As thermoset polymers find frequent implementation in engineering design, their application in structural engineering is rather limited. One key reason relies on the ongoing curing process in typical applications such as post-installed adhesive anchors, joints by structural elements or surface-mounted laminates glued by adhesive polymers. Mechanochemistry including curing and aging under thermal as well as mechanical loading causes a multiphysics problem to be discussed. For restricting the variety of material models based on empirical observations, we aim at a thermodynamically sound strategy for modeling thermosets. By providing a careful analysis and clearly identifying the assumptions and simplifications, we present the general framework for modeling and computational implementation of thermo-mechano-chemical processes by using open-source codes.

Chair of Continuum Mechanics and Constitutive Theory Institute of Mechanics Technische Universität Berlin Einsteinufer 5 10587 Berlin Germany

Christian Doppler Laboratory LiCRoFast University of Natural Resources and Life Sciences Peter Jordan Straße 82 1190 Vienna Austria

Faculty of Civil Engineering Czech Technical University Prague Thákurova 7 166 29 Prague 6 Czech Republic

Magnel Vandepitte Laboratory Department of Structural Engineering and Building Materials Ghent University Technologiepark Zwijnaarde 60 9052 Ghent Belgium

Zobrazit více v PubMed

Hong H. Assessment of reliability of aging reinforced concrete structures. J. Struct. Eng. 2000;126(12):1458–1465.

Wang C, Li Q, Ellingwood BR. Time-dependent reliability of ageing structures: an approximate approach. Struct. Infrastruct. Eng. 2016;12(12):1566–1572.

Wan L, Wendner R, Liang B, Cusatis G. Analysis of the behavior of ultra high performance concrete at early age. Cem. Concr. Compos. 2016;74:120–135.

Czernuschka, L., Nincevic, K., Boumakis, I., Wan-Wendner, L., Wan-Wendner, R.: Aging behavior of normal and high strength concretes. In: Computational Modelling of Concrete Structures: Proceedings of the Conference on Computational Modelling of Concrete and Concrete Structures (EURO-C 2018), February 26-March 1, 2018, Bad Hofgastein, Austria, p. 197, CRC Press (2018)

González, A., Barrias, A., Teixeira, R., Martinez, D., Heitner, B., Antonopoulou, S., Zou, G., Gonzalez Merino, A., Sourav, S.N.A., Casas, J.R., et al.: Truss, a european innovative training network dealing with the challenges of an aging infrastructure network. In: The 7th Asia-Pacific Workshop on Structural Health Monitoring (APWSHM 2018), Hong Kong, China, 12–15 November 2018 (2018)

Kim S-G, Park Y-S, Lee Y-H. Rate-type age-dependent constitutive formulation of concrete loaded at an early age. Materials. 2019;12(3):514. PubMed PMC

Ulm F-J, Constantinides G, Heukamp F. Is concrete a poromechanics materials? A multiscale investigation of poroelastic properties. Mater. Struct. 2004;37(1):43–58.

Aigner E, Lackner R, Pichler C. Multiscale prediction of viscoelastic properties of asphalt concrete. J. Mater. Civil Eng. 2009;21(12):771–780.

Unger JF, Eckardt S. Multiscale modeling of concrete. Arch. Comput. Methods Eng. 2011;18(3):341.

Contrafatto L, Cuomo M, Greco L. Meso-scale simulation of concrete multiaxial behaviour. Eur. J. Environ. Civil Eng. 2017;21(7–8):896–911.

Giorgio I, Scerrato D. Multi-scale concrete model with rate-dependent internal friction. Eur. J. Environ. Civil Eng. 2017;21(7–8):821–839.

Scerrato D, Giorgio I, Della Corte A, Madeo A, Dowling N, Darve F. Towards the design of an enriched concrete with enhanced dissipation performances. Cem. Concr. Res. 2016;84:48–61.

Scerrato D, Giorgio I, Della Corte A, Madeo A, Limam A. A micro-structural model for dissipation phenomena in the concrete. Int. J. Numer. Anal. Methods Geomech. 2015;39(18):2037–2052.

Alam SY, Loukili A. Transition from energy dissipation to crack openings during continuum-discontinuum fracture of concrete. Int. J. Fract. 2017;206(1):49–66.

Chiaia B, Kumpyak O, Placidi L, Maksimov V. Experimental analysis and modeling of two-way reinforced concrete slabs over different kinds of yielding supports under short-term dynamic loading. Eng. Struct. 2015;96:88–99.

dell’Isola F, Bragov AM, Igumnov LA, Abali BE, Lomunov AK, Lamzin DA, Konstantinov AY. Mechanical Response Change in Fine Grain Concrete Under High Strain and Stress Rates, New Achievements in Continuum Mechanics and Thermodynamics. Berlin: Springer; 2019. pp. 71–80.

Van Mier JG. Concrete Fracture: A Multiscale Approach. Cambridge: CRC Press; 2012.

Contrafatto L, Cuomo M, Gazzo S. A concrete homogenisation technique at meso-scale level accounting for damaging behaviour of cement paste and aggregates. Comput. Struct. 2016;173:1–18.

Wan-Wendner L, Wan-Wendner R, Cusatis G. Age-dependent size effect and fracture characteristics of ultra-high performance concrete. Cem. Concr. Compos. 2018;85:67–82.

Sauer RA. A survey of computational models for adhesion. J. Adhes. 2016;92(2):81–120.

Boumakis, I., Marcon, M., Nincevic, K., Czernuschka, L.-M., Wan-Wendner, R.: Concrete creep effect on bond stress in adhesive fastening systems. In: 3rd International Symposium on Connections between Steel and Concrete, pp. 396–406 (2017)

Podroužek J, Vorel J, Wan-Wendner R. Design for lifecycle robustness of fastening systems. Beton-und Stahlbetonbau. 2018;113:62–66.

Wan-Wendner R, Podroužek J. Robust power law extrapolation for adhesive anchors under sustained load. ACI Struct. J. 2019;116(1):71–81.

Ninčević K, Boumakis I, Meissl S, Wan-Wendner R. Consistent time-to-failure tests and analyses of adhesive anchor systems. Appl. Sci. 2020;10(4):1527.

Marcon M, Vorel J, Ninčević K, Wan-Wendner R. Modeling adhesive anchors in a discrete element framework. Materials. 2017;10(8):917. PubMed PMC

Kiasat, M.: Curing shrinkage and residual stresses in viscoelastic thermosetting resins and composites, Ph.D. thesis, Technical University of Delft (2000)

Yagimli B, Lion A. Experimental investigations and material modelling of curing processes under small deformations. ZAMM-J. Appl. Math. Mech./Zeitschrift für Angewandte Mathematik und Mechanik. 2011;91(5):342–359.

Liao Z, Hossain M, Yao X, Mehnert M, Steinmann P. On thermo-viscoelastic experimental characterisation and numerical modelling of VHB polymer. Int. J. Non-Linear Mech. 2019;118:103263.

Singer G, Sinn G, Lichtenegger HC, Veigel S, Zecchini M, Wan-Wendner R. Evaluation of in-situ shrinkage and expansion properties of polymer composite materials for adhesive anchor systems by a novel approach based on digital image correlation. Polymer Test. 2019;79:106035.

Bradler PR, Fischer J, Wan-Wendner R, Lang RW. Shear test equipment for testing various polymeric materials by using standardized multipurpose specimens with minor adaptions. Polymer Test. 2019;75:93–98.

Fischer J, Bradler PR, Schmidtbauer D, Lang RW, Wan-Wendner R. Long-term creep behavior of resin-based polymers in the construction industry. Mater. Today Commun. 2019;18:60–65.

Hossain M, Steinmann P. Modelling and simulation of the curing process of polymers by a modified formulation of the arruda-boyce model. Arch. Mech. 2011;63(5–6):621–633.

André M, Wriggers P. Thermo-mechanical behaviour of rubber materials during vulcanization. Int. J. Solids Struct. 2005;42(16–17):4758–4778.

Mahnken R. Thermodynamic consistent modeling of polymer curing coupled to visco-elasticity at large strains. Int. J. Solids Struct. 2013;50(13):2003–2021.

Dal H, Zopf C, Kaliske M. Micro-sphere based viscoplastic constitutive model for uncured green rubber. Int. J. Solid. Struct. 2018;132:201–217.

Johlitz M, Lion A. Chemo-thermomechanical ageing of elastomers based on multiphase continuum mechanics. Continuum Mech. Thermodyn. 2013;25(5):605–624.

Nguyen T-T, Waldmann D, Bui TQ. Phase field simulation of early-age fracture in cement-based materials. Int. J. Solids Struct. 2019;191:157.

Klinge S, Bartels A, Steinmann P. The multiscale approach to the curing of polymers incorporating viscous and shrinkage effects. Int. J. Solids Struct. 2012;49(26):3883–3900.

Klinge S, Hackl K. Application of the multiscale fem to the modeling of nonlinear composites with a random microstructure. Int. J. Multiscale Comput. Eng. 2012;10(3):36–391.

Otero F, Oller S, Martinez X. Multiscale computational homogenization: review and proposal of a new enhanced-first-order method. Arch. Comput. Methods Eng. 2018;25(2):479–505.

Zohdi T, Wriggers P. Phenomenological modeling and numerical simulation of the environmental degradation of multiphase engineering materials. Arch. Appl. Mech. 2000;70(1–3):47–64.

Hossain M, Possart G, Steinmann P. A small-strain model to simulate the curing of thermosets. Comput. Mech. 2009;43(6):769–779.

Hossain M, Steinmann P. Degree of cure-dependent modelling for polymer curing processes at small-strain. Part I: consistent reformulation. Comput. Mech. 2014;53(4):777–787.

Hossain M, Possart G, Steinmann P. A finite strain framework for the simulation of polymer curing. Part I: elasticity. Comput. Mech. 2009;44(5):621–630.

Hossain M, Possart G, Steinmann P. A finite strain framework for the simulation of polymer curing. Part II. Viscoelasticity and shrinkage. Comput. Mech. 2010;46(3):363–375.

Sain T, Loeffel K, Chester S. A thermo-chemo-mechanically coupled constitutive model for curing of glassy polymers. J. Mecha. Phys. Solids. 2018;116:267–289.

Landgraf R, Rudolph M, Scherzer R, Ihlemann J. Modelling and simulation of adhesive curing processes in bonded piezo metal composites. Comput. Mech. 2014;54(2):547–565.

Hu, S., Chen, Y.: A fem coupling model for properties prediction during the curing of an epoxy adhesive for a novel assembly of radio telescope panel, Advances in Optical and Mechanical Technologies for Telescopes and Instrumentation, vol. 9151, p. 915132. International Society for Optics and Photonics (2014)

Leistner C, Hartmann S, Abliz D, Ziegmann G. Modeling and simulation of the curing process of epoxy resins using finite elements. Continuum Mech. Thermodyn. 2020;32(2):327–350.

Alnaes MS, Logg A, Mardal KA, Skavhaug O, Langtangen HP. Unified framework for finite element assembly. Int. J. Comput. Sci. Eng. 2009;4(4):231–244.

Logg A, Mardal KA, Wells G. Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book. Berlin: Springer; 2012.

Lion A, Höfer P. On the phenomenological representation of curing phenomena in continuum mechanics. Arch. Mech. 2007;59(1):59–89.

Shechter L, Wynstra J, Kurkjy RP. Glycidyl ether reactions with amines. Ind. Eng. Chem. 1956;48(1):94–97.

Kamal MR. Thermoset characterization for moldability analysis. Polym. Eng. Sci. 1974;14(3):231–239.

Heinrich C, Aldridge M, Wineman AS, Kieffer J, Waas AM, Shahwan KW. Generation of heat and stress during the cure of polymers used in fiber composites. Int. J. Eng. Sci. 2012;53:85–111.

Flammersheim H-J, Opfermann JR. Investigation of epoxide curing reactions by differential scanning calorimetry-formal kinetic evaluation. Macromol. Mater. Eng. 2001;286(3):143–150.

Chern C-S, Poehlein GW. A kinetic model for curing reactions of epoxides with amines. Polym. Eng. Sci. 1987;27(11):788–795.

Wise CW, Cook WD, Goodwin AA. Chemico-diffusion kinetics of model epoxy-amine resins. Polymer. 1997;38(13):3251–3261.

Rabinowitch E. Collision, co-ordination, diffusion and reaction velocity in condensed systems. Trans. Faraday Soc. 1937;33:1225–1233.

Doolittle AK. Studies in Newtonian flow. II. The dependence of the viscosity of liquids on free-space. J. Appl. Phys. 1951;22(12):1471–1475.

Williams ML, Landel RF, Ferry JD. The temperature dependence of relaxation mechanisms in amorphous polymers and other glass-forming liquids. J. Am. Chem. Soc. 1955;77(14):3701–3707.

Hesekamp D, Broecker HC, Pahl MH. Chemo-rheology of cross-linking polymers. Chem. Eng. Technol. Ind. Chem. Plant Equip. Process Eng. Biotechnol. 1998;21(2):149–153.

Venditti R, Gillham J. A relationship between the glass transition temperature (tg) and fractional conversion for thermosetting systems. J. Appl. Polym. Sci. 1997;64(1):3–14.

Abali BE. Computational Reality, Solving Nonlinear and Coupled Problems in Continuum Mechanics, vol. 55 of Advanced Structured Materials. Singapore: Springer Nature; 2017.

Abali BE, Müller WH, dell’Isola F. Theory and computation of higher gradient elasticity theories based on action principles. Arch. Appl. Mech. 2017;87(9):1495–1510.

Truesdell, C., Toupin, R.A.: Principles of classical mechanics and field theory, Handbuch der Physik Vol. III/1 (Ed. by Flügge, S.) (1960)

Placidi L, Barchiesi E. Energy approach to brittle fracture in strain-gradient modelling. Proc. R. Soc. A Math. Phys. Eng. Sci. 2018;474(2210):20170878. PubMed PMC

Caratheodory C. Untersuchungen über die Grundlagen der Thermodynamik. Mathematische Annalen. 1909;67(3):355–386.

O’Brien DJ, Mather PT, White SR. Viscoelastic properties of an epoxy resin during cure. J. Compos. Mater. 2001;35(10):883–904.

Chern B-C, Moon TJ, Howell JR, Tan W. New experimental data for enthalpy of reaction and temperature- and degree-of-cure-dependent specific heat and thermal conductivity of the Hercules 3501–6 epoxy system. J. Compos. Mater. 2002;36(17):2061–2072.

Landgraf, R.: Modellierung und Simulation der Aushärtung polymerer Werkstoffe, Ph.D. thesis, Technical University of Chemnitz (2016)

Zohdi TI. Finite Element Primer for Beginners. Berlin: Springer; 2018.

Abali, B.E.: Supply code (2019). http://bilenemek.abali.org

GNU Public: Gnu general public license (2007). http://www.gnu.org/copyleft/gpl.html

Still M, Venzke H, Durst F, Melling A. Influence of humidity on the convective heat transfer from small cylinders. Exp. Fluids. 1998;24(2):141–150.

Oleinik EF. Glassy polymers as matrices for advanced composites. Polymer J. 1987;19(1):105–117.