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REVIEW 5 major objections 5 minor 58 references

Numerical Simulation Informed Rapid Cure Process Optimization of Composite Structures using Constrained Bayesian Optimization

T0 review · 5 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read The paper claims that constrained Bayesian optimization with Gaussian-process surrogates and expected constrained improvement solves the composite cure optimization problem to within 4% of a genetic algorithm's result while using 40–50…

desk verdict Useful cBO application to cure-cycle design, but the efficiency claim leans on a non-converged GA benchmark and an omitted slope constraint. read the letter →

arxiv 2505.24775 v1 pith:R4EKAPE5 submitted 2025-05-30 stat.AP

Madhura Limaye , Yezhuo Li , Qiong Zhang , Gang Li This is my paper
classification stat.AP MSC 90C2662-0865K10
keywords curecycleoptimizationconstrainedBayesianGaussianprocesssurrogateexpectedimprovementprocess-induceddeformationcompositelaminatesdegreeofNSGA-II
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper claims that constrained Bayesian optimization—using Gaussian-process surrogates for deformation and degree of cure, with an expected constrained improvement acquisition function—can solve the composite cure optimization problem to essentially the same optimum as a genetic algorithm. Across a flat rectangular laminate and an L-shaped laminate, the deformation and final degree of cure found by cBO agree with NSGA-II to within 4%, while requiring only 40–50 finite-element simulations instead of more than 1000, a computational efficiency above 96%. If correct, manufacturers can replace expensive global search over cure cycles with a surrogate-guided search that finds near-identical optimized cure-induced deformation for flat and L-shaped composite laminates at a fraction of the cost.

What carries the argument

The central object is the constrained Bayesian optimizer, which fits two independent Gaussian processes to the finite-element outputs—one for deformation $u(x)$ and one for degree of cure $g(x)$—and chooses each new simulation by maximizing expected constrained improvement, $$\mathrm{EIC}(x)=\mathrm{EI}(x)\cdot \Pr(g(x)\ge c),$$ where $c$ is the required final degree of cure and $\Pr(g(x)\ge c)$ is the Gaussian-process probability that the candidate satisfies the constraint. Candidate points are drawn from a Latin-hypercube pool, and the next design is the candidate with the largest $\mathrm{EIC}$. Underneath this sits the sequential finite-element cure model—a thermo-chemical step followed by a stress-deformation step with a modified CHILE resin modulus law depending on degree of cure, plus a cure-shrinkage model—which supplies the black-box deformation and degree-of-cure responses that both optimizers query.

What would settle it

Physically cure L-shaped laminates using the reported Q1 and Q2 optimum cycles, measure the resulting spring-in and twisting deformation, and compare with the predicted values (1.598 mm for Q1 and roughly 71.6–74.0 mm for Q2); disagreement beyond the flat-model validation error would show the optimized cycles do not transfer to real parts.

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Extended reading notes

Core claim

The paper's central discovery is that the cure-optimization problem—minimize process-induced deformation $u$ by selecting the coordinates of a non-isothermal cure cycle subject to a degree-of-cure constraint—can be reliably solved by constrained Bayesian optimization. On the flat laminate, cBO's optimum deformation differs from GA's by 0.04% (R1) and 0.02% (R2), with identical final degrees of cure; on the L-shaped laminate, the differences are 0.27% for the [0/0] case and 3.4% for the [45/-45] case. The optimized cycles reduce baseline deformation by 9–10% on the flat laminate, reduce spring-in on the [0/0] L-shape from 2.700 mm to 1.598 mm (41.4%), and reduce the twisting deformation of the [45/-45] L-shape from 81.71 mm to 71.58 mm (12.4%). The paper explains the improvement through non-isothermal cycles whose slow second heating phase makes thermal expansion counteract cure shrinkage between gelation and vitrification.

Load-bearing premise

The load-bearing premise is that the finite-element cure model faithfully represents real cure behavior; the flat-laminate model matches one literature case to 3.4%, but the L-shaped model is not directly validated against physical parts.

Editorial extensions

If this is right

  • A manufacturer evaluating a new laminate geometry could run fewer than 50 finite-element cure simulations instead of more than 1000 genetic-algorithm evaluations and still land on a cure cycle whose predicted deformation is within a few percent of the expensive search's optimum.
  • The surrogate-guided search extends to more complex geometries and higher-dimensional cure-cycle parameterizations, since the four-variable L-shaped cases converged within 35 learning steps and the harder [45/-45] case showed 97.5% computational efficiency.
  • Optimum cure cycles favor a longer, slower second heating phase so that thermal expansion and cure shrinkage counteract each other for a longer time; the quantified benefits are 9–10% deformation reduction on flat laminates and up to 41.4% spring-in reduction on L-shaped laminates.
  • Because the comparison target is NSGA-II running on the same finite-element model, the reported <4% error means the surrogate reproduces the genetic algorithm's optimum inside that model, so the computational gain holds independently of how well the model matches physical parts.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The large mismatch in the optimal early-heating time $t_1$ for case Q2 (26.3%) alongside a deformation error below 4% suggests the deformation objective is nearly flat in $t_1$; a sensitivity analysis over that variable would reveal how much schedule freedom manufacturers have at no deformation cost.
  • With only 10–15 initial finite-element samples, the surrogate's global accuracy depends on the smoothness of the deformation and degree-of-cure response surfaces; applying cBO to a layup or geometry with sharp response features would likely require more initial samples or a different kernel.
  • The same constrained-BO recipe could optimize other cure-quality objectives, such as void content, temperature overshoot, or cure time, whenever a feasible constraint function can be simulated.
  • An experimental campaign on actual flat and L-shaped laminates cured with the reported optimum cycles would test whether the predicted 9–10% and 41.4% deformation reductions appear in physical parts; until then, the practical benefit hinges on the unvalidated L-shaped finite-element model.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

5 major / 5 minor

Summary. The paper proposes using constrained Bayesian optimization (cBO) with Gaussian-process surrogates and expected constrained improvement to replace genetic-algorithm-based global search for optimizing cure cycles of composite laminates. The optimization objective is to minimize cure-induced deformation subject to a final degree-of-cure constraint. The approach is demonstrated on two case studies: a flat rectangular cross-ply laminate (two design variables, cases R1/R2) and an L-shaped laminate (four design variables, cases Q1/Q2), with the cure process modeled in ABAQUS/COMPRO using coupled thermo-chemical and stress-deformation analyses. The central claim is that cBO matches NSGA-II within 4% error in deformation and final degree of cure while using fewer than 50 simulation evaluations instead of more than 1000, yielding computational efficiency above 96%. A numerical verification on polynomial surrogates fitted to case-study data is also reported.

Significance. If the central claim holds, the paper offers a practically valuable recipe: manufacturers of thermoset composite parts could replace expensive global search over cure cycles with a surrogate-guided search that obtains nearly the same optimized deformation at a fraction of the simulation budget. The paper gives some credit-worthy ingredients: a physically motivated two-step cure model, a literature-based validation of the flat-laminate model (3.4% curvature difference vs. Shah et al. 2018), a constrained BO formulation with separate GP surrogates for objective and constraint, a numerical verification with percentile bands, and a direct comparison against NSGA-II on four optimization cases. However, the significance is currently limited by several evidence gaps: the GA baselines are not converged, the two algorithms solve different constrained problems in the flat-laminate case, and the L-shaped model is not experimentally validated. These gaps mean the headline efficiency and accuracy numbers should be read as promising but not yet established.

major comments (5)
  1. [Section 5.2.1 and Table 7] The claimed '< 4%' accuracy is measured against a GA that the manuscript itself describes as not converged. In Section 5.2.1 the authors state that 'GA continues to have oscillations even after 1000 iterations,' and in Section 5.2.2 they state that the Q2 GA 'continues to manifest oscillatory behavior at the end of GA execution, suggesting the need for additional iterations.' With no multiple seeds, no stopping-rule criterion, and no uncertainty intervals for the GA trajectories, the reported GA optimum is a snapshot of a non-stationary search. The <4% agreement therefore demonstrates agreement with a GA incumbent, not with a converged or true optimum. The authors should either run GA to a stable plateau (e.g., with more generations, multiple restarts, and a tolerance-based convergence check) or explicitly reframe the comparison as 'agreement with the GA solution at the tested budget' and avoid claiming that cBO attains the optimum with <4% error.
  2. [Section 4.1] The flat-laminate cBO omits the slope constraint slope(S1) > slope(S2) that is imposed in the GA baseline. The text states that 'we omit the slope constraints in the Bayesian optimization approach' because the constraint is assumed automatically satisfied in real-world scenarios. This means the two algorithms are solving different constrained problems: the cBO is free to explore regions that the GA excludes, and the reported efficiency gain of 96% is not attributable solely to the optimization algorithm but may partly reflect this mismatch. The authors should either incorporate the slope constraint into cBO (for example, by the candidate-filtering approach already used for the L-shaped case) or provide numerical evidence that the omitted constraint is inactive over the cBO-sampled region and at the reported optimum.
  3. [Section 4.2 and Tables 8-9] The L-shaped laminate cure model is not validated against any experimental or independently published result. The only validation in the paper is the flat-laminate curvature comparison (difference = 3.4%) against Shah et al. (2018) in Section 4.1. Since the Q1/Q2 optimized cure cycles are presented as solutions for L-shaped parts, the unvalidated L-shaped model weakens the transferability of the conclusions. The authors should either add a validation case for the L-shaped geometry (e.g., against a measured spring-in value from the literature) or explicitly limit the claims to 'optimization within the unvalidated simulation model' and state that physical validation is required before the optimized cycles are applied.
  4. [Section 5.1, Eqs. (17)-(18)] The numerical verification benchmarks cBO on second-order polynomial regressions fitted to data from case study 1, not on the actual cure-process FEM model. This is a mild self-consistency check: it shows that cBO performs well on a smooth surrogate of the same data, but it does not establish that cBO finds the global optimum of the true cure model. The GA comparison in this section also uses 150-650 evaluations on the fitted polynomials, so it is not a comparison on the FEM model. The authors should state this limitation explicitly and, if possible, validate cBO on a test problem with a known closed-form global optimum or on the actual simulation model with a verified reference.
  5. [Section 5.2 and Tables 7 and 9] The 'computational efficiency' metric is defined as the ratio of convergence steps (GA steps vs. cBO steps), not as wall-clock time or total computational cost. cBO incurs additional overhead by fitting and updating GP surrogates and by evaluating a candidate pool of 10,000 points at each iteration, while GA evaluations are direct simulation calls. The >96% efficiency claim is therefore an upper bound on savings in simulation evaluations, not necessarily a savings in total computation. The authors should clarify this distinction and, if wall-clock times are available, report them.
minor comments (5)
  1. [Sections 4.1 and 4.2] The text refers to 'Equation (18)' when describing the candidate-selection rule for cBO, but the acquisition function is defined in Eqs. (15)-(16); the cross-references should be corrected.
  2. [Appendix A] Appendix A says 'The flowchart shown in Figure 3 presents Bayesian Optimization framework,' but no Figure 3 appears in the appendix and Figure 1 already shows the general workflow; the figure reference is inconsistent.
  3. [Section 4.1] The phrase 'derived from the cure of flat rectangular laminate experiment' should read 'numerical experiment' or 'simulation,' since the study does not perform physical experiments on the flat laminate.
  4. [Tables 7 and 9] The abstract states 'error < 4%' qualitatively, but the tables report much smaller errors in some cases (e.g., 0.020-0.041% for R1/R2); reporting the actual ranges would be more informative.
  5. [General] The manuscript does not state whether the implementation code or the numerical data used for the figures and tables will be made available; providing such artifacts would greatly improve reproducibility, given the reliance on commercial software (ABAQUS, COMPRO, ModeFRONTIER).

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central cBO-vs-GA comparison is an independent numerical benchmark, not a reduction of the predictions to the model inputs.

full rationale

The paper's claimed result is that cBO with GP surrogates and expected constrained improvement matches NSGA-II within 4% while using far fewer FEM evaluations. The objective u and constraint DoC are treated as black-box functions; the GP surrogates are trained on FEM-generated samples and the final reported u and DoC values are re-evaluated on the cure-process FEM model, so the reported optima are not equal to the surrogate predictions by construction. The comparison baseline, NSGA-II, is an independent optimization algorithm and is not built from cBO outputs. The numerical verification in Sec. 5.1 fits a second-order polynomial to case-study data and benchmarks cBO on that polynomial; this is an algorithm-mechanics check and is not the source of the physical cure-optimization claim, so it does not make the central result circular. The model validation against Shah et al. (2018) is an external literature benchmark, and the small self-citation in the introduction (e.g., Pradeep et al. 2024, which includes two of the present authors) is contextual and non-load-bearing. Concerns about GA non-convergence and the omitted slope constraint in the flat-laminate cBO runs are benchmark-validity and fairness issues, not circularity: they do not show that any prediction reduces by definition to the fitted inputs. Accordingly, the derivation chain is self-contained with respect to circularity.

Assumptions & free parameters 6 free parameters · 5 assumptions · 0 invented entities

The ledger shows that the paper introduces no new physical entities and no new constitutive laws. It imports multiple empirically fitted material parameter sets from earlier literature, makes GP smoothness assumptions, and sets optimization budgets by hand. The main claim, that cBO matches GA with fewer evaluations, is a numerical observation conditional on this assembled model and on the chosen budgets.

free parameters (6)
  • Cure kinetic model constants (A1, A2, activation energies, exponents) for 3501-6 epoxy = Calibrated by Woo, Loos and Springer 1982, not re-fit here
    Equation (3) determines the cure rate used in the thermo-chemical simulation; the optimized cure cycle and the degree-of-cure constraint depend on these empirically fitted constants.
  • CHILE resin modulus development parameters (Er0, Erin, alpha_gel, alpha_vit, gamma) = Values taken from Johnston 1997 and Liu et al. 2021, not reported in the paper
    Equation (4) governs modulus evolution from gelation to vitrification, which directly sets the stress-deformation response used as the optimization objective.
  • Cure shrinkage model parameters (V_shmax, A, alpha_p, alpha_vit) = Values from Bogetti and Gillespie 1992, not reported in the paper
    Equations (5) and (6) generate cure shrinkage strains, a primary contributor to process-induced deformation and thus to the objective function being minimized.
  • GP hyperparameters for u and DoC surrogates (ARD Matern 5/2 length scales, signal variance) = Estimated internally by MATLAB fitrgp; values not disclosed
    The cBO acquisition function and predictions depend on these fitted hyperparameters; disclosing them would help independent replication.
  • cBO initial sample and iteration budgets = 10 initial + 30 iterations for flat cases; 15 initial + 35 iterations for L-shaped cases
    The claimed computational efficiency of 96-97.5% is computed from these hand-chosen budgets, so the efficiency figure depends on this choice.
  • Design variable bounds for t1, T1, t2, T2 = t1 in [1,110] or [10,110]; T1 in [125,180]; t2 in [120,200]; T2 in [150,180]
    Bounds were chosen after trial runs showed infeasibility outside them; they define the search space and therefore the reported optima.
assumptions (5)
  • domain assumption The objective f(x) = deformation u and constraint g(x) = degree of cure are realizations of two independent Gaussian processes with constant mean and Matern 5/2 correlation.
    Section 3 (Eqs. 9-11) builds the surrogate on this assumption. If the true response is not smooth or stationary over the search space, the acquisition function can select poor points. No GP diagnostics are shown.
  • domain assumption The sequentially coupled thermo-chemical and stress-deformation FEM cure model accurately represents the physical process-induced deformation.
    The optimized cycles are judged by their deformation in this model. Only the flat-laminate case is validated against Shah et al. 2018; the L-shaped model in Section 4.2 has no direct experimental check.
  • domain assumption The cure kinetic law in Eq. (3) and its 3501-6 constants apply over the full explored temperature range, including lower-temperature cycles.
    The kinetic constants are imported from Woo, Loos and Springer 1982 without re-fitting or uncertainty analysis, yet the optimized cycles explore T1 down to 125-180 degrees C.
  • ad hoc to paper The slope constraint slope(S1) > slope(S2) is automatically satisfied in the flat-laminate cBO runs and can be omitted.
    Section 4.1 states the slope constraints are omitted in BO because real-world slopes of S1 and S2 are non-negative with S1 steeper. If this reasoning fails for some candidate designs, cBO may evaluate cycles that the GA formulation would exclude.
  • domain assumption One GA run per case is enough to represent the GA result for comparison.
    NSGA-II is stochastic, and Tables 7 and 9 report a single run per case. The claimed error of less than 4% between GA and cBO lacks a distribution over GA outcomes.

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Cite this review

Pith. "Pith review of Numerical Simulation Informed Rapid Cure Process Optimization of Composite Structures using Constrained Bayesian Optimization." pith.science (2026). https://pith.science/paper/R4EKAPE5

@misc{pith2026250524775,
  author       = {Pith},
  title        = {Pith review of: Numerical Simulation Informed Rapid Cure Process Optimization of Composite Structures using Constrained Bayesian Optimization},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/R4EKAPE5}},
  note         = {Machine review of arXiv:2505.24775}
}
read the original abstract

The present study aimed to solve the cure optimization problem of laminated composites through a statistical approach. The approach consisted of using constrained Bayesian Optimization (cBO) along with a Gaussian process model as a surrogate to rapidly solve the cure optimization problem. The approach was implemented to two case studies including the cure of a simpler flat rectangular laminate and a more complex L-shaped laminate. The cure optimization problem with the objective to minimize cure induced distortion was defined for both case studies. The former case study was two-variable that is used two cure cycle parameters as design variables and was constrained to achieve full cure, while the latter was four-variable and had to satisfy constraints of full cure as well as other cure cycle parameters. The performance of cBO for both case studies was compared to the traditional optimization approach based on Genetic Algorithm (GA). The comparison of results from GA and cBO including deformation and final degree of cure showed significant agreement (error < 4%). The computational efficiency of cBO was calculated by comparing the convergence steps for GA (>1000) and cBO (<50). The computational efficiency of cBO for all optimization cases was found to be > 96%. The case studies conclude that cBO is promising in terms of computational time and accuracy for solving the cure optimization problem.

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Works this paper leans on

58 extracted references · 45 canonical work pages

  1. [1]

    These structural parts have found extensive applications in aerospace and automotive industries (McIlhagger, Archer, and McIlhagger 2020; Pradeep et al

    Introduction Thermoset based fiber reinforced composite laminates are popularly processed by the cure process to produce structural parts. These structural parts have found extensive applications in aerospace and automotive industries (McIlhagger, Archer, and McIlhagger 2020; Pradeep et al. 2024). A typical input to the cure process is a temperature and p...

    work page 2020

  2. [2]

    Workflow of the cure optimization problem with black-box optimization tools. 2.1 Heat generation and transfer model The thermal model of cure process governed by Fourier’s heat conduction equation with heat generation is given as 𝜕𝜕𝑡8𝜌𝐶!𝑇:=𝛻(𝒌𝛻𝑇)+𝑄̇ (1) where 𝜌 is the density of the composite laminate, 𝐶! is the specific heat, k is the anisotropic thermal...

    work page 2015

  3. [4]

    The first case study includes cure of a flat rectangular laminate with a cross-ply layup that leads to out-of-plane PID at the end of cure

    Implementation of Cure Process Optimization Approaches through Case Studies The two optimization approaches described in Section 2 were implemented for each of two case studies that have different cure scenarios and geometric configurations. The first case study includes cure of a flat rectangular laminate with a cross-ply layup that leads to out-of-plane...

    work page 2018

  4. [9]

    The Q2 case shows higher prediction discrepancy in parameter t1 with a maximum error of 26.3%

    The GA and cBO results for Q1 have good agreement with and a 96% computational efficiency of cBO. The Q2 case shows higher prediction discrepancy in parameter t1 with a maximum error of 26.3%. However, the corresponding error in u is < 4% indicating the cure cycle parameter t1 is not sensitive to the deformation results, which is also observed in the flat...

    work page 2000

  5. [11]

    Since the laminate is symmetric about the curved plane, results are displayed for only one half of the laminate

    Comparison of deformation u and DoC for Q1 and Q2 cases and estimate of computational efficiency of cBO Case u (mm) % error DoC % error Convergence steps Computational Efficiency of cBO (%) GA cBO GA cBO GA cBO Q1 1.598 1.6023 0.269 0.999 0.999 0 > 1000 < 40 > 96 Q2 71.58 74.02 3.409 0.990 0.991 0.101 > 2000 < 50 > 97.5 Fig 11(a) and (b) show the deformat...

    work page 2000

  6. [12]

    Thermosetting Bismaleimide/Reactive Rubber Blends: Curing Kinetics and Mechanical Behavior

    “Thermosetting Bismaleimide/Reactive Rubber Blends: Curing Kinetics and Mechanical Behavior.” Journal of Applied Polymer Science 65 (5). https://doi.org/10.1002/(SICI)1097-4628(19970801)65:5<979::AID-APP16>3.0.CO;2-N. Agius, S. L., M. Joosten, B. Trippit, C. H. Wang, and T. Hilditch

    work page doi:10.1002/(sici)1097-4628(19970801)65:5

  7. [15]

    Analysis of Cure Induced Deformation of CFRP U-Shaped Laminates

    “Analysis of Cure Induced Deformation of CFRP U-Shaped Laminates.” Composite Structures 197 (August):1–9. https://doi.org/10.1016/j.compstruct.2018.05.038. Benavente, Maria, Lionel Marcin, Alice Courtois, Martin Lévesque, and Edu Ruiz

    work page doi:10.1016/j.compstruct.2018.05.038 2018

  8. [16]

    Numerical Analysis of Viscoelastic Process-Induced Residual Distortions during Manufacturing and Post-Curing

    “Numerical Analysis of Viscoelastic Process-Induced Residual Distortions during Manufacturing and Post-Curing.” Composites Part A: Applied Science and Manufacturing 107 (April):205–16. https://doi.org/10.1016/j.compositesa.2018.01.005. Boey, F. Y.C., X. L. Song, S. K. Rath, and C. Y. Yue

    work page doi:10.1016/j.compositesa.2018.01.005

Show all 58 references
  1. [18]

    Process-Induced Stress and Deformation in Thick-Section Thermoset Composite Laminates

    “Process-Induced Stress and Deformation in Thick-Section Thermoset Composite Laminates.” Journal of Composite Materials 26 (5): 626–60. https://doi.org/10.1177/002199839202600502. Chen, Weijia, and Dianyun Zhang

    doi

  2. [20]

    A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II

    “A Fast and Elitist Multiobjective Genetic Algorithm: NSGA-II.” IEEE Transactions on Evolutionary Computation 6 (2). https://doi.org/10.1109/4235.996017. Ding, Anxin, Shuxin Li, Jihui Wang, Aiqing Ni, Liangliang Sun, and Lei Chang

  3. [21]

    Prediction of Process-Induced Distortions in L-Shaped Composite Profiles Using Path-Dependent Constitutive Law

    “Prediction of Process-Induced Distortions in L-Shaped Composite Profiles Using Path-Dependent Constitutive Law.” Applied Composite Materials 23 (5): 1027–45. https://doi.org/10.1007/s10443-016-9501-8. Ding, Anxin, Shuxin Li, Jihui Wang, Aiqing Ni, and Lei Zu

    doi

  4. [23]

    Bayesian Optimization

    “Bayesian Optimization.” In Recent Advances in Optimization and Modeling of Contemporary Problems, 255–78. INFORMS. https://doi.org/10.1287/educ.2018.0188. Gardner, Jacob R., Matt J. Kusner, Zhixiang Xu, Kilian Q. Weinberger, and John P. Cunningham

    2018

  5. [26]

    The Curing Kinetics of a Modified Bismaleimide

    “The Curing Kinetics of a Modified Bismaleimide.” Polymer International 32 (1). https://doi.org/10.1002/pi.4990320114. Gopal, Ajith K., Sarp Adali, and Viktor E. Verijenko

    doi

  6. [27]

    Optimal Temperature Profiles for Minimum Residual Stress in the Cure Process of Polymer Composites

    “Optimal Temperature Profiles for Minimum Residual Stress in the Cure Process of Polymer Composites.” Composite Structures. https://doi.org/10.1016/S0263-8223(99)00080-X. Hahn, H. Thomas

    doi

  7. [29]

    Quantitative Analysis of Bismaleimide-Diamine Thermosets Using near Infrared Spectroscopy

    “Quantitative Analysis of Bismaleimide-Diamine Thermosets Using near Infrared Spectroscopy.” Polymer 41 (23). https://doi.org/10.1016/S0032-3861(00)00198-1. Hui, Xinyu, Yingjie Xu, Wenchang Zhang, and Weihong Zhang

    doi

  8. [31]

    Efficient Global Optimization of Expensive Black-Box Functions

    “Efficient Global Optimization of Expensive Black-Box Functions.” Journal of Global Optimization 13 (4). https://doi.org/10.1023/A:1008306431147. Kravchenko, Oleksandr G., Sergii G. Kravchenko, and R. Byron Pipes

    doi

  9. [32]

    Chemical and Thermal Shrinkage in Thermosetting Prepreg

    “Chemical and Thermal Shrinkage in Thermosetting Prepreg.” Composites Part A: Applied Science and Manufacturing. https://doi.org/10.1016/j.compositesa.2015.10.001. ———

    2015 doi

  10. [33]

    Cure History Dependence of Residual Deformation in a Thermosetting Laminate

    “Cure History Dependence of Residual Deformation in a Thermosetting Laminate.” Composites Part A: Applied Science and Manufacturing. https://doi.org/10.1016/j.compositesa.2017.04.006. Li, C., N. Zobeiry, K. Keil, S. Chatterjee, and A. Poursartip

    2017 doi

  11. [34]

    A Comparison of Curing Process-Induced Residual Stresses and Cure Shrinkage in Micro-Scale Composite Structures with Different Constitutive Laws

    “A Comparison of Curing Process-Induced Residual Stresses and Cure Shrinkage in Micro-Scale Composite Structures with Different Constitutive Laws.” Applied Composite Materials 25 (1): 67–84. https://doi.org/10.1007/s10443-017-9608-6. Li, Xuerui, Xu Han, Shuyong Duan, and Gui Rong Liu

    doi

  12. [36]

    Study on Cure-Induced Residual Stresses and Spring-in Deformation of L-Shaped Composite Laminates Using a Simplified Constitutive Model Considering Stress Relaxation

    “Study on Cure-Induced Residual Stresses and Spring-in Deformation of L-Shaped Composite Laminates Using a Simplified Constitutive Model Considering Stress Relaxation.” Composite Structures 272 (September). https://doi.org/10.1016/j.compstruct.2021.114203. Ma, Yunrong, Jilin H...

  13. [38]

    New Method to Reduce Cure-Induced Stresses in Thermoset Polymer Composites, Part I: Test Method

    “New Method to Reduce Cure-Induced Stresses in Thermoset Polymer Composites, Part I: Test Method.” Journal of Composite Materials 34 (22). https://doi.org/10.1106/HUCY-DY2B-2N42-UJBX. McIlhagger, A, E Archer, and R McIlhagger

    doi

  14. [40]

    Characterization of the Cure Reactions of Bismaleimide Composite Matrices

    “Characterization of the Cure Reactions of Bismaleimide Composite Matrices.” Polymer 38 (3). https://doi.org/10.1016/S0032-3861(96)00542-3. Phelan, John C., and Chong Sook Paik Sung

    doi

  15. [41]

    Cure Characterization in Bis(Maleimide)/Diallylbisphenol A Resin by Fluorescence, FT-IR, and UV-Reflection Spectroscopy

    “Cure Characterization in Bis(Maleimide)/Diallylbisphenol A Resin by Fluorescence, FT-IR, and UV-Reflection Spectroscopy.” Macromolecules 30 (22). https://doi.org/10.1021/ma961887f. Pradeep, Sai Aditya, Amit M Deshpande, Madhura Limaye, Rakesh K Iyer, Hakan Kazan, Gang Li, and...

    doi

  16. [44]

    Gaussian Processes for Machine Learning

    Gaussian Processes for Machine Learning. Gaussian Processes for Machine Learning. The MIT Press. https://doi.org/10.7551/mitpress/3206.001.0001. Russell, John D., Madhu S. Madhukar, Mohamed S. Genidy, and Andre Y. Lee

    doi

  17. [45]

    New Method to Reduce Cure-Induced Stresses in Thermoset Polymer Composites, Part III: Correlating Stress History to Viscosity, Degree of Cure, and Cure Shrinkage

    “New Method to Reduce Cure-Induced Stresses in Thermoset Polymer Composites, Part III: Correlating Stress History to Viscosity, Degree of Cure, and Cure Shrinkage.” Journal of Composite Materials 34 (22). https://doi.org/10.1106/UY9U-F2QW-2FKK-91KG. 26 Sarrazin, Hugo, Beomkeun...

    doi

  18. [47]

    Optimal Cure Cycle Parameters for Minimizing Residual Stresses in Fiber-Reinforced Polymer Composite Laminates

    “Optimal Cure Cycle Parameters for Minimizing Residual Stresses in Fiber-Reinforced Polymer Composite Laminates.” Journal of Composite Materials 52 (6): 773–92. https://doi.org/10.1177/0021998317714317. Sreekantamurthy, T., T. B. Hudson, T. H. Hou, and B. W. Grimsley

    doi

  19. [48]

    Modelling and Experiment of Process-Induced Distortions in Unsymmetrical Laminate Plates

    “Modelling and Experiment of Process-Induced Distortions in Unsymmetrical Laminate Plates.” Composite Structures 182 (December):524–32. https://doi.org/10.1016/j.compstruct.2017.09.018. Svanberg, J. Magnus, and J. Anders Holmberg

    2017 doi

  20. [50]

    Composite Temperature Profile and Tooling Optimization via Deep Reinforcement Learning

    “Composite Temperature Profile and Tooling Optimization via Deep Reinforcement Learning.” Composites Part A: Applied Science and Manufacturing 142 (March). https://doi.org/10.1016/j.compositesa.2020.106235. Takagaki, Kazunori, Shu Minakuchi, and Nobuo Takeda

    2020

  21. [51]

    Process-Induced Strain and Distortion in Curved Composites. Part II: Parametric Study and Application

    “Process-Induced Strain and Distortion in Curved Composites. Part II: Parametric Study and Application.” Composites Part A: Applied Science and Manufacturing 103 (December):219–29. https://doi.org/10.1016/j.compositesa.2017.09.019. Wang, Qi, Xufeng Yang, Xiaowen Zhang, Xin Cha...

    2017 doi

  22. [52]

    Effect of Cure Cycles on Residual Stresses in Thick Composites Using Multi-Physics Coupled Analysis with Multiple Constitutive Models

    “Effect of Cure Cycles on Residual Stresses in Thick Composites Using Multi-Physics Coupled Analysis with Multiple Constitutive Models.” Materials Today Communications 32 (August):104094. https://doi.org/10.1016/J.MTCOMM.2022.104094. White, Scott R., and Yeong Kim

  23. [53]

    Process-Induced Residual Stress Analysis of AS4/3501-6 Composite Material

    “Process-Induced Residual Stress Analysis of AS4/3501-6 Composite Material.” Mechanics of Composite Materials and Structures 5 (2): 153–86. https://doi.org/10.1080/10759419808945897. White, S.R., and H.T. Hahn

    doi

  24. [54]

    Cure Cycle Optimization for the Reduction of Processing-Induced Residual Stresses in Composite Materials

    “Cure Cycle Optimization for the Reduction of Processing-Induced Residual Stresses in Composite Materials.” Journal of Composite Materials 27 (14): 1352–78. https://doi.org/10.1177/002199839302701402. Woo, Il Lee, Alfred C. Loos, and George S. Springer

    doi

  25. [57]

    Process-Induced Deformation of L-Shaped Variable-Stiffness Composite Structures during Cure

    “Process-Induced Deformation of L-Shaped Variable-Stiffness Composite Structures during Cure.” Composite Structures 230 (December). https://doi.org/10.1016/j.compstruct.2019.111461. 27 Zhao, L. G., N. A. Warrior, and A. C. Long

    2019

  26. [1976]

    Residual Stresses in Polymer Matrix Composite Laminates

    “Residual Stresses in Polymer Matrix Composite Laminates.” Journal of Composite Materials. https://doi.org/10.1177/002199837601000401. Hopewell, J. L., G. A. George, and D. J.T. Hill

    doi

  27. [1982]

    Heat of Reaction, Degree of Cure, and Viscosity of Hercules 3501-6 Resin

    “Heat of Reaction, Degree of Cure, and Viscosity of Hercules 3501-6 Resin.” Journal of Composite Materials 16 (6). https://doi.org/10.1177/002199838201600605. Zeng, X., and J. Raghavan

    doi

  28. [1986]

    Autoclave Moulding of Carbon Fibre-Reinforced Epoxies

    “Autoclave Moulding of Carbon Fibre-Reinforced Epoxies.” Composites. https://doi.org/10.1016/0010-4361(86)90250-8. Rasmussen, Carl Edward, and Christopher K. I. Williams

    doi

  29. [1992]

    ",6:7() (𝑖,𝑗=1−6) (7) Where 𝐶,76 are the stiffness coefficients in the kth increment, and 𝜀78

    𝑉#4(V 0.0 𝛼≤𝛼+) 𝐴𝛼4+(𝑉#42−𝐴)𝛼4* 𝛼+)≤𝛼≤𝛼+*𝑉#42, 𝛼≥𝛼+*W (5) Again, 𝛼+) and 𝛼+* are the DoC parameters for cure shrinkage model. Referring to Fig 2, 𝛼+) is the DoC corresponding to Point P while, 𝛼+* is to the DoC corresponding to Point V. Where 𝑉#42 is the maximum volumetric shr...

    1992

  30. [1993]

    The phenomenological models are based on empirical rate laws and do not incorporate the details of the resin reaction

    and mechanistic models (Phelan and Sung 1997; Hopewell, George, and Hill 2000). The phenomenological models are based on empirical rate laws and do not incorporate the details of the resin reaction. The mechanistic models take into account the details of the reaction such as s...

    1997

  31. [1995]

    Effects of Processing Temperature and Layup on Springback

    “Effects of Processing Temperature and Layup on Springback.” Journal of Composite Materials. https://doi.org/10.1177/002199839502901001. Shah, PH, VA Halls, JQ Zheng, and RC Batra

    doi

  32. [1997]

    and glass transition temperature Tg (Liu et al. 2021). The modified CHILE model implemented in the present study is CHILE(𝛼) such that the modulus development is assumed to occur from gelation upto vitrification of the resin. This is demonstrated with the help of a Polymerizat...

    2021

  33. [1998]

    (𝑥@B))}€𝑌@

    is one such acquisition function that measures the expected amount of improvement in the objective function value over the current best-known value at a given point. For our problem which is a minimization problem, 𝐸𝐼 at a point 𝑥@B) is defined as 𝐸𝐼(𝑥@B))=𝔼8𝑚𝑎𝑥{0,𝑌min−𝑌"(𝑥@B)...

    2014

  34. [2000]

    New Method to Reduce Cure-Induced Stresses in Thermoset Polymer Composites, Part II: Closed Loop Feedback Control System

    “New Method to Reduce Cure-Induced Stresses in Thermoset Polymer Composites, Part II: Closed Loop Feedback Control System.” Journal of Composite Materials 34 (22). https://doi.org/10.1106/3M0Y-44XM-6WP8-WT7J. Gigliotti, M., M. R. Wisnom, and K. D. Potter

    doi

  35. [2002]

    Cure Reaction for Modified Diallylbisphenol A/Diaminodiphenylsulfone/Bismaleimide

    “Cure Reaction for Modified Diallylbisphenol A/Diaminodiphenylsulfone/Bismaleimide.” Journal of Applied Polymer Science 85 (2). https://doi.org/10.1002/app.10386. Bogetti, Travis A., and John W. Gillespie

    doi

  36. [2003]

    Development of Curvature during the Cure of AS4/8552 [0/90] Unsymmetric Composite Plates

    “Development of Curvature during the Cure of AS4/8552 [0/90] Unsymmetric Composite Plates.” Composites Science and Technology. https://doi.org/10.1016/S0266-3538(02)00195-1. Goodwin, A. A

    doi

  37. [2004]

    Prediction of Shape Distortions Part I. FE-Implementation of a Path Dependent Constitutive Model

    “Prediction of Shape Distortions Part I. FE-Implementation of a Path Dependent Constitutive Model.” Composites Part A: Applied Science and Manufacturing 35 (6): 711–21. https://doi.org/10.1016/j.compositesa.2004.02.005. Szarski, Martin, and Sunita Chauhan

    2004 doi

  38. [2005]

    A Linear Finite Element Model to Predict Processing-Induced Distortion in FRP Laminates

    “A Linear Finite Element Model to Predict Processing-Induced Distortion in FRP Laminates.” Composites Part A: Applied Science and Manufacturing 36 (12): 1666–74. https://doi.org/10.1016/j.compositesa.2005.03.018. Bellini, Costanzo, and Luca Sorrentino

    2005 doi

  39. [2006]

    A Micromechanical Study of Residual Stress and Its Effect on Transverse Failure in Polymer-Matrix Composites

    “A Micromechanical Study of Residual Stress and Its Effect on Transverse Failure in Polymer-Matrix Composites.” International Journal of Solids and Structures. https://doi.org/10.1016/j.ijsolstr.2005.08.012. 28 Appendix A: Bayesian Optimization Overview Given a limited computa...

    2005 doi

  40. [2010]

    Role of Tool-Part Interaction in Process-Induced Warpage of Autoclave-Manufactured Composite Structures

    “Role of Tool-Part Interaction in Process-Induced Warpage of Autoclave-Manufactured Composite Structures.” In Composites Part A: Applied Science and Manufacturing, 41:1174–83. https://doi.org/10.1016/j.compositesa.2010.04.017. Zhang, Guiming, Jihui Wang, Aiqing Ni, Haixiao Hu,...

    2010 doi

  41. [2014]

    (𝑥) and 𝑌?(𝑥) defined similarly as in Eq. (9). Let 𝑋@={𝑥),⋯,𝑥@} be the initial input points, and 𝑌@

    , statistical models should be customized by the optimization problem. A general framework of BO is reviewed in Appendix A. In our problem, we use Gaussian process models as surrogate models for objective function and constraint function and employ expected constrained improve...

    2005

  42. [2015]

    Numerical Simulation of Curing Deformation of Resin Matrix Composite Curved Structure

    “Numerical Simulation of Curing Deformation of Resin Matrix Composite Curved Structure.” Fuhe Cailiao Xuebao/Acta Materiae Compositae Sinica 32 (3). https://doi.org/10.13801/j.cnki.fhclxb.20141028.004. Madhukar, Madhu S., Mohamed S. Genidy, and John D. Russell

    doi

  43. [2016]

    Rapidly Cured Epoxy/Anhydride Composites: Effect of Residual Stress on Laminate Shear Strength

    “Rapidly Cured Epoxy/Anhydride Composites: Effect of Residual Stress on Laminate Shear Strength.” Composites Part A: Applied Science and Manufacturing. https://doi.org/10.1016/j.compositesa.2016.06.013. Bapanapalli, Satish K., and Lloyd V. Smith

    2016 doi

  44. [2017]

    A New Path-Dependent Constitutive Model Predicting Cure-Induced Distortions in Composite Structures

    “A New Path-Dependent Constitutive Model Predicting Cure-Induced Distortions in Composite Structures.” Composites Part A: Applied Science and Manufacturing 95 (April):183–96. https://doi.org/10.1016/j.compositesa.2016.11.032. Ersoy, Nuri, Tomasz Garstka, Kevin Potter, Michael ...

    2016 doi

  45. [2018]

    Bayesian optimization efficiently manages the trade-off between exploring new areas and exploiting known regions to optimize an objective function

    proficiently handles the optimization of black-box functions that are expensive or lack analytical expressions by iteratively developing a statistical model, typically a Gaussian process (GP) (Rasmussen and Williams 2005), capturing uncertainty to guide the optimization proces...

    2005

  46. [2019]

    Improved Prediction of Residual Stress Induced Warpage in Thermoset Composites Using a Multiscale Thermo-Viscoelastic Processing Model

    “Improved Prediction of Residual Stress Induced Warpage in Thermoset Composites Using a Multiscale Thermo-Viscoelastic Processing Model.” Composites Part A: Applied Science and Manufacturing 126 (November). https://doi.org/10.1016/j.compositesa.2019.105575. Deb, Kalyanmoy, Amr...

  47. [2020]

    3 - Manufacturing Processes for Composite Materials and Components for Aerospace Applications

    “3 - Manufacturing Processes for Composite Materials and Components for Aerospace Applications.” In Polymer Composites in the Aerospace Industry (Second Edition), edited by Philip Irving and Constantinos Soutis, Second Edi, 59–81. Woodhead Publishing Series in Composites Scien...

    doi

  48. [2021]

    A Two-Stage Genetic Algorithm for Molding Parameters Optimization for Minimized Residual Stresses in Composite Laminates During Curing

    “A Two-Stage Genetic Algorithm for Molding Parameters Optimization for Minimized Residual Stresses in Composite Laminates During Curing.” Applied Composite Materials 28 (4): 1315–34. https://doi.org/10.1007/s10443-021-09912-z. Liu, Xiaodong, Zhidong Guan, Xiaodong Wang, Ting J...

    doi

  49. [2022]

    Multiscale Collaborative Optimization for the Thermochemical and Thermomechanical Cure Process during Composite Manufacture

    “Multiscale Collaborative Optimization for the Thermochemical and Thermomechanical Cure Process during Composite Manufacture.” Composites Science and Technology 224 (June). https://doi.org/10.1016/j.compscitech.2022.109455. Johnston, Andrew a

    2022

  50. [2024]

    31 - A Perspective on the Evolution of Plastics and Composites in the Automotive Industry

    “31 - A Perspective on the Evolution of Plastics and Composites in the Automotive Industry.” In Applied Plastics Engineering Handbook (Third Edition), edited by Myer Kutz, 705–48. William Andrew Publishing. https://doi.org/https://doi.org/10.1016/B978-0-323-88667-3.00016-3. Pu...

    doi

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.