Abstract
The mechanical response, serviceability, and load-bearing capacity of materials and structural components can be adversely affected due to external stimuli, which include exposure to a corrosive chemical species, high temperatures, temperature fluctuations (i.e., freezing–thawing), cyclic mechanical loading, just to name a few. It is, therefore, of paramount importance in several branches of engineering—ranging from aerospace engineering, civil engineering to biomedical engineering—to have a fundamental understanding of degradation of materials, as the materials in these applications are often subjected to adverse environments. As a result of recent advancements in material science, new materials such as fiber-reinforced polymers and multi-functional materials that exhibit high ductility have been developed and widely used, for example, as infrastructural materials or in medical devices (e.g., stents). The traditional small-strain approaches of modeling these materials will not be adequate. In this paper, we study degradation of materials due to an exposure to chemical species and temperature under large strain and large deformations. In the first part of our research work, we present a consistent mathematical model with firm thermodynamic underpinning. We then obtain semi-analytical solutions of several canonical problems to illustrate the nature of the quasi-static and unsteady behaviors of degrading hyperelastic solids.
Article PDF
Similar content being viewed by others
Explore related subjects
Discover the latest articles, news and stories from top researchers in related subjects.Avoid common mistakes on your manuscript.
Abbreviations
- \(\rho \) :
-
Density of solid in deformed configuration \((\mathrm {kg}\,\mathrm {m}^{-3})\)
- A :
-
Specific Helmholtz potential \((\mathrm {J}\,\mathrm {kg}^{-1})\)
- \(\zeta \) :
-
Dissipation functional \((\mathrm {J}\,\mathrm {kg}^{-1}\,\mathrm {s}^{-1})\)
- \(\psi \) :
-
Strain energy density functional \((\mathrm {J}\,\mathrm {m}^{-3})\)
- \(\lambda \), \(\mu \) :
-
Lamé parameters \((\mathrm {Pa})\)
- \(\kappa \) :
-
Bulk modulus \((\mathrm {Pa})\)
- \(\mathbf {u}\) :
-
Displacement \((\mathrm {m})\)
- \(\mathbf {v}\) :
-
Velocity \((\mathrm {m}\,\mathrm {s}^{-1})\)
- \(\vartheta \) :
-
Temperature \((\mathrm {K})\)
- c :
-
Concentration \((\hbox {l})\)
- \(R_s\) :
-
Specific vapor constant \((\mathrm {J}\,\mathrm {kg}^{-1}\,\mathrm {K}^{-1})\)
- \(c_p\) :
-
Heat capacity \((\mathrm {J}\,\mathrm {kg}^{-1}\,\mathrm {K}^{-1})\)
- \(\mathbf {M}_{\vartheta \mathbf {E}}\) :
-
Thermal expansion tensor \((\mathrm {J}\,\mathrm {m}^{-3}\,\mathrm {K}^{-1})\)
- \(\mathbf {M}_{c \mathbf {E}}\) :
-
Chemical expansion tensor \((\mathrm {J}\,\mathrm {m}^{-3})\)
- \(d_{\vartheta c}\) :
-
Thermo–chemo coupled parameter \((\mathrm {J}\,\mathrm {kg}^{-1}\,\mathrm {K}^{-1})\)
- \(\varkappa \) :
-
Specific chemical potential \((\mathrm {J}\,\mathrm {kg}^{-1})\)
- \(\eta \) :
-
Specific entropy \((\mathrm {J}\,\mathrm {kg}^{-1}\,\mathrm {K}^{-1})\)
- \(\mathbf {D}_{\vartheta \vartheta }\) :
-
Thermal diffusion tensor \((\mathrm {m}^2\,\mathrm {s}^{-1})\)
- \(\mathbf {D}_{\varkappa \varkappa }\) :
-
Diffusivity tensor \((\mathrm {m}^2\,\mathrm {s}^{-1})\)
- \(\mathbf {D}_{\vartheta \varkappa }\), \(\mathbf {D}_ {\varkappa \vartheta }\) :
-
Dufour–Soret effect tensors \((\mathrm {m}^2\,\mathrm {s}^{-1})\)
- \(\mathbf {T}\) :
-
Cauchy stress \((\mathrm {Pa})\)
- \(\mathbf {h}\) :
-
Diffusive flux vector \((\mathrm {kg}\,\mathrm {m}^{-2}\,\mathrm {s}^{-1})\)
- \(\mathbf {q}\) :
-
Heat flux vector \((\mathrm {J}\,\mathrm {m}^{-2}\,\mathrm {s}^{-1})\)
- h :
-
Volumetric source \((\mathrm {kg}\,\mathrm {m}^{-3}\,\mathrm {s}^{-1})\)
- q :
-
Volumetric heat source \((\mathrm {J}\,\mathrm {m}^{-3}\,\mathrm {s}^{-1})\)
References
ABAQUS/CAE/Standard, Version 6.14-1. Simulia, Providence. www.simulia.com (2014)
Adler, S.B.: Chemical expansivity of electrochemical ceramics. J. Am. Ceram. Soc. 84, 2117–2119 (2001)
Allam, S.M., Elbakry, H.M.F., Rabeai, A.G.: Behavior of one-way reinforced concrete slabs subjected to fire. Alex. Eng. J. 52, 749–761 (2013)
ANSYS Multiphysics, Version 16.0. ANSYS, Inc., Canonsburg. www.ansys.com (2015)
Antman, S.S.: Nonlinear Problems of Elasticity. Springer, New York (1995)
Batchelor, A.W., Lam, L.N., Chandrasekaran, M.: Materials Degradation and Its Control by Surface Engineering, 3rd edn. Imperial College Press, London (2003)
Bhowmick, S., Shenoy, V.B.: Effect of strain on the thermal conductivity of solids. J. Chem. Phys. 125, 164513 (2006)
Björk, F., Eriksson, C.A., Karlsson, S., Khabbaz, F.: Degradation of components in flooring systems in humid and alkaline environments. Constr. Build. Mater. 17, 213–221 (2003)
Blond, E., Richet, N.: Thermomechanical modelling of ion-conducting membrane for oxygen separation. J. Eur. Ceram. Soc. 28, 793–801 (2008)
Bouadi, H., Sun, C.T.: Hygrothermal effects on the stress field of laminated composites. J. Reinf. Plast. Compos. 8, 40–54 (1989)
Bouadi, H., Sun, C.T.: Hygrothermal effects on structural stiffness and structural damping of laminated composites. J. Mater. Sci. 25, 499–505 (1990)
Bowen, R.M.: Theory of mixtures. In: Eringen, A.C. (ed.) Continuum Physics, vol. III. Academic Press, New York (1976)
Buonsanti, M., Leonard, G., Scoppelliti, F.: Equilibrium state of a binary granular solids mixture. Appl. Mech. Mater. 52, 389–392 (2011)
Cai, L.W., Weitsman, Y.J.: Non-Fickian moisture diffusion in polymeric composites. J. Compos. Mater. 28, 130–154 (1994)
Černy, R., Rovnaníková, P.: Transport Processes in Concrete. CRC Press, New York (2002)
Cho, D.W., Kim, K.: The mechanisms of moisture damage in asphalt pavement by applying chemistry aspects. KSCE J. Civ. Eng. 14, 333–341 (2010)
Coleman, B.D., Dill, E.H.: On thermodynamics and the stability of motions of materials with memory. Arch. Ration. Mech. Anal. 51, 1–53 (1973)
COMSOL Multiphysics User’s Guide, Version 5.0-1. COMSOL, Inc., Burlington. www.comsol.com (2014)
Coussy, O.: Poromechanics. John Wiley & Sons Inc, New York (2004)
Criscione, J.C., Humphrey, J.D., Douglas, A.S., Hunter, W.C.: An invariant basis for natural strain which yields orthogonal stress response terms in isotropic hyperelasticity. J. Mech. Phys. Solids 48, 2445–2465 (2000)
Darbha, S., Rajagopal, K.R.: Unsteady motions of degrading or aging linearized elastic solids. Int. J. Non Linear Mech. 44, 478–485 (2009)
Dym, C.L.: Stability Theory and Its Applications to Structural Mechanics. Dover Publications, New York (2002)
Ericksen, J.L.: Thermoelastic stability. In: Proceedings of the 5th US National Congress of Applied Mechanics, pp. 187–193 (1966)
Farrar, C.R., Worden, K.: Structural Health Monitoring: A Machine Learning Perspective. Wiley, West Sussex (2013)
Gawin, D., Pesavento, F., Schrefler, B.A.: Modeling deterioration of cementitious materials exposed to calcium leaching in non-isothermal conditions. Comput. Methods Appl. Mech. Eng. 198, 3051–3083 (2009)
Glasser, F.P., Marchand, J., Samson, E.: Durability of concrete degradation phenomena involving detrimental chemical reactions. Cem. Concr. Res. 38, 226–246 (2008)
Grasberger, S., Meschke, G.: Thermo-hygro-mechanical degradation of concrete: from coupled 3D material modeling to durability-oriented multifield structural analyses. Mater. Struct. 37, 244–256 (2004)
Gros, X.E.: NDT Data Fusion. Wiley, London (1997)
Gu, J.D., Ford, T.E., Berke, N.S., Mitchell, R.: Biodeterioration of concrete by the fungus Fusarium. Int. Biodeterior. Biodegrad. 41, 101–109 (1998)
Gurtin, M.E.: Thermodynamics and stability. Arch. Ration. Mech. Anal. 59, 53–96 (1975)
Hale, J.K., Kocak, H.: Dynamics and Bifurcations. Springer, New York (1991)
Harper, C.A.: Handbook of Plastics, Elastomers, & Composites, 4th edn. McGraw-Hill, New York (2002)
Heath, M.T.: Scientific Computing—An Introductory Survey, 2nd edn. McGraw-Hill, New York (2005)
Herrmann, A.W.: ASCE 2013 Report Card for America’s Infrastructure. In: IABSE Symposium Report, vol. 99, pp. 9–10. International Association for Bridge and Structural Engineering (2013)
Holzapfel, G.A.: Nonlinear Solid Mechanics. Wiley, Chichester (2000)
Jarkova, E., Pleiner, H., Müller, H.W., Fink, A., Brand, H.R.: Hydrodynamics of nematic ferrofluids. Eur. Phys. J. E 5, 583–588 (2001)
Jung, Y.G., Peterson, I.M., Kim, D.K., Lawn, B.R.: Lifetime-limiting strength degradation from contact fatigue in dental ceramics. J. Dent. Res. 79, 722–731 (2000)
Kachanov, L.: Introduction to Continuum Damage Mechanics. Springer, Dordrecht (1986)
Kaplan, M.F.: Concrete Radiation Shielding: Nuclear Physics, Concrete Properties, Design and Construction. Wiley, New York (1989)
Karra, S., Rajagopal, K.R.: Degradation and healing in a generalized neo-Hookean solid due to infusion of a fluid. Mech. Time-Depend. Mater. 16, 85–104 (2012)
Klepach, D., Zohdi, T.I.: Strain assisted diffusion: modeling and simulation of deformation-dependent diffusion in composite media. Compos. Part B Eng. 56, 413–423 (2014)
Kolberg, R., Wineman, A.: Response of beams of non-linear viscoelastic materials exhibiting strain-dependent stress relaxation. Int. J. Non Linear Mech. 32, 863–883 (1997)
Lai, W.M., Hou, J.S., Mow, V.C.: A triphasic theory for the swelling and deformation behaviors of articular cartilage. J. Biomech. Eng. 113, 245–258 (1991)
Lemaitre, J., Desmorat, R.: Engineering Damage Mechanics: Ductile, Creep, Fatigue and Brittle Failures. Springer, Berlin (2005)
Li, V.C.: On engineered cementitious composites (ECC). J. Adv. Concr. Technol. 1, 215–230 (2006)
Lurie, A.I.: Nonlinear Theory of Elasticity, North Holland Series in Applied Mathematics and Mechanics. Elsevier Science, Amsterdam (1990)
MATLAB: The MathWorks Inc. Natick, Massachusetts (2012)
Maugin, G.A.: The Thermomechanics of Nonlinear Irreversible Behaviours: An Introduction. World Scientific Publishing Company, New Jersey (1998)
McAfee, K.B.: Stress-enhanced diffusion in glass I. Glass under tension and compression. J. Chem. Phys. 28, 218–226 (1958a)
McAfee, K.B.: Stress-enhanced diffusion in glass II. Glass under shear. J. Chem. Phys. 28, 226–229 (1958b)
Morozovska, A.N., Eliseev, E.A., Tagantsev, A.K., Bravina, S.L., Chen, L.Q., Kalinin, S.V.: Thermodynamics of electromechanically coupled mixed ionic–electronic conductors: deformation potential, Vegard strains, and flexoelectric effect. Phys. Rev. B 83, 195313 (2011)
Mudunuru, M.K., Nakshatrala, K.B.: A framework for coupled deformation–diffusion analysis with application to degradation/healing. Int. J. Numer. Methods Eng. 89, 1144–1170 (2012)
Muliana, A., Rajagopal, K.R., Subramanian, S.C.: Degradation of an elastic composite cylinder due to the diffusion of a fluid. J. Compos. Mater. 43, 1225–1249 (2009)
Myers, E.R., Lai, W.M., Mow, V.C.: A continuum theory and an experiment for the ion-induced swelling behavior of articular cartilage. J. Biomech. Eng. 106, 151–158 (1984)
Naus, D.J.: Primer on durability of nuclear power plant reinforced concrete structures—a review of pertinent factors. Technical report, Oak Ridge National Laboratory (ORNL), NUREG/CR–6927 (2007)
Ogden, R.W.: Nonlinear Elastic Deformations. Dover Publications, New York (1997)
Onsager, L.: Reciprocal relations in irreversible processes. I. Phys. Rev. 37, 405 (1931a)
Onsager, L.: Reciprocal relations in irreversible processes. II. Phys. Rev. 38, 2265 (1931b)
Peng, S.T., Landel, R.F.: Induced anisotropy of thermal conductivity of polymer solids under large strains. J. Appl. Polym. Sci. 19, 49–68 (1975)
Picard, R., Leis, R.: Some remarks on the horizontal line method. Math. Methods Appl. Sci. 2, 471–479 (1980)
Pierron, F., Grédiac, M.: The Virtual Fields Method: Extracting Constitutive Mechanical Parameters From Full-Field Deformation Measurements. Springer, New York (2009)
Plešek, J., Kruisová, A.: Formulation, validation and numerical procedures for Hencky’s elasticity model. Comput. Struct. 84, 1141–1150 (2006)
Rajagopal, K.R., Srinivasa, A.R., Wineman, A.S.: On the shear and bending of a degrading polymer beam. Int. J. Plast. 23, 1618–1636 (2007)
Rothe, E.: Zweidimensionale parabolische randwertaufgaben als grenzfall eindimensionaler randwertaufgaben. Math. Ann. 102, 650–670 (1930)
Sadd, M.H.: Elasticity: Theory, Applications, and Numerics, 3rd edn. Academic Press, Oxford (2014)
Saltelli, A., Tarantola, S., Campolongo, F., Ratto, M.: Sensitivity Analysis in Practice: A Guide to Assessing Scientific Models. Wiley, West Sussex (2004)
Saltelli, A., Ratto, M., Andres, T., Campolongo, F., Cariboni, J., Gatelli, D., Saisana, M., Tarantola, S.: Global Sensitivity Analysis: The Primer. Wiley, West Sussex (2008)
Sih, G.C., Michopoulos, J.G., Chou, S.C.: Hygrothermoelasticity. Martinus Nijhoff Publishers, Dordrecht (1986)
Springman, R.M., Bassani, J.L.: Mechano-chemical coupling in the adhesion of thin-shell structures. J. Mech. Phys. Solids 57, 909–931 (2009)
Strogatz, S.H.: Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering. Westview Press, Cambridge (2001)
Sutton, M.A., Orteu, J.J., Schreier, H.W.: Image Correlation for Shape, Motion and Deformation Measurements: Basic Concepts, Theory, and Applications. Springer, New York (2009)
Swamy, R.N.: The Alkali-Silica Reaction in Concrete. CRC Press, New York (2002)
Ulm, J.F., Coussy, O., Kefei, L., Larive, C.: Thermo-chemo-mechanics of ASR expansion in concrete structures. J. Eng. Mech. 126, 233–242 (2000)
Venerus, D.C., Schieber, J.D., Balasubramanian, V., Bush, K., Smoukov, S.: Anisotropic thermal conduction in a polymer liquid subjected to shear flow. Phys. Rev. Lett. 93, 098301 (2004)
Voyiadjis, G.Z., Kattan, P.I.: Damage Mechanics. CRC Press, Taylor & Francis Group, Boca Raton (2005)
Wang, S., Li, V.C.: High-early-strength engineered cementitious composites. ACI Mater. J. 103, 97–105 (2006)
Weitsman, Y.J.: Coupled damage and moisture-transport in fiber-reinforced, polymeric composites. Int. J. Solids Struct. 23, 1003–1025 (1987)
Weitsman, Y.J.: Anomalous fluid sorption in polymeric composites and its relation to fluid-induced damage. Compos. Part A Appl. Sci. Manuf. 37, 617–623 (2006)
Weitsman, Y.J., Guo, Y.J.: A correlation between fluid-induced damage and anomalous fluid sorption in polymeric composites. Compos. Sci. Technol. 62, 889–908 (2002)
Wiggins, S.: Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd edn. Springer, New York (2003)
Willam, K., Rhee, I., Xi, Y.: Thermal degradation of heterogeneous concrete materials. J. Mater. Civ. Eng. 17, 276–285 (2005)
Zheng, R., Tanner, R.I., Fan, X.J.: Injection Molding: Integration of Theory and Modeling Methods. Springer, Berlin (2011)
Ziegler, H.: An Introduction to Thermomechanics. North Holland Publishing Company, Amsterdam (1983)
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by Andreas Öchsner.
C. Xu and M.K. Mudunuru are graduate students at University of Houston.
Rights and permissions
About this article
Cite this article
Xu, C., Mudunuru, M.K. & Nakshatrala, K.B. Material degradation due to moisture and temperature. Part 1: mathematical model, analysis, and analytical solutions. Continuum Mech. Thermodyn. 28, 1847–1885 (2016). https://doi.org/10.1007/s00161-016-0511-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00161-016-0511-4