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arxiv: 2605.10961 · v1 · submitted 2026-05-06 · ❄️ cond-mat.soft · cond-mat.mtrl-sci

Recognition: 2 theorem links

· Lean Theorem

A Guide to Fully Characterize the Fracture Properties of Cementitious Materials from Simple Experiments

Subhrangsu Saha , Bruce J. Moore , Ben Manaugh , Jeffery R. Roesler , Oscar Lopez-Pamies
Authors on Pith no claims yet

Pith reviewed 2026-05-13 06:04 UTC · model grok-4.3

classification ❄️ cond-mat.soft cond-mat.mtrl-sci
keywords fracture characterizationcementitious materialsuniaxial compressionBrazilian testwedge split testfracture toughnessstrength surfacequasi-static loading
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The pith

Three simple experiments measure the elasticity, strength surface, and toughness that govern fracture nucleation and propagation in cementitious structures under monotonic quasi-static loads.

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

The paper proposes a minimal set of three laboratory tests that together extract the macroscopic properties needed to forecast when and where cracks will form and grow in any cementitious structure. A uniaxial compression test on a cylinder supplies the elastic constants and compressive strength. A Brazilian disk test supplies the tensile strength, which together with the compressive value permits an interpolated strength surface such as a Drucker-Prager fit. A wedge-split test on a notched cube supplies the fracture toughness. Direct comparisons with four-point and three-point bending of both notched and unnotched beams confirm that these three quantities are sufficient to predict observed fracture behavior, provided length scales remain separated.

Core claim

The elasticity, strength surface, and fracture toughness measured from uniaxial cylinder compression, Brazilian splitting, and wedge splitting on notched cubes are sufficient to predict the nucleation and propagation of fracture for any structure made of cementitious materials under arbitrary monotonic quasi-static loading, granted separation of length scales.

What carries the argument

The three-property characterization consisting of elastic constants and compressive strength from cylinder compression, interpolated strength surface from compressive plus tensile strengths, and fracture toughness from wedge splitting.

Load-bearing premise

That interpolating between only the uniaxial compressive and tensile strengths reliably supplies the full strength surface, and that length-scale separation ensures these macroscopic properties alone control structural fracture.

What would settle it

A monotonic quasi-static test on a cementitious structure whose observed crack nucleation or propagation path deviates from the prediction obtained by feeding the three measured properties into a standard fracture model.

Figures

Figures reproduced from arXiv: 2605.10961 by Ben Manaugh, Bruce J. Moore, Jeffery R. Roesler, Oscar Lopez-Pamies, Subhrangsu Saha.

Figure 1
Figure 1. Figure 1: Schematics of the geometry of the specimen and the applied loading for the proposed test to extract the Young’s modulus E, the Poisson’s ratio ν, and the uniaxial compressive strength σcs. The figure also includes a picture of the setup for the tests performed on mortar (H = 30 cm, Hg = 15 cm, and R = 7.5 cm). 0 10 20 30 40 50 60 0 5 10-4 1 10-3 1.5 10-3 2 10-3 2.5 10-3 Experiment Theory 1 0.5 0 [PITH_FUL… view at source ↗
Figure 2
Figure 2. Figure 2: Response from three uniaxial compression tests on mortar. The results show the global stress S = P/(πR2 ) versus the axial strain −(hg − Hg)/Hg and an image of one of the specimens after crack nucleation at S = Smax. For direct comparison, the corresponding predictions generated from the phase-field theory (5)-(6) are also included [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: illustrates the specimen geometry and loading conditions for the second proposed test, a Brazil￾ian test on a disk of height H and radius R ≥ 1.5H using flat platens, which was similarly selected for its practical advantages. Introduced by Lobo Carneiro [24] in the 1940s, the Brazilian test has become a popular test for indi￾rectly probing the tensile strength not only of cementitious materials, but also r… view at source ↗
Figure 4
Figure 4. Figure 4: Response from four Brazilian tests on mortar. The results show the global stress S = P/(πRH) versus the global strain u/R and an image of one of the specimens after crack nucleation at S = Smax. For direct comparison, the corresponding predictions generated from the phase-field theory (5)-(6) are also included [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Schematics of the geometry of the specimen and the applied loading (φ = 10◦ ) for the proposed test to extract the fracture toughness Gc. The figure also includes a picture of the setup for the tests performed on mortar (L = H = D = 25 cm, Ln = 4.8 cm, Hn = 2.5 cm, ln = 0.4 cm, A = 7.5 cm). 0 1 2 3 4 0 5 10 15 20 25 30 35 40 Experiment Theory (w/o friction) 1 0.5 0 Front Back [PITH_FULL_IMAGE:figures/full… view at source ↗
Figure 6
Figure 6. Figure 6: Response from one of the wedge split tests on mortar. The results show the global vertical force PV versus the horizontal displacement u, measured at both the front and back faces, and a close-up image of the crack growth on the front face at u = 40 µm. For direct comparison, the corresponding predictions generated from the phase-field theory (5)-(6) are also included for the idealized case when there is n… view at source ↗
Figure 7
Figure 7. Figure 7: Predictions generated from the phase-field theory (5)-(6) for the crack growth in the wedge split tests on mortar. The line plot presents the crack length a, at the center and at the front and back faces of the specimen, as a function of the horizontal displacement u, while the contour plot shows the phase field v at u = 40 µm, over the right half of the specimen for better visualization. For comparison, a… view at source ↗
Figure 8
Figure 8. Figure 8: Schematics of the geometry of the unnotched (L = 40 cm, H = D = 7.5 cm) and notched (L = 40 cm, H = D = 7.5 cm, A = 2.5 cm, ln = 0.4 cm) beams and the four-point (Ls = 30 cm, Ll = 10 cm) and three-point (Ls = 30 cm) bending applied to them. 12 [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Comparison between the theoretical phase-field predictions — based on the material properties (E, ν, σcs, σts, Gc) extracted from the tests proposed in Section 2 — and the experimental results for four-point bending tests on unnotched mortar beams. The line plot presents the global stress S = 3P(Ls − Ll)/(DH2 ) versus the applied displacement u, while the images show select beams immediately before (simula… view at source ↗
Figure 10
Figure 10. Figure 10: Comparison between the theoretical phase-field predictions — based on the material properties (E, ν, σcs, σts, Gc) extracted from the tests proposed in Section 2 — and the experimental results for three-point bending tests on unnotched mortar beams. The line plot presents the global stress S = 3P Ls/(2DH2 ) versus the applied displacement u, while the images show select beams immediately before (simulatio… view at source ↗
Figure 11
Figure 11. Figure 11: Comparison between the theoretical phase-field predictions — based on the material properties (E, ν, σcs, σts, Gc) extracted from the tests proposed in Section 2 — and the experimental results for three-point bending tests on notched mortar beams. The line plot presents the force P versus the applied displacement u, while the images show select beams immediately before (simulation) and after complete fail… view at source ↗
read the original abstract

Guided by recent advances in the understanding of nucleation and propagation of fracture in elastic brittle materials, this paper proposes a suite of three simple experiments that permit the measurement of the three macroscopic material properties governing when and where cracks nucleate and propagate in structures made of cementitious materials that are subjected to arbitrary monotonic quasi-static loading conditions. The first experiment is that of the uniaxial compression of a cylindrical specimen, which enables the extraction of the elastic properties -- namely, the Young's modulus and Poisson's ratio -- as well as the uniaxial compressive strength. The second experiment is the Brazilian fracture test, performed with flat platens on a material disk to determine the uniaxial tensile strength. Having knowledge of the uniaxial compressive and uniaxial tensile strengths then allows for the estimation of the strength surface of the material via interpolation (e.g., a Drucker-Prager fit). Finally, the third experiment is the wedge split test on a notched cube, which yields the fracture toughness. We demonstrate by means of direct comparisons with four-point and three-point bending tests on both unnotched and notched beams made of a 3D-printable mortar mixture that the elasticity, strength, and toughness properties obtained from the proposed tests are sufficient to predict the nucleation and propagation of fracture for any structure (granted separation of length scales) made of cementitious materials under any monotonic quasi-static loading condition.

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

3 major / 3 minor

Summary. The paper claims that three simple experiments suffice to extract the full set of macroscopic properties (Young's modulus E, Poisson's ratio ν, uniaxial compressive strength f_c, uniaxial tensile strength f_t, and mode-I fracture toughness K_Ic) needed to predict crack nucleation and propagation in any cementitious structure under monotonic quasi-static loading, provided length-scale separation holds. Uniaxial compression of a cylinder yields E, ν and f_c; the Brazilian disk test yields f_t; these two strengths are used to fit a Drucker-Prager (or similar) strength surface; and the wedge-split test on a notched cube yields K_Ic. Direct comparisons with three- and four-point bending tests (notched and unnotched) on a 3D-printable mortar are presented as validation that the extracted parameters are predictive.

Significance. If the central claim is substantiated, the work supplies a practical, low-complexity protocol for obtaining the minimal parameter set required for predictive fracture modeling of cementitious materials, which would be valuable for both research and engineering practice. The direct experimental comparisons to bending configurations provide concrete evidence that the proposed tests recover consistent elasticity, strength and toughness values. The approach also avoids circularity by deriving all quantities from independent measurements.

major comments (3)
  1. [strength-surface estimation section] § on strength-surface estimation (following the Brazilian-test description): the assertion that a Drucker-Prager surface fitted exclusively to the two uniaxial strengths f_c and f_t is adequate for arbitrary multiaxial stress states is load-bearing for the claim of applicability to 'any structure.' The validation experiments are confined to beam bending, in which the tensile zone remains essentially uniaxial and the compressive zone stays below f_c; no direct check is provided for biaxial compression, pure shear, or confined regimes where cementitious materials commonly deviate from Drucker-Prager. This leaves the generality of the interpolated surface untested.
  2. [Methods paragraph on Drucker-Prager fit] Methods paragraph describing the Drucker-Prager fit: the manuscript provides only limited detail on the precise fitting procedure, the choice of internal-friction parameter, and any post-processing or outlier rejection applied to the strength data. Without these specifics it is difficult to reproduce the surface or to quantify the interpolation error that would propagate into nucleation predictions for general geometries.
  3. [Validation section] Validation section (comparisons with four-point and three-point bending): while the reported load-displacement and crack-path agreement is encouraging, these tests do not exercise the full strength surface under the combined shear and confinement conditions that arise in many practical structures (shear walls, anchors, plates). Consequently the evidence does not yet fully support the claim that the three-test suite is sufficient for fracture prediction 'under any monotonic quasi-static loading condition.'
minor comments (3)
  1. [Notation] Notation for the fitted strength surface parameters should be introduced explicitly and used consistently when the surface is later invoked in the fracture simulations.
  2. [Figure of wedge-split test] Figure showing the wedge-split geometry would benefit from an additional panel or annotation clarifying the exact notch depth and loading platen contact conditions used in the experiments.
  3. [Discussion] A short discussion or reference to the known limitations of Drucker-Prager for concrete (e.g., under biaxial compression) would help readers assess the range of applicability.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and insightful comments, which help clarify the scope and limitations of our proposed protocol. We address each major point below and will revise the manuscript accordingly to improve clarity and precision without overstating the generality of the results.

read point-by-point responses

  1. Referee: [strength-surface estimation section] § on strength-surface estimation (following the Brazilian-test description): the assertion that a Drucker-Prager surface fitted exclusively to the two uniaxial strengths f_c and f_t is adequate for arbitrary multiaxial stress states is load-bearing for the claim of applicability to 'any structure.' The validation experiments are confined to beam bending, in which the tensile zone remains essentially uniaxial and the compressive zone stays below f_c; no direct check is provided for biaxial compression, pure shear, or confined regimes where cementitious materials commonly deviate from Drucker-Prager. This leaves the generality of the interpolated surface untested.

    Authors: We agree that a Drucker-Prager surface fitted only to uniaxial strengths represents a standard engineering approximation rather than a complete multiaxial characterization, and that cementitious materials can exhibit deviations under confinement or shear. The manuscript presents this fit as one possible interpolation method when only the two uniaxial strengths are available. The bending validations confirm predictive capability for the stress states encountered there. In revision, we will add explicit discussion of the approximation's limitations and note that for regimes outside the validated range, additional multiaxial tests could be used to refine the surface. This preserves the practical value of the three-test suite while avoiding overgeneralization. revision: partial

  2. Referee: Methods paragraph describing the Drucker-Prager fit: the manuscript provides only limited detail on the precise fitting procedure, the choice of internal-friction parameter, and any post-processing or outlier rejection applied to the strength data. Without these specifics it is difficult to reproduce the surface or to quantify the interpolation error that would propagate into nucleation predictions for general geometries.

    Authors: We thank the referee for highlighting the need for greater reproducibility. The original description was intentionally concise, but we acknowledge that more detail is required. In the revised manuscript, we will expand the Methods section to include the exact Drucker-Prager parameter relations (friction angle and cohesion derived directly from the ratio f_c/f_t), confirmation that no outlier rejection was applied due to consistent specimen data, and the equations used for the fit. This will allow full reproduction and error assessment. revision: yes

  3. Referee: Validation section (comparisons with four-point and three-point bending): while the reported load-displacement and crack-path agreement is encouraging, these tests do not exercise the full strength surface under the combined shear and confinement conditions that arise in many practical structures (shear walls, anchors, plates). Consequently the evidence does not yet fully support the claim that the three-test suite is sufficient for fracture prediction 'under any monotonic quasi-static loading condition.'

    Authors: The referee is correct that the chosen validation configurations primarily involve near-uniaxial tension and compression. These tests were selected as they are standard for assessing fracture in cementitious materials and directly compare nucleation and propagation predictions. While they support the protocol for such cases, they do not cover all multiaxial conditions. We will revise the abstract, introduction, and conclusions to moderate the language, stating that the extracted parameters enable predictive modeling for monotonic quasi-static loading in geometries where the stress states align with the validated regime and the Drucker-Prager approximation holds. The core claim regarding the minimal parameter set from fracture mechanics principles remains intact. revision: partial

Circularity Check

0 steps flagged

No significant circularity; measurements and predictions remain independent

full rationale

The paper extracts Young's modulus, Poisson's ratio, and compressive strength directly from uniaxial cylinder compression, tensile strength from the Brazilian disk test, and fracture toughness from the wedge-split test. These measured values are then inserted into a standard Drucker-Prager interpolation (fitted only to the two uniaxial strengths) and a fracture-mechanics model to generate predictions for separate four-point and three-point bending specimens. Because the validation data are distinct experiments whose outcomes are not used in any fitting step, and because the central claim rests on externally established fracture-mechanics relations rather than self-referential definitions or load-bearing self-citations, no derivation step reduces to its own inputs by construction.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on the elastic-brittle model and the assumption that two uniaxial strengths suffice to define the entire strength surface via a chosen interpolation function, plus the length-scale separation condition.

free parameters (1)
  • Drucker-Prager fit parameters
    The strength surface is estimated via interpolation (e.g., Drucker-Prager) from the measured uniaxial compressive and tensile strengths.
axioms (2)
  • domain assumption The material behaves as an elastic brittle solid under monotonic quasi-static loading
    Guided by recent advances in the understanding of nucleation and propagation of fracture in elastic brittle materials.
  • domain assumption Separation of length scales between material and structure
    The prediction holds granted separation of length scales.

pith-pipeline@v0.9.0 · 5564 in / 1285 out tokens · 175340 ms · 2026-05-13T06:04:41.215757+00:00 · methodology

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Reference graph

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