{"id":"aeada87a-ad47-4f7d-af35-b11dc26f6bc7","arxiv_id":"1908.03078","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"PMMA honeycombs loaded in tension in the creep regime fail by diffuse, scattered strut fractures, and a dispersion in strut ductility, not geometric defects alone, controls this damage-tolerant behavior.","lead":"Experiments on laser-cut PMMA honeycombs pulled in tension near their glass transition temperature show that struts fail one by one at random locations before a single macroscopic crack forms, unlike the sudden brittle cracking at room temperature. The study maps how manufacturing and design defects affect creep strength and shows a surprisingly high tolerance to missing cell walls and solid inclusions.","discovery_kind":"new_application","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The FE model's material ductility dispersion is calibrated from the same lattice-level failure-strain distribution used for validation, so the diffuse-damage mechanism is not independently established.","rationale":"The reader's weakest assumption is exactly the calibration loop I identify: the material ductility dispersion is taken from the measured lattice-level strut failure strain distribution and then used to validate the predicted distribution. This is the most load-bearing point because the paper's central mechanistic claim, that strut-to-strut material ductility variation is essential for diffuse damage, rests on the FE model reproducing diffuse failure only when εfs,sd/εfs is set to 0.4. The value of 0.4 is not independently measured; it is inferred from the same lattice experiments that the FE model is intended to explain. The geometry-only simulation with εfs,sd = 0 provides partial support by showing that geometric defects alone produce a narrow p(ef) and correlated failure, but this does not establish that the true material-level scatter is large enough to control the failure mode. A direct measurement of single-strut failure strain scatter, or a parametric sweep of εfs,sd against experimental observables, would settle whether the diffuse-damage claim is robust or an artifact of the calibration. I therefore agree with the reader's conditional verdict and do not see a reason to change it: the concern is real but not disqualifying, and it is addressable with additional data or simulations.","tokens_in":14915,"tokens_out":4170,"duration_ms":48461,"concrete_test":"Measure the scatter in failure strain of a large number of single strut specimens (same PMMA batch, same laser-cutting parameters, same testing temperature and strain rate, and gauge length comparable to the lattice strut length, or with a size-effect correction). If the directly measured εfs,sd/εfs is substantially smaller than 0.4, re-run the FE model of Section 6.2.1 with that independently measured dispersion and check whether the first-failure strain, the diffuse failure mode, and the predicted p(ef) still match the experiments. If the diffuse mode disappears or the first-failure strain is no longer reproduced, the central mechanism is an artifact of the calibrated input rather than an independently supported material property.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim, articulated in Section 6.2.1, is that 'a dispersion in strut ductility is essential' to produce the observed early strut failure and diffuse damage. The FE model assigns a material ductility dispersion of εfs,sd/εfs = 0.4, explicitly 'taken to equal the measured value ef,sd/ef of strut ductility from Fig. 8.' That measured quantity is the coefficient of variation of effective strut failure strains measured inside the lattice, not the dispersion of the parent material's failure strain measured on isolated struts. The same measured distribution is then used to validate the FE prediction, with the statement that the predicted p(ef) 'is in excellent agreement with the observed distribution, implying that the assumed scatter in material failure strain is of the correct level.' This is a calibration-and-validation loop: the comparison cannot independently confirm the input. The companion FE run with εfs,sd = 0 does provide some evidence that geometric scatter alone yields a narrow p(ef) and a correlated failure mode, so the claim that some material-level dispersion is required has partial support. However, the magnitude 0.4, and therefore the assertion that material-level scatter is large enough to be the controlling origin of the diffuse mode, is inferred from the very lattice-level response it is used to explain. The paper reports no direct measurement of the dispersion of single-strut failure strain; only the mean (εfs = 1.3) is given. If the true material-level scatter were smaller, and the broad measured ef distribution instead arose from finite-rotation nominal strain definitions, DIC resolution, or unmodeled stress-redistribution effects, the diffuse damage mode would not be reproduced and the central claim would fail.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper reports an experimental and finite element study of uniaxial tensile failure of 2D PMMA honeycomb lattices tested at 100°C, i.e., slightly below the glass transition temperature, where PMMA is visco-plastic. The authors observe that, unlike the room-temperature brittle response of the same lattices, the high-temperature failure is diffuse: struts fail at uncorrelated locations before a single macroscopic crack forms. They quantify the dispersion of strut-level failure strain, and they use FE simulations that incorporate measured geometric imperfections and a scatter in material ductility to argue that strut-to-strut ductility dispersion is essential for reproducing the early strut failures and the diffuse damage mode. The paper also experimentally characterizes the sensitivity of the macroscopic strength to three designed defects—randomly perturbed joints, missing cell walls, and solid inclusions—and concludes that the visco-plastic lattice is highly damage tolerant to missing cell walls and inclusions because of its large transition flaw size.","tokens_in":15271,"tokens_out":2857,"duration_ms":33376,"significance":"The experimental observation that hexagonal PMMA lattices fail diffusely in the creep regime, in contrast to their correlated room-temperature failure, is a valuable and well-documented contribution. The measurements of defect sensitivity (missing cell walls, inclusions, joint perturbations) provide clear evidence of high damage tolerance in the visco-plastic regime, and the comparison with the companion brittle-lattice study is instructive. The FE study is a useful step toward mechanistic understanding, and the demonstration that a ductility dispersion is needed to reproduce the diffuse mode—while geometric imperfections alone produce a narrow failure-strain distribution and correlated failure—is qualitatively convincing. However, the quantitative identification of the ductility dispersion magnitude from the very lattice-level failure-strain distribution that is later used for validation introduces a circularity that weakens the force of the central mechanistic claim. If the authors can resolve this calibration issue, the paper would be a strong contribution to the mechanics of lattice materials.","major_comments":[{"comment":"The FE input for material ductility scatter, εfs,sd/εfs = 0.4, is explicitly taken to equal the measured coefficient of variation of effective strut failure strains (ef,sd/ef = 0.4) obtained from within the lattice. The predicted p(ef) distribution is then compared with this same measured distribution and declared to be in 'excellent agreement,' implying the assumed scatter is of the correct level. This is a calibration-and-validation loop: the agreement does not independently test the hypothesis that material-level scatter has a coefficient of variation of 0.4, because the measured ey distribution includes geometric and structural contributions (thickness variation, Plateau borders, stress concentrations) that are not separated from material scatter. The comparison with the εfs,sd=0 case does show that some material-level dispersion is needed, but the specific magnitude of 0.4 and the relative roles of material versus geometric scatter remain unquantified. I recommend either direct measurement of the single-strut failure-strain distribution (rather than only its mean) or validation against an independent observable, such as the spatial statistics of failure locations in a specimen not used for calibration.","section":"§6.2.1, Fig. 8"},{"comment":"The statement 'a dispersion in strut ductility is essential to lead to early strut failure and diffuse damage' is based on FE simulations where the dispersion parameter is calibrated from the lattice-level failure-strain distribution that the model is then used to reproduce. Because the input and the validation target are the same measured quantity, the claim cannot be considered quantitatively established. The qualitative conclusion that some material-level scatter is required is supported by the contrast between the εfs,sd=0 and εfs,sd/εfs=0.4 cases, but the magnitude of the scatter and its dominance over geometric effects are not independently verified. I suggest adding a sensitivity study with intermediate values of εfs,sd/εfs (e.g., 0.1 and 0.2) and comparing not only p(ef) but also the spatial correlation of failure events with the experimental observations.","section":"§6.2.1, Fig. 8"},{"comment":"The experimental evidence for the diffuse failure mode is based on a small number of specimens (three per relative density, with one representative failure sequence shown in Fig. 4). The claim of 'uncorrelated locations' would be strengthened by quantitative spatial statistics, such as a nearest-neighbor distance distribution of failed struts compared with a random Poisson process, and by reporting the number of specimens that exhibited the diffuse mode. Without such analysis, the visual impression of randomness is suggestive but not definitive, especially since the specimen width is only 11 cells and boundary effects could artificially decorrelate failures.","section":"§5, Fig. 4"}],"minor_comments":[{"comment":"The notation for the ductility dispersion is inconsistent: the text uses both εfs,sd/εf and εfs,sd/εfs. Please define the notation once and use it consistently throughout, including in the figure captions and the map of Fig. 9(a).","section":"§6.1.1, Eq. (6)"},{"comment":"The ordinate of Fig. 8 is labeled as a probability distribution function p(ef) but the axis is not normalized; please clarify whether the plotted quantity is a probability density or a histogram count, and provide the corresponding units.","section":"Fig. 8"},{"comment":"The observed elevation in net section strength at finite crack lengths is mentioned as 'unclear' and left for future work. A slightly fuller discussion of the possible mechanisms (citing the crack-tip blunting analysis of Tankasala et al. and the Voronoi honeycomb study of Mangipudi and Onck) would help the reader place this counterintuitive result.","section":"§7.2, Fig. 11(a)"},{"comment":"The abstract states that 'the dispersion in macroscopic strength is measured,' but the main reported quantity is the strength at first strut failure (and the associated ductility). Please harmonize the abstract and the main text so that the terminology is consistent.","section":"Abstract and §5"},{"comment":"The sentence 'The value of Δε follows from the specified work of fracture in the softening regime, Γf, and the characteristic length associated with the finite element, 𝓁c' is clear, but it would be helpful to state explicitly that the influence of element size on the mesh-dependence is removed by this scaling, as is implied by the reference to Oliver (1989).","section":"§6.1.1"}],"recommendation":"major_revision","confidential_remarks":"The paper is experimentally strong and the topic is well suited to Acta Materialia. The main concern is the calibration-validation circularity in the FE treatment of ductility scatter. This is, in my view, fixable within the scope of the paper: the authors could either measure the single-strut failure-strain distribution directly (even on a modest sample) or reframe the FE claim as a qualitative demonstration rather than a quantitative validation. I would not recommend rejection, but the central mechanistic claim needs to be more carefully supported."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things worth knowing before you read it. First, the experiments are the real content: 100°C tensile tests on laser-cut PMMA honeycombs with CT-characterized as-manufactured defects and designed defects (missing walls, inclusions, perturbed joints). The observation that initial failure is diffuse, with struts failing at uncorrelated locations before a transverse crack forms, is new and convincing, and it contrasts cleanly with the brittle companion study. Second, the FE model genuinely needs a dispersion in strut ductility to reproduce the diffuse mode; the run with zero dispersion gives a correlated crack, and that contrast is the paper's strongest evidence.\n\nThe soft spot the stress-test note flags is real: the dispersion magnitude εfs,sd/εfs = 0.4 is taken from the measured lattice-level coefficient of variation of strut failure strain, and the same measured distribution is then used to 'validate' the predicted failure-strain distribution. That is a calibration-and-validation loop. But it does not doom the paper. The zero-dispersion FE run already shows that geometric scatter alone yields a narrow ef distribution and a correlated mode, so the qualitative claim that material-level scatter is required survives. What is not established is the magnitude: if true material scatter were much smaller than 0.4, the predicted damage tolerance would change, though the mode transition would likely remain.\n\nA smaller but genuine issue: the concluding remarks say both classes of defect have a significant effect on strength, while the abstract and results emphasize negligible knock-down for missing walls and inclusions. The data show high damage tolerance for cracks up to a0/l ≈ 5 and mild strengthening for inclusions; the only potent defect is the most severe joint perturbation. That is a wording inconsistency, not a substantive flaw. Also, with three specimens per defect configuration, the quantitative knock-down numbers are rough, and the authors acknowledge this in places.\n\nOverall: the central claim—that strut ductility dispersion drives diffuse failure in the creep regime—is qualitatively supported, and the experimental contribution is solid and reproducible in style. The calibration loop deserves a sensitivity study or direct single-strut ductility measurements, but this is the kind of issue that peer review can resolve rather than a reason to reject. I would take this seriously as a referee and send it out.","headline":"Solid experimental study of creep failure in PMMA honeycombs; the diffuse-damage story holds up qualitatively, but the FE validation of the ductility-scatter magnitude runs a calibration loop.","tokens_in":15821,"tokens_out":1645,"would_cite":true,"duration_ms":19858,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["62.20.Hg","62.20.M-"],"model":"deepseek-v4-flash","headline":"A honeycomb near its glass temperature fails diffusely: strut fractures scatter across the lattice before a transverse crack forms, and this diffuse mode, driven by strut-to-strut ductility scatter, tolerates missing walls and inclusions.","keywords":["lattice materials","hexagonal honeycomb","visco-plastic creep","diffuse damage","strut ductility dispersion","damage tolerance","transition flaw size","rapid prototyping defects"],"falsifier":"Make a large number of individual laser-cut PMMA struts and tensile-test each one in isolation at 100 °C, measuring the coefficient of variation of the true failure strains: if the intrinsic material scatter is well below 0.4, the central mechanism is unsupported because the simulation input was extracted from in-lattice measurements that mix geometry with material scatter. A complementary test: manufacture lattices with deliberately homogenised struts (annealed or printed with uniform thickness and identical heat history) and check whether first-failure strains and damage patterns remain diffuse; the paper's claim predicts they should become correlated.","tokens_in":14709,"feed_emoji":"🕸️","tokens_out":22397,"duration_ms":200912,"temperature":0.7,"pith_summary":"Uniaxial tension tests on laser-cut PMMA honeycombs at 100 °C (just below the glass-transition temperature) show a failure mode that is the opposite of the room-temperature one: struts fracture one by one at uncorrelated locations across the gauge section, the load stays nearly constant while roughly the first six struts fail, and only later does a single transverse crack form and run across the lattice. The paper argues that this diffuse damage mode requires two ingredients that the creep regime supplies: struts that are ductile enough to give the lattice a large transition flaw size (hundreds of cell lengths), and a dispersion in strut-to-strut ductility (coefficient of variation about 0.4) that seeds early failures at random sites. Finite-element simulations on the CT-scanned as-manufactured geometry reproduce the diffuse pattern only when that ductility dispersion is included; geometric defects alone give correlated, crack-like failure. If this mechanism is right, lattices in the creep regime are strikingly damage tolerant: removing up to four cell walls or filling cells with solid inclusions barely changes tensile strength, while the most damaging imperfection is randomly misplaced joints. These results distinguish which manufacturing tolerances matter for creep applications: joint position is critical, cell-wall continuity is not.","feed_headline":"Scatter in strut strength spreads creep failure across a honeycomb","feed_subtitle":"Near its glass temperature, PMMA honeycombs fail strut-by-strut, so missing walls and inclusions barely weaken them.","key_machinery":"The chain of explanation runs through two dimensionless knobs. The transition flaw size, $a_T \\approx (1/\\pi)(K_{IC}/\\sigma^\\infty_f)^2$, is the crack semi-length below which a lattice fails by strength rather than by fracture toughness; it is about one cell length for the brittle hexagonal lattice and about 250 cell lengths for a ductile lattice whose struts fail by stretching at a true failure strain of 1.3. The second knob is the dispersion in strut ductility, $\\varepsilon_{fs,sd}/\\varepsilon_{fs}$, taken as 0.4. Plotted against each other, the two knobs organise a four-case map — brittle/deterministic (A), ductile/deterministic (B), ductile/dispersed (C), brittle/dispersed (D) — that predicts whether failure will be correlated or diffuse. The load-carrying device inside the finite-element model is a Johnson-Cook-type damage law: damage nucleates at a local true plastic strain of 1.3 and softens linearly over a fracture energy $\\Gamma_f = 2.5$ kJ/m$^2$, regularised by a characteristic element length so the prediction is mesh-independent; this converts the measured constitutive response of PMMA into strut fracture near the joints, at the locations where the dispersion in ductility first seeds it.","core_discovery":"The central claim is that the failure mode of a hexagonal lattice switches from correlated to diffuse when the cell-wall solid moves from elastic-brittle to visco-plastic, and that the diffuse mode is what confers damage tolerance. In the creep regime at $T = 100\\,^\\circ\\mathrm{C} \\approx 0.97\\,T_g$, first strut failure occurs at a macroscopic strain near 0.18 at a site that need not be the most highly stressed edge; subsequent failures land at random locations, with roughly half of the failed struts inclined at $\\pm 60^\\circ$ to the loading axis, until a critical cluster of failed struts reaches about half the specimen width and a transverse crack runs across. The same lattice at room temperature fails in a correlated, brittle manner with a crack advancing from one edge. FE simulations on the CT-scanned geometry show that as-manufactured geometric defects alone — dispersion in strut thickness $t_{sd}/t \\approx 0.19$ and in Plateau-border radius — shift first failure from 0.76 to 0.42 macroscopic strain but still give a correlated crack-like mode; the observed early (0.18) and diffuse failure appears only when a dispersion in strut ductility $\\varepsilon_{fs,sd}/\\varepsilon_{fs} = 0.4$ is assigned strut by strut. The paper concludes that a dispersion in strut ductility is essential for the early strut failure and diffuse damage observed, and that together with the large transition flaw size of a ductile lattice ($a_T \\approx 250\\ell$) it makes the creep-regime lattice tolerant to missing cell walls and solid inclusions.","pith_inferences":["Deliberately widening strut-to-strut ductility scatter — by process control, local heat treatment, or designed weak struts — should push other creep-ductile lattices (metallic or ceramic, not just PMMA) into the diffuse-damage class, provided their struts are ductile enough to keep the transition flaw size large.","The near-flat load plateau while several struts fail means a creep lattice gives a long, observable warning before fast fracture; counting failed struts by imaging or acoustic emission could serve as a remaining-life indicator, an application the paper does not discuss.","The paper leaves the net-section strength elevation at small crack sizes unexplained; a high-resolution DIC study of strut rotation at the tip of a two-to-three-cell pre-crack could test whether crack-tip blunting is the mechanism, and whether deliberately compliant blunting cells could enlarge the effect.","The four-case map is built at one relative density (0.11); since the transition flaw size involves the density scaling of both toughness and strength, the diffuse/correlated boundary may shift with density — a testable direction using the $\\rho = 0.07$ and 0.19 data already reported."],"forward_implications":["Creep-regime lattices keep essentially their full tensile strength with up to about four missing cell walls and with solid inclusions present, so holes and inclusions introduced by manufacturing or in-service damage do not need to be treated as critical flaws.","The same missing-row defect that is strength-limiting in the brittle lattice is almost harmless in the creep regime, because a large transition flaw size moves the lattice from toughness-controlled to strength-controlled failure.","Randomly misplaced joints are the most potent defect, cutting first-failure strength by a factor of about two at $R/\\ell = 0.5$; joint positioning accuracy, not cell-wall integrity, should be the manufacturing priority.","The $a_T/\\ell$ versus $\\varepsilon_{fs,sd}/\\varepsilon_{fs}$ map divides lattices into four classes with predictable failure modes, giving a design rule: diffuse damage and tolerance need both a large transition flaw size and a dispersion in strut ductility.","Dispersion in strut ductility is not merely a nuisance: it is the enabling condition for the diffuse damage that produces the near-flat load plateau and a long, observable sequence of strut failures before fast fracture."],"supporting_citations":[{"why":"Supplies the relative-density scaling, the strength and stiffness scaling laws, and the power-law creep-rate scaling for honeycombs that frame the experiments and the transition-flaw analysis.","marker":"[1]"},{"why":"Companion brittle study: same manufacturing and CT characterisation of as-manufactured geometry, and the room-temperature correlated-failure results (cases A and D) against which the creep regime is contrasted.","marker":"[13]"},{"why":"Johnson-Cook strain-initiated damage criterion with linear softening, the constitutive device that converts local plastic strain into strut fracture near joints in the FE model.","marker":"[19]"},{"why":"Supplies the PMMA fracture toughness, $K_{IC} = 1$ MPa$\\sqrt{\\mathrm{m}}$, used with the Irwin relation to set the work of fracture $\\Gamma_f = 2.5$ kJ/m$^2$ in the damage evolution law.","marker":"[20]"},{"why":"Provides the characteristic-length regularisation for smeared cracking that makes the softening branch and the predicted failure response mesh-independent in the FE simulations.","marker":"[21]"},{"why":"Predicted that a ductile hexagonal lattice failing by strut stretching has a transition flaw size near 250 cell lengths, the property that makes creep lattices insensitive to missing cell walls.","marker":"[24]"},{"why":"Supplies the random joint-perturbation scheme (perturbations within a disc of radius R) used to manufacture the imperfect lattices and the associated density correction.","marker":"[25]"},{"why":"Crack-tip field analysis for a long crack in a ductile hexagonal lattice, invoked to explain the crack-tip blunting responsible for elevated net-section strength.","marker":"[26]"},{"why":"Voronoi-honeycomb centre-cracked-panel computations showing a small elevation of net-section strength as crack size grows, cited as independent support for the measured strengthening.","marker":"[27]"}],"fun_headline_variants":["Strut ductility scatter drives diffuse creep failure in honeycombs","Diffuse failure lets creep honeycombs shrug off missing cells","Missing walls don't weaken creep honeycombs; ductility scatter does","Strut ductility scatter, not missing walls, guides honeycomb creep failure","Honeycombs fail diffusely in creep, so as-printed defects barely matter"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the scatter in strut ductility used in the simulations, $\\varepsilon_{fs,sd}/\\varepsilon_{fs} = 0.4$, really is a material-level scatter: the paper takes this value from the measured spread of effective failure strains of struts inside the lattice, which mixes genuine material variability with geometric and structural effects, and then treats the agreement of the simulated and measured failure-strain distributions as confirmation of that same input; if the intrinsic material scatter were substantially smaller, the simulated failure would become correlated and the diffuse-damage mechanism would collapse.","fun_headline_variants_meta":{"raw":{"variants":["Strut ductility scatter drives diffuse creep failure in honeycombs","Diffuse failure lets creep honeycombs shrug off missing cells","Missing walls don't weaken creep honeycombs; ductility scatter does","Strut ductility scatter, not missing walls, guides honeycomb creep failure","Honeycombs fail diffusely in creep, so as-printed defects barely matter"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000704,"raw_usage":{"total_tokens":3279,"prompt_tokens":1155,"completion_tokens":2124,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":771,"completion_tokens_details":{"reasoning_tokens":2027}},"tokens_in":771,"tokens_out":2124,"duration_ms":16020,"temperature":1.0,"reasoning_tokens":2027,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T14:37:50.131727+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Make a large number of individual laser-cut PMMA struts and tensile-test each one in isolation at 100 °C, measuring the coefficient of variation of the true failure strains: if the intrinsic material scatter is well below 0.4, the central mechanism is unsupported because the simulation input was extracted from in-lattice measurements that mix geometry with material scatter. A complementary test: manufacture lattices with deliberately homogenised struts (annealed or printed with uniform thickness and identical heat history) and check whether first-failure strains and damage patterns remain diffuse; the paper's claim predicts they should become correlated.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the relative-density scaling, the strength and stiffness scaling laws, and the power-law creep-rate scaling for honeycombs that frame the experiments and the transition-flaw analysis."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Companion brittle study: same manufacturing and CT characterisation of as-manufactured geometry, and the room-temperature correlated-failure results (cases A and D) against which the creep regime is contrasted."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Johnson-Cook strain-initiated damage criterion with linear softening, the constitutive device that converts local plastic strain into strut fracture near joints in the FE model."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the PMMA fracture toughness, $K_{IC} = 1$ MPa$\\sqrt{\\mathrm{m}}$, used with the Irwin relation to set the work of fracture $\\Gamma_f = 2.5$ kJ/m$^2$ in the damage evolution law."},{"cited_title":"Oliver, A consistent characteristic length for smeared cracking models, International Journal for Numerical Methods in Engineering 28 (1989) 461–474","cited_arxiv_id":null,"evidence_quote":"Provides the characteristic-length regularisation for smeared cracking that makes the softening branch and the predicted failure response mesh-independent in the FE simulations."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Predicted that a ductile hexagonal lattice failing by strut stretching has a transition flaw size near 250 cell lengths, the property that makes creep lattices insensitive to missing cell walls."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the random joint-perturbation scheme (perturbations within a disc of radius R) used to manufacture the imperfect lattices and the associated density correction."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Crack-tip field analysis for a long crack in a ductile hexagonal lattice, invoked to explain the crack-tip blunting responsible for elevated net-section strength."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Voronoi-honeycomb centre-cracked-panel computations showing a small elevation of net-section strength as crack size grows, cited as independent support for the measured strengthening."}],"review_version":1}