to heat generation; it does not reduce any claimed prediction to an input by construction, nor does it rely on self-citation chains, self-definitional relations, or renaming of known results. The provided abstract and description contain no evidence of the enumerated circularity patterns.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The method rests on the assumption that a thermo-hyperelastic constitutive model correctly links deformation to heat generation and that thermophysical parameters are known a priori; no new entities are postulated.

free parameters (1)

hyperelastic model parameters
These are the quantities the method is designed to identify; their values are adjusted to match the two heat-source fields.

axioms (1)

domain assumption The material obeys a thermo-hyperelastic constitutive relation that links kinematics to internal heat generation
Invoked in the second reconstruction approach described in the abstract.

pith-pipeline@v0.9.0 · 5664 in / 1234 out tokens · 27092 ms · 2026-05-25T02:03:51.510831+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

the heat source is given by: S = N k T (λ + B λ^{B-1} - B + 1 λ^{-B-1}) dλ/dt
IndisputableMonolith/Foundation/AbsoluteFloorClosure.lean absolute_floor_iff_bare_distinguishability unclear

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unclear
Relation between the paper passage and the cited Recognition theorem.

identification does not require any boundary conditions since it is carried out at the local scale

What do these tags mean?

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supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.