{"id":"54a62af1-9a75-4a62-a945-4e74f11450e5","arxiv_id":"2505.20244","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"A data-driven hyperelastic model and the configurational force method together estimate the J-integral at crack onset for five soft elastomers under equi-biaxial loading.","lead":"Researchers stretched five soft elastomers in two directions at once, each with a pre-cut notch, and measured how and when the cracks began to grow. The study combines these original experiments with a data-driven material model and a crack-tip force method to estimate fracture toughness.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The proposed fracture criterion is not independently validated: FCNF,C values are computed at the experimentally known onset displacement, so the claim that fracture onset is 'predicted' is unsupported.","rationale":"The reader's conditional verdict is well founded. The proposed criterion is central to the paper, yet it is never used predictively: FCNF,C is extracted at the experimentally observed onset, so the claim that onset is 'predicted' is not demonstrated. This is a load-bearing gap, but it is addressable and does not require rejection. The reader's weakest_assumption focused on mesh convergence and the 0.1 mm summation radius; that is a related numerical concern, but even perfect mesh convergence would not establish that FCNF,C is a predictive fracture criterion. Hence I agree partially: the reader's rationale mentions the lack of independent validation, but the stated weakest assumption centers on the numerical estimate. My recommended verdict remains UNCHANGED because the conditional verdict already captures the need for validation, uncertainty quantification, and numerical convergence checks.","tokens_in":27091,"tokens_out":7795,"duration_ms":83780,"concrete_test":"Run a blind validation: for one material (e.g., VHB), use the already calibrated data-adaptive energy function and the reported threshold FCNF,C = 0.4228 N/m. Simulate a different geometry not used in calibration, such as a single-edge-notch specimen or a different initial notch length under equibiaxial (or uniaxial) loading, and compute the grip displacement at which the total configurational force crosses FCNF,C. Perform the corresponding physical experiment at the same 0.01 s^-1 rate and compare predicted versus measured onset displacement; if the mismatch exceeds the run-to-run scatter in Table 1, the criterion is not predictive. A parallel mesh/radius convergence check (halve element size near the tip; vary the summation radius from 0.05 to 0.5 mm) should accompany this test to confirm that the threshold is numerically stable.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim (Section 4.2) is that fracture onset is predicted when the total crack-tip configurational force reaches a critical value FCNF,C, and that FCNF,C is a material toughness measure. What the paper actually shows is weaker: for each material, the FE model is run up to the experimentally measured average displacement at crack onset (Table 1) and FCNF,C is read off at that displacement. The critical values are therefore calibration outputs on the same data from which the constitutive model was also calibrated. No independent experiment or simulation uses FCNF,C to predict onset for a different geometry, loading condition, or crack length; no comparison with an existing toughness measurement is given. In addition, Table 1 shows large run-to-run scatter (e.g., VHB onset displacement 48.8 ± 13.7 mm), but FCNF,C is reported without uncertainty, so even the ranking of the five materials may not be robust. Because the criterion is the paper's central new claim, the missing predictive test is the least secure load-bearing condition; the mesh/radius issue noted by the reader is a contributing numerical concern but would not by itself establish predictivity.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript combines original equi-biaxial fracture experiments on five soft elastomers (Elastosil P7670 at three mixing ratios, Sylgard 184, and VHB 4905) with a data-adaptive hyperelastic constitutive framework and a post-processing Configurational Force Method. The constitutive model represents the isochoric strain energy as B-spline functions of the invariants, calibrated by finite element model updating against DIC displacement fields and reaction forces. The authors then compute the total crack-tip configurational force as an estimator of the J-integral and report critical values at crack onset, proposing a fracture criterion based on a critical configurational force FCNF,C. The paper also provides a public dataset on Zenodo.","tokens_in":27355,"tokens_out":5237,"duration_ms":48460,"significance":"If the quantitative claims are robust, the paper would offer a useful finite-strain alternative to contour-integral J evaluation for soft elastomers under multiaxial loading, and the B-spline data-adaptive constitutive framework is a flexible contribution. The experimental dataset, including full-field DIC data and force-displacement curves for five materials, is a valuable community resource. The authors are transparent about limitations, including the ad hoc I1-only reduction, the directional shortcoming for Elastosil 1:1, and a discrepancy with an earlier value in [52]. However, the central fracture-criterion claim is not independently validated, and the numerical convergence of the reported FCNF,C values is not established.","major_comments":[{"comment":"The proposed fracture criterion in §4.2 is not demonstrated as predictive. The critical values FCNF,C are computed by running each forward simulation up to the experimentally measured average displacement at crack onset (Table 1) and reading off the configurational force at that loading stage. Therefore, FCNF,C is a calibration output on the same experiments used to fit the constitutive model, not a prediction of onset. No test applies FCNF,C to a different geometry, crack length, or loading condition, and no independent toughness comparison is provided. I recommend either an out-of-sample predictive test or a revised framing that presents FCNF,C as a descriptive characterization rather than a fracture criterion.","section":"§4.2, Table 1"},{"comment":"The numerical robustness of FCNF,C is not established. The paper states in §4.2 that nodal configurational forces depend on the FE mesh, yet no mesh-convergence study is reported. Likewise, the choice of a 0.1 mm cylinder radius for summing spurious configurational forces (§4.1) is not justified by a radius-sensitivity study. Since the reported critical values and the material ranking depend on these two numerical choices, a convergence and sensitivity analysis (e.g., two additional mesh densities and radii) is needed before the quantitative values can be relied upon.","section":"§4.1, §4.2"},{"comment":"Uncertainty in the experimentally measured onset displacement is not propagated to FCNF,C. For example, VHB has onset displacement 48.8 ± 13.7 mm and Sylgard 5.6 ± 0.4 mm, but FCNF,C is reported as a single number computed at the mean onset displacement. Because the configurational force is a nonlinear function of displacement, the value at the mean need not equal the mean value, and the ordering of materials (e.g., Sylgard 0.1286 N/m vs Elastosil 1:1 0.2149 N/m) may not be robust. The authors should compute FCNF,C for each experimental repetition and report the distribution, or provide a sensitivity analysis.","section":"Table 1, §4.2"},{"comment":"The data-adaptive constitutive functions are validated only in-sample: the force and displacement errors in Figures 7–11 are on the same biaxial experiments used for calibration. Since the accuracy of the configurational forces depends directly on the constitutive model, an independent check (e.g., prediction of a uniaxial or different biaxial test, or comparison with an independent modulus or toughness measurement) would substantially strengthen the claim. The paper itself acknowledges in §3.4 that the I1-only reduction is ad hoc, which further motivates such a check.","section":"§3.3, §3.4"}],"minor_comments":[{"comment":"The heading contains a typo: “postpocessing” should be “post-processing.”","section":"§3 heading"},{"comment":"The phrase “fracture fracture” appears in the Discussion; one of the two words should be removed.","section":"§5.1"},{"comment":"The word “compreshensive” is misspelled; it should be “comprehensive.”","section":"§3.3"},{"comment":"The term “configurational-forced-based” should be “configurational-force-based.”","section":"§4.2"},{"comment":"The caption lists panels (a), (b.1), and (b.2), but the text refers to panel (c) for the critical-force bar plot; the panel labels should be made consistent.","section":"Figure 12"},{"comment":"The objective function is split across two numbered equations with dangling terms; it would be clearer to present it as a single equation or to explicitly reference the undisplayed remainder.","section":"Eqs. (10)–(11)"}],"recommendation":"major_revision","confidential_remarks":"The experimental and constitutive-modeling contributions are solid and within the scope of the journal. The fracture-criterion claim, however, overreaches the evidence: FCNF,C is evaluated at the experimentally known onset displacement, and no out-of-sample test or independent toughness comparison is provided. The absence of mesh/radius convergence and uncertainty propagation is the main technical gap. I would be comfortable with acceptance only after the framing is corrected or an out-of-sample test is added."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Short version: read this for the experiments, not for the claimed fracture criterion. The equi-biaxial dataset on five elastomers is a real asset, and the data-adaptive hyperelastic calibration looks careful. But the paper says fracture onset is 'predicted' when the total configurational force reaches FCNF,C, and then reads FCNF,C off the simulation at the experimentally observed onset displacement. That is a fit, not a prediction. No independent geometry, crack length, or loading case is used to test the criterion, and no comparison with an established toughness measurement is offered.\n\nWhat is actually new: original force-displacement curves, full-field DIC strain maps, and crack-onset values for five soft elastomers under equibiaxial loading, with the raw data deposited on Zenodo. That alone is a useful contribution. The combination of B-spline hyperelastic energies (their own prior work) with the configurational force method as a J-estimator is a legitimate integration, and the calibration produces force and displacement errors that look small across four repetitions. They are also transparent about the sideways-fracture case: they admit the method predicts the wrong crack direction for Elastosil 1:1 and explain why.\n\nThe main soft spot is the circularity, and it is load-bearing. The constitutive model is calibrated on these same tests, and the critical configurational force is evaluated at the measured onset displacement. So the reported ranking of materials by FCNF,C is a description of the calibration data, not an independent inference. I'd add two smaller issues: there is no mesh or summing-radius convergence study for the configurational force, even though the paper notes nodal forces are mesh-dependent; and the FCNF,C values are reported as points without uncertainty, while Table 1 shows large run-to-run scatter in onset displacement (VHB: 48.8 ± 13.7 mm). The code is also not released.\n\nThese are fixable. An independent validation—e.g., a different specimen geometry or a single-edge notch test—would give the criterion real predictive teeth. A mesh/radius study and propagating the onset scatter into FCNF,C would make the reported numbers credible.\n\nUseful for: experimentalists working on soft fracture who want multiaxial data; computational mechanicians who want a worked example of data-adaptive constitutive fitting with FEMU. It deserves serious peer review, but the review should be conditional and push hard on the predictive test.","headline":"Solid biaxial dataset and a coherent pipeline, but the headline fracture criterion is calibrated to the same onset data and is not yet a prediction.","tokens_in":27886,"tokens_out":1929,"would_cite":true,"duration_ms":19119,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["74B20","74R10","74S05"],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper claims that the magnitude of the total crack-tip configurational force at crack onset gives a finite-strain fracture-toughness criterion for soft elastomers under equi-biaxial loading.","keywords":["configurational forces","fracture toughness","soft elastomers","equi-biaxial loading","hyperelasticity","J-integral","data-driven constitutive modeling","digital image correlation"],"falsifier":"Refine the finite-element mesh near the crack tip and vary the summation radius around 0.1 mm while recomputing the total configurational force at crack onset; if the reported critical values (0.0386 to 0.4228 N/m) change substantially, the proposed fracture criterion is not reliable. An independent check would evaluate the contour J-integral on a Pacman-shaped domain in the same virtual experiments and test whether it equals the summed nodal configurational force.","tokens_in":26910,"feed_emoji":"💥","tokens_out":5032,"duration_ms":46333,"temperature":0.7,"pith_summary":"This paper argues that fracture onset in soft elastomers under equi-biaxial stretching can be predicted by a single computed number: the total configurational force at the crack tip. The authors run equi-biaxial experiments to rupture on five elastomers (Sylgard, three Elastosil blends, and VHB tape) and observe a wide behavioral spectrum, from brittle Sylgard to VHB with crack-tip strains above 150%. They combine these experiments with a data-adaptive B-spline hyperelastic model and a post-processing Configurational Force Method that estimates the J-integral without contour integration. At the experimentally observed crack onset, the critical configurational force values (0.0386 to 0.4228 N/m) rank the materials consistently with their measured total work of fracture. If the criterion holds, the critical configurational force offers a computationally efficient, finite-strain fracture-toughness parameter for soft solids.","feed_headline":"Crack-tip force predicts fracture onset in soft elastomers","feed_subtitle":"Equi-biaxial tests on five elastomers yield critical configurational-force values that rank materials by toughness.","key_machinery":"The framework rests on two components. First, a data-adaptive hyperelastic strain energy density is represented by additive cubic B-spline interpolation over the isochoric invariants \\bar I_1 and \\bar I_2, with interpolation points and values identified by nonlinear least-squares optimization against reaction forces and DIC displacement fields from the biaxial tests; the optimizer consistently set the \\bar I_2 contribution to zero, leaving \\bar I_1-only energy functions. Second, the Configurational Force Method is implemented as a post-processing algorithm: after solving the forward boundary-value problem with the identified energy, the Eshelby stress tensor is computed and integrated against the FE basis-function gradients to produce nodal configurational forces, and the nodal forces inside a 0.1 mm radius cylinder around the crack tip are summed to give the total crack-tip configurational force, which the paper equates with the J-integral.","core_discovery":"The central claim is that the magnitude of the total crack-tip configurational force at crack onset serves as a measure of the material's fracture toughness, leading to a configurational-force-based fracture criterion: fracture onset occurs when the total configurational force reaches a critical value, F_CNF = F_CNF,C. This force is computed by summing nodal configurational forces derived from the Eshelby stress inside a small cylindrical region of radius 0.1 mm around the crack tip, and is presented as a computationally efficient estimate of the J-integral under finite strains and biaxial loading. The authors report F_CNF,C values of 0.0386 N/m for Elastosil 2:1, 0.0994 N/m for Elastosil 8:5, 0.2149 N/m for Elastosil 1:1, 0.1286 N/m for Sylgard, and 0.4228 N/m for VHB. They note that Sylgard's intermediate critical force combined with its low total work of fracture indicates brittle behavior, while VHB's high values mark a highly deformable fracture response. For the sideways-fracturing Elastosil 1:1, the method yields a forward-oriented configurational force, which the authors attribute to the isotropic hyperelastic model lacking anisotropic fracture resistance.","pith_inferences":["Because the paper states that nodal configurational forces depend on the FE mesh yet reports no mesh-convergence study, the specific F_CNF,C values should be treated as provisional until a denser-mesh verification stabilizes them.","A natural next experiment would be to apply the same B-spline calibration to uniaxial or shear data and test whether the resulting \\bar I_1-only energy reproduces the biaxial force-displacement curves, which would probe the transferability of the data-adaptive model across loading modes.","The reported consistency between F_CNF,C and total work of fracture suggests that the method could rank fracture toughness in other soft solids, but the directional limitation seen in Elastosil 1:1 implies that the magnitude, not the crack-growth direction, is the trustworthy output for isotropic models.","Comparing F_CNF,C against an independent contour J-integral evaluated on the same finite-element solution would directly test whether the 0.1 mm summation radius is the load-bearing numerical choice."],"forward_implications":["Fracture onset under biaxial loading could be predicted without contour integration or crack-growth simulation by stopping at the loading stage where the total configurational force reaches the material's critical value.","The reported critical values provide a finite-strain toughness ranking across a stiffness range of roughly 5 to 350 kPa, with VHB about eleven times tougher than Elastosil 2:1 by this measure.","The data-adaptive optimization identifies \\bar I_1-only energy functions as sufficient for the biaxial constitutive response of these elastomers, supporting simpler calibrations for this class of materials.","The same virtual testbed could be reused for non-equi-biaxial loading paths and, with added anisotropic fracture resistance, for post-onset crack propagation predictions."],"supporting_citations":[{"why":"Establishes the mathematical equivalence between the J-integral and the crack-tip configurational force using Pacman-shaped domains, providing the theoretical basis for the fracture criterion.","marker":"[52]"},{"why":"Supplies the computational setting for computing nodal configurational forces from the discretized Eshelby stress tensor.","marker":"[53]"},{"why":"Introduces the practice of summing spurious configurational forces in a region around the crack tip, which the paper adopts with a 0.1 mm radius cylinder.","marker":"[55]"},{"why":"Develops the data-adaptive hyperelastic energy framework that the present work extends to biaxial experiments and fracture assessment.","marker":"[98]"},{"why":"Provides the discrete data-adaptive approximation of hyperelastic energy functions underlying the B-spline calibration methodology.","marker":"[99]"},{"why":"Documents the Elastosil material variants, their crosslinking-dependent fracture behavior, and the sideways cracking mechanism used to interpret the Elastosil 1:1 results.","marker":"[45]"},{"why":"Supports the finding that \\bar I_1-only models can adequately capture multiaxial behavior, which the optimizer's deactivation of \\bar I_2 corroborates.","marker":"[104]"}],"fun_headline_variants":["Configurational force at crack tip predicts fracture onset","Critical crack-tip force sets fracture toughness in elastomers","Biaxial tests yield critical configurational force for fracture onset","Crack-tip configurational force predicts fracture in soft solids","New fracture criterion for soft elastomers uses crack-tip force"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The numerical estimate of the total configurational force equals the true J-integral for the chosen mesh and the 0.1 mm summation radius, an equality inherited from prior work rather than demonstrated by a convergence study in this paper.","fun_headline_variants_meta":{"raw":{"variants":["Configurational force at crack tip predicts fracture onset","Critical crack-tip force sets fracture toughness in elastomers","Biaxial tests yield critical configurational force for fracture onset","Crack-tip configurational force predicts fracture in soft solids","New fracture criterion for soft elastomers uses crack-tip force"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000888,"raw_usage":{"total_tokens":3907,"prompt_tokens":1097,"completion_tokens":2810,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":713,"completion_tokens_details":{"reasoning_tokens":2726}},"tokens_in":713,"tokens_out":2810,"duration_ms":19420,"temperature":1.0,"reasoning_tokens":2726,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-07T13:56:26.790695+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Refine the finite-element mesh near the crack tip and vary the summation radius around 0.1 mm while recomputing the total configurational force at crack onset; if the reported critical values (0.0386 to 0.4228 N/m) change substantially, the proposed fracture criterion is not reliable. An independent check would evaluate the contour J-integral on a Pacman-shaped domain in the same virtual experiments and test whether it equals the summed nodal configurational force.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Introduces the practice of summing spurious configurational forces in a region around the crack tip, which the paper adopts with a 0.1 mm radius cylinder."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Develops the data-adaptive hyperelastic energy framework that the present work extends to biaxial experiments and fracture assessment."},{"cited_title":"& Steinmann, P","cited_arxiv_id":null,"evidence_quote":"Provides the discrete data-adaptive approximation of hyperelastic energy functions underlying the B-spline calibration methodology."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Documents the Elastosil material variants, their crosslinking-dependent fracture behavior, and the sideways cracking mechanism used to interpret the Elastosil 1:1 results."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supports the finding that \\bar I_1-only models can adequately capture multiaxial behavior, which the optimizer's deactivation of \\bar I_2 corroborates."}],"review_version":1}