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arxiv: 2606.03816 · v1 · pith:K7SKXEKBnew · submitted 2026-06-02 · 💻 cs.CE

Learning finite viscoelasticity with DAVIS: A supervised framework for generalized standard materials

Simon Wiesheier , Paul Steinmann , Miguel Angel Moreno-Mateos This is my paper

Pith reviewed 2026-06-28 07:50 UTC · model grok-4.3

classification 💻 cs.CE
keywords finite viscoelasticitydata-driven modelingspline interpolationparameter identificationgeneralized standard materialsnon-equilibrium branchesstaggered optimizationDAVIS framework
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The pith

A staggered block-alternating optimization in DAVIS decouples interpolation domains from spline coefficients to remove scaling ambiguities that impair conditioning in viscoelastic inverse problems.

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

The paper revisits the DAVIS spline-based formulation for finite viscoelasticity in the generalized standard materials framework and introduces two targeted changes to better capture non-equilibrium branches in generalized Maxwell-type models. Curvature-based variables replace the original spline representation so that monotonicity and convexity hold by construction through a smooth mapping of parameters. The adaptation of interpolation domain endpoints is moved to an outer loop that uses statistics of sampled invariants, while spline coefficients are fitted in an inner loop for fixed domains. This separation addresses an inherent scaling ambiguity between domains and coefficients. The approach is tested on homogeneous uniaxial loading-unloading paths within the Reese-Govindjee finite-strain viscoelasticity model, with the goal of making parameter identification via finite-element model updating more robust.

Core claim

The central claim is that expressing the spline representation through curvature-based variables and employing a staggered, block-alternating strategy for domain endpoints and coefficients together improve the robustness and identifiability of non-equilibrium branches while preserving thermodynamic consistency and the underlying Reese-Govindjee constitutive structure.

What carries the argument

The staggered block-alternating strategy that optimizes spline coefficients for fixed interpolation domains in an inner loop and updates domain endpoints in an outer loop based on smooth statistics of sampled invariants.

If this is right

  • The curvature reformulation automatically satisfies monotonicity and convexity requirements without additional constraints during optimization.
  • Decoupling domain adaptation removes the scaling ambiguity that previously impaired numerical conditioning in viscoelastic parameter identification.
  • The method remains compatible with finite-element model updating while retaining thermodynamic consistency of the generalized standard materials setting.
  • Non-equilibrium branch parameters become more reliably identifiable from loading-unloading response data.

Where Pith is reading between the lines

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

  • The same staggered separation of domain and coefficient fitting could be applied to other spline-based constitutive models outside viscoelasticity.
  • Extending the assessment to full-field heterogeneous deformation data would test whether the improved conditioning translates to more complex inverse problems.
  • The curvature-based parameterization might reduce the need for manual tuning of interpolation ranges in related data-driven material identification tasks.

Load-bearing premise

Homogeneous uniaxial loading-unloading tests supply sufficient information to demonstrate identifiability and robustness of the non-equilibrium branches in general cases.

What would settle it

Failure to recover consistent, physically plausible non-equilibrium parameters on multi-axial or inhomogeneous deformation data would indicate that the staggered strategy does not resolve the conditioning issues beyond the tested homogeneous cases.

Figures

Figures reproduced from arXiv: 2606.03816 by Miguel Angel Moreno-Mateos, Paul Steinmann, Simon Wiesheier.

Figure 1
Figure 1. Figure 1: Schematic overview of the proposed extensions to the DAVIS framework. (a) Curvature-based spline representation of the constitutive functions, in which convexity and monotonicity are enforced by construction through non-negative curvature coefficients and boundary slopes. (b) Block-alternating identification strategy, separating the optimization of spline parameters from the adaptation of the interpolation… view at source ↗
Figure 2
Figure 2. Figure 2: Multi-start robustness study. Final objective values obtained from a deterministic tensor grid of initializations for the original value-based DAVIS formulation and for the proposed method. The value-based formulation exhibits a pronounced spread of final objective values, whereas enhanced DAVIS consistently converges to the same solution. 4.1 Original DAVIS formulation exhibits robustness limitations As a… view at source ↗
Figure 3
Figure 3. Figure 3: Calibration results for a model with two Maxwell elements and n = 5 spline coefficients per scalar constitutive function. (a) Rheological schematic. (b) Stress–stretch curves for both datasets together with the identified model response. (c) Identified constitutive spline functions; rug plots indicate the sampled invariant values obtained from the forward simulation with the calibrated model, and the soft-… view at source ↗
Figure 4
Figure 4. Figure 4: Validation against unseen experimental data. Comparison of the numerical predictions obtained with the learned constitutive functions from Figure 3b and the experimental loading–unloading data of VHB Tape 4910 from [65] (not included during calibration) for different maximum stretches λmax = {1.5, 2.0, 2.5} and stretch rates λ˙ max = {0.01, 0.03, 0.05} s −1 . The equilibrium branch remains essentially unch… view at source ↗
Figure 5
Figure 5. Figure 5: Calibration results for the same rheological structure as in [PITH_FULL_IMAGE:figures/full_fig_p019_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Calibration results for a model with five Maxwell elements and n = 5 spline coefficients per scalar constitutive function. (a) Rheological schematic. (b) Stress–stretch curves for both datasets together with the identified model response. (c) Identified constitutive spline functions; rug plots indicate the sampled invariant values and markers denote the soft-maximum targets for the adaptive domain endpoint… view at source ↗
Figure 7
Figure 7. Figure 7: Calibration results for a highly overparameterized model with five Maxwell elements and n = 20 spline coefficients per scalar constitutive function. (a) Rheological schematic. (b) Stress–stretch curves for both datasets together with the identified response. (c) Identified constitutive spline functions and sampled invariant values. (d) Evolution of the adaptive domain endpoints. The macroscopic response re… view at source ↗
Figure 8
Figure 8. Figure 8: Sparsity analysis. (a) Heat map of the branch activity measures along the sparsity path for all five Maxwell elements. (b) Data loss Jdata as a function of λsparse together with the corresponding number of active Maxwell branches. and a branch is classified as active if Aα maxk Ak > εact, εact = 10−3 . The results are shown in [PITH_FULL_IMAGE:figures/full_fig_p022_8.png] view at source ↗
read the original abstract

This work revisits the recently proposed data-adaptive viscoelasticity (DAVIS) framework, a spline-based formulation of finite viscoelasticity within the generalized standard materials setting. DAVIS enables a data-driven representation of equilibrium and non-equilibrium constitutive functions while retaining thermodynamic consistency and supporting parameter identification via finite element model updating. The present contribution focuses on improving the robustness and identifiability of non-equilibrium branches in generalized Maxwell-type models. To this end, two extensions of the original formulation are introduced. First, the spline representation is reformulated in terms of curvature-based variables, which is especially convenient to enforce monotonicity and convexity constraints by construction through a smooth parameter mapping. Second, the adaptation of interpolation domains is decoupled from the inner parameter identification by means of a staggered, block-alternating strategy: spline coefficients are optimized for fixed domain endpoints, while the endpoints are updated in an outer loop based on smooth statistics of sampled invariants. This separation alleviates an inherent scaling ambiguity between interpolation domains and spline coefficients that can impair conditioning in viscoelastic inverse problems. The underlying constitutive model remains the finite strain viscoelasticity framework of Reese and Govindjee. The proposed identification strategy is assessed for homogeneous uniaxial loading-unloading tests, which facilitates the study of identifiability and robustness of non-equilibrium branches.

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.

Referee Report

1 major / 0 minor

Summary. The manuscript revisits the DAVIS spline-based formulation of finite viscoelasticity in the generalized standard materials setting, building on the Reese-Govindjee framework. It introduces two extensions: a curvature-based reformulation of the splines to enforce monotonicity and convexity by construction via a smooth mapping, and a staggered block-alternating optimization that fixes domain endpoints while optimizing spline coefficients in an inner loop (with endpoints updated in an outer loop using statistics of sampled invariants). The goal is to resolve a scaling ambiguity between domains and coefficients that impairs conditioning. The strategy is assessed only on homogeneous uniaxial loading-unloading tests for identifiability and robustness of non-equilibrium branches.

Significance. The curvature-based reformulation offers a clean way to embed thermodynamic constraints. If the staggered strategy demonstrably improves conditioning in full finite-element inverse problems with non-homogeneous fields, it would strengthen data-driven identification for viscoelastic materials. The current numerical evidence, however, does not yet establish this benefit.

major comments (1)
  1. [Abstract] Abstract: The central claim that the staggered, block-alternating strategy alleviates an inherent scaling ambiguity that impairs conditioning in viscoelastic inverse problems is not supported by the reported assessment. The assessment uses only homogeneous uniaxial loading-unloading tests, which permit pointwise evaluation of the stress response without a global finite-element solve. Consequently, the mesh-dependent sensitivities, non-homogeneous strain fields, and multiple load cases that would exercise the claimed conditioning problems are never tested.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the detailed and constructive report. The central concern is that the numerical assessment does not yet demonstrate the claimed improvement in conditioning for full finite-element inverse problems. We address this point directly below and indicate the revisions we will make.

read point-by-point responses

  1. Referee: [Abstract] Abstract: The central claim that the staggered, block-alternating strategy alleviates an inherent scaling ambiguity that impairs conditioning in viscoelastic inverse problems is not supported by the reported assessment. The assessment uses only homogeneous uniaxial loading-unloading tests, which permit pointwise evaluation of the stress response without a global finite-element solve. Consequently, the mesh-dependent sensitivities, non-homogeneous strain fields, and multiple load cases that would exercise the claimed conditioning problems are never tested.

    Authors: We agree that the reported assessment is restricted to homogeneous uniaxial loading-unloading tests and therefore does not exercise mesh-dependent sensitivities or non-homogeneous strain fields that arise in full finite-element model updating. The scaling ambiguity between interpolation domains and spline coefficients is already visible in the pointwise identification problem, and the staggered strategy demonstrably improves robustness and convergence behavior in that setting. Nevertheless, the stronger claim that the approach alleviates conditioning issues specifically in viscoelastic inverse problems with non-homogeneous fields is not directly supported by the current experiments. We will revise the abstract and the concluding section to clarify the scope of the numerical study, remove the phrasing that implies full inverse-problem conditioning benefits, and explicitly state that extension to non-homogeneous finite-element cases remains future work. revision: yes

Circularity Check

0 steps flagged

No significant circularity; extensions are independent methodological choices.

full rationale

The paper explicitly retains the Reese-Govindjee finite-strain viscoelasticity framework as its underlying constitutive model via external citation and introduces two new extensions (curvature-based spline variables with smooth monotonicity mapping, and the decoupled staggered block-alternating optimization) as independent contributions. No equation or claim reduces a derived quantity to its own inputs by construction, renames a fitted parameter as a prediction, or relies on a self-citation chain for a uniqueness theorem. The assessment on homogeneous uniaxial tests is presented directly as a means to study identifiability; the derivation chain remains self-contained against the cited external base model without any load-bearing step that equates output to input.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The approach relies on the generalized standard materials framework and Reese-Govindjee finite strain viscoelasticity as background; spline coefficients and domain endpoints are fitted parameters introduced to represent constitutive functions.

free parameters (2)
  • spline coefficients
    Optimized during inner parameter identification loop for fixed domains.
  • domain endpoints
    Updated in outer loop based on smooth statistics of sampled invariants.
axioms (1)
  • domain assumption Thermodynamic consistency of the constitutive model within the generalized standard materials setting
    Retained from the base Reese-Govindjee framework and stated as preserved by the spline representation.

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