{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,2]],"date-time":"2026-08-02T04:47:20Z","timestamp":1785646040428,"version":"3.56.0"},"reference-count":30,"publisher":"MDPI AG","issue":"15","license":[{"start":{"date-parts":[[2026,7,31]],"date-time":"2026-07-31T00:00:00Z","timestamp":1785456000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"crossref","award":["WUT:203101002"],"award-info":[{"award-number":["WUT:203101002"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100012226","name":"Fundamental Research Funds for the Central Universities","doi-asserted-by":"crossref","award":["WUT:203201006"],"award-info":[{"award-number":["WUT:203201006"]}],"id":[{"id":"10.13039\/501100012226","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Polymers"],"abstract":"<jats:p>A multi-scale framework is proposed for predicting the equivalent engineering elastic constants of carbon\/glass hybrid composite laminates with different fiber volume fractions Vf by integrating multiscale finite element homogenization with analytical micromechanics. Biaxial carbon fiber fabric reinforced vinyl ester composites are used as the target material system, and representative volume element (RVE) models are constructed sequentially at the lamina, laminate, and hybrid-laminate scales. At the lamina scale, the analytical self-consistent field micromechanics (SCFM) approach and the RVE method give highly consistent predictions for the fiber-dominated longitudinal modulus E1 and in-plane shear modulus G12, with deviations below 2%. However, the SCFM approach overestimates the transverse modulus E2 and transverse Poisson\u2019s ratio \u03bd23 as the Vf rises. The unidirectional lamina constants predicted by SCFM and RVE are then used as inputs for an analytical solution for predicting elastic constants (ASPE) and a finite-element-analysis-based micromechanics (FEAM) model of laminate and hybrid-laminate. At the laminate scale, the moduli predicted by ASPE(SCFM) and ASPE(RVE) differ by less than 2%, whereas the out-of-plane properties are sensitive to the transverse lamina inputs. Experimental validation shows that the Ex values predicted by ASPE(RVE) and FEAM(RVE) deviate from the measured average by approximately 3.5%, with good agreement also obtained for Gxy and \u03bdxy. At the hybrid-laminate scale, ASPE(RVE) and FEAM(RVE) exhibit only minor differences in estimating the in-plane moduli, out-of-plane moduli, and Poisson\u2019s ratios.<\/jats:p>","DOI":"10.3390\/polym18151882","type":"journal-article","created":{"date-parts":[[2026,7,31]],"date-time":"2026-07-31T08:46:41Z","timestamp":1785487601000},"page":"1882","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Multiscale Prediction of Equivalent Elastic Properties of Carbon\/Glass Hybrid Composite Laminates"],"prefix":"10.3390","volume":"18","author":[{"given":"Qi","family":"Luo","sequence":"first","affiliation":[{"name":"Luoyang Ship Material Research Institute, Luoyang 471023, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Lexian","family":"Zhang","sequence":"additional","affiliation":[{"name":"Luoyang Ship Material Research Institute, Luoyang 471023, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Fengjia","family":"Zhang","sequence":"additional","affiliation":[{"name":"Luoyang Ship Material Research Institute, Luoyang 471023, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tianke","family":"Tuo","sequence":"additional","affiliation":[{"name":"Luoyang Ship Material Research Institute, Luoyang 471023, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yibo","family":"Wu","sequence":"additional","affiliation":[{"name":"Luoyang Ship Material Research Institute, Luoyang 471023, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Anxin","family":"Ding","sequence":"additional","affiliation":[{"name":"School of Materials Science and Engineering, Wuhan University of Technology, Wuhan 430070, China"},{"name":"Hubei Longzhong Laboratory, Wuhan University of Technology Xiangyang Demonstration Zone, Xiangyang 441100, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,7,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"101158","DOI":"10.1016\/j.coco.2022.101158","article-title":"A simple methodology for predicting process-induced spring-in of curved composite parts","volume":"32","author":"Xu","year":"2022","journal-title":"Compos. Commun."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"101022","DOI":"10.1016\/j.pmatsci.2022.101022","article-title":"A comparative review of multiscale models for effective properties of nano- and micro-composites","volume":"132","author":"Elmasry","year":"2023","journal-title":"Prog. Mater. Sci."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"113685","DOI":"10.1016\/j.compstruct.2021.113685","article-title":"A review of multi-scale numerical modeling of three-dimensional woven fabric","volume":"263","author":"Gao","year":"2021","journal-title":"Compos. Struct."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"106450","DOI":"10.1016\/j.compositesa.2021.106450","article-title":"Micro-mesoscopic prediction of void defect in 3D braided composites","volume":"147","author":"Fu","year":"2021","journal-title":"Compos. Part A Appl. Sci. Manuf."},{"key":"ref_5","unstructured":"Chamis, C.C. (2026, June 10). Simplified Composite Micromechanics Equations for Hygral, Thermal and Mechanical Properties, Proceedings of the Annual Conference of the Society of the Plastics Industry (SPI) Reinforced Plastics\/Composites Institute, Available online: https:\/\/ntrs.nasa.gov\/citations\/19830011546."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"2933","DOI":"10.1016\/0020-7683(94)90060-4","article-title":"Formulas for the stiffness of composites with periodic microstructure","volume":"31","author":"Luciano","year":"1994","journal-title":"Int. J. Solids Struct."},{"key":"ref_7","unstructured":"Stein, E., and Ramm, E. (2001). Error-Controlled Adaptive Finite Elements in Solid Mechanics, John Wiley & Sons."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1016\/0266-3538(95)00141-7","article-title":"Prediction of composite properties from a representative volume element","volume":"56","author":"Sun","year":"1996","journal-title":"Compos. Sci. Technol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"109204","DOI":"10.1016\/j.compscitech.2021.109204","article-title":"Three-dimensional, multiscale homogenization for hybrid woven composites with fiber-matrix debonding","volume":"218","author":"Budzik","year":"2022","journal-title":"Compos. Sci. Technol."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"172","DOI":"10.1016\/j.commatsci.2014.07.034","article-title":"Identification of the mechanical properties of the carbon fiber and the interphase region based on computational micromechanics and Kriging metamodel","volume":"95","author":"Lu","year":"2014","journal-title":"Comput. Mater. Sci."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1016\/0045-7825(93)90198-7","article-title":"A material based finite element analysis of heterogeneous media involving Dirichlet tessellations","volume":"104","author":"Ghosh","year":"1993","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"316","DOI":"10.1016\/j.commatsci.2006.03.005","article-title":"Random models versus periodic models for fibre reinforced composites","volume":"38","author":"Trias","year":"2006","journal-title":"Comput. Mater. Sci."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1016\/j.ijsolstr.2020.08.009","article-title":"Multiscale homogenization method for the prediction of elastic properties of fiber-reinforced composites","volume":"203","author":"Shu","year":"2020","journal-title":"Int. J. Solids Struct."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"629","DOI":"10.1177\/002199838802200703","article-title":"Three-Dimensional Effective Elastic Constants for Thick Laminates","volume":"22","author":"Sun","year":"1988","journal-title":"J. Compos. Mater."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"977","DOI":"10.1177\/002199839002400905","article-title":"Analysis of Thick Section Composite Laminates Using Effective Moduli","volume":"24","author":"Sun","year":"1990","journal-title":"J. Compos. Mater."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"112287","DOI":"10.1016\/j.compstruct.2020.112287","article-title":"Multi-scale elastic property prediction of 3D five-directional braided composites considering pore defects","volume":"244","author":"Ge","year":"2020","journal-title":"Compos. Struct."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1177\/1056789520944986","article-title":"Fully integrated multi-scale modelling of damage and time-dependency in thermoplastic-based woven composites","volume":"30","author":"Praud","year":"2021","journal-title":"Int. J. Damage Mech."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"113725","DOI":"10.1016\/j.compstruct.2021.113725","article-title":"Micro-damage initiation evaluation of z-pinned laminates based on a new three-dimension RVE model","volume":"263","author":"Wang","year":"2021","journal-title":"Compos. Struct."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"112344","DOI":"10.1016\/j.compstruct.2020.112344","article-title":"Adaptive importance sampling based neural network framework for reliability and sensitivity prediction for variable stiffness composite laminates with hybrid uncertainties","volume":"245","author":"Mathew","year":"2020","journal-title":"Compos. Struct."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"113482","DOI":"10.1016\/j.cma.2020.113482","article-title":"Smart constitutive laws: Inelastic homogenization through machine learning","volume":"373","author":"Logarzo","year":"2021","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"2300185","DOI":"10.1002\/smsc.202300185","article-title":"Multiscale Computational and Artificial Intelligence Models of Linear and Nonlinear Composites: A Review","volume":"4","author":"Agarwal","year":"2024","journal-title":"Small Sci."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"118479","DOI":"10.1016\/j.compstruct.2024.118479","article-title":"Multiscale homogenization of thermo-mechanical viscoelastic response of 3D orthogonal composites with time-dependent CTEs","volume":"347","author":"Huang","year":"2024","journal-title":"Compos. Struct."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"114514","DOI":"10.1016\/j.commatsci.2026.114514","article-title":"A machine learning approach to modeling the effects of fiber shape and interphase on the thermoelastic properties of composites","volume":"265","author":"Sun","year":"2026","journal-title":"Comput. Mater. Sci."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"112972","DOI":"10.1016\/j.compositesb.2025.112972","article-title":"Multiscale modelling of residual thermal stresses and off-axis bending in 3D braided composites","volume":"308","author":"Song","year":"2026","journal-title":"Compos. Part B Eng."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"108604","DOI":"10.1016\/j.ijmecsci.2023.108604","article-title":"Multiscale progressive damage model for plain woven composites","volume":"259","author":"Sun","year":"2023","journal-title":"Int. J. Mech. Sci."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1311","DOI":"10.1177\/0021998306068072","article-title":"Shear-lag Analysis of the Effect of Thickness on Spring-in of Curved Composites","volume":"41","author":"Wisnom","year":"2007","journal-title":"J. Compos. Mater."},{"key":"ref_27","unstructured":"(2025). Standard Test Method for Tensile Properties of Polymer Matrix Composite Materials (Standard No. ASTM D3039\/D3039M-17(2025))."},{"key":"ref_28","unstructured":"(2025). Standard Test Method for Shear Properties of Composite Materials by V-Notched Rail Shear Method (Standard No. ASTM D7078\/D7078M-20(2025))."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"626","DOI":"10.1177\/002199839202600502","article-title":"Process-Induced Stress and Deformation in Thick-Section Thermoset Composite Laminates","volume":"26","author":"Bogetti","year":"1992","journal-title":"J. Compos. Mater."},{"key":"ref_30","unstructured":"Hartmann, M., Strebinger, M., and Hinterh\u00f6lzl, R.M. (2026, June 15). An Approach Towards a Basic Materials Characterization for the Simulation of Process Induced Deformations. Available online: https:\/\/mediatum.ub.tum.de\/1233249."}],"container-title":["Polymers"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-4360\/18\/15\/1882\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,2]],"date-time":"2026-08-02T04:22:58Z","timestamp":1785644578000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-4360\/18\/15\/1882"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,7,31]]},"references-count":30,"journal-issue":{"issue":"15","published-online":{"date-parts":[[2026,8]]}},"alternative-id":["polym18151882"],"URL":"https:\/\/doi.org\/10.3390\/polym18151882","relation":{},"ISSN":["2073-4360"],"issn-type":[{"value":"2073-4360","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,7,31]]}}}