Moscow University Mechanics Bulletin

, Volume 72, Issue 3, pp 55–58 | Cite as

General properties of relaxation curves in the case of the initial stage of strain with a constant rate in the linear heredity theory

Article
  • 19 Downloads

Abstract

Qualitative properties of relaxation curves are analytically studied in the case of linear-time strain at the initial stage. These curves are induced by an integral constitutive relation of viscoelasticity with an arbitrary relaxation function. Among these properties are the intervals of monotonicity and convexity, jumps, breaks, the asymptotics of curves, their dependence on the parameters of the initial stage of strain and on the properties of a relaxation function, the convergence type of a family of relaxation curves when the duration of the initial stage tends to zero, etc.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    A. A. Adamov, V. P. Matveenko, N. A. Trufanov, and I. N. Shardakov, Methods of Applied Viscoelasticity (Izd-vo UrO RAN, Ekaterinenburg, 2003) [in Russian].Google Scholar
  2. 2.
    J. S. Bergstrom, Mechanics of Solid Polymers. Theory and Computational Modeling (William Andrew, Elsevier, 2015).Google Scholar
  3. 3.
    S. Lee and W. G. Knauss, “A Note on the Determination of Relaxation and Creep Data from Ramp Tests,” Mech. Time-Dependent Mater. 4 (1), 1–7 (2000).ADSCrossRefGoogle Scholar
  4. 4.
    A. Flory and G. B. McKenna, “Finite Step Rate Corrections in Stress Relaxation Experiments: A Comparison of Two Methods,” Mech. Time-Dependent Mater. 8 (1), 17–37 (2004).ADSCrossRefGoogle Scholar
  5. 5.
    J. Sorvari and M. Malinen, “Determination of the Relaxation Modulus of a Linearly Viscoelastic Material,” Mech. Time-Dependent Mater. 10 (2), 125–133 (2006).ADSCrossRefGoogle Scholar
  6. 6.
    W. G. Knauss and J. Zhao, “Improved Relaxation Time Coverage in Ramp-Strain Histories,” Mech. Time- Dependent Mater. 11 (3), 199–216 (2007).ADSCrossRefGoogle Scholar
  7. 7.
    A. V. Khokhlov, “Fracture Criteria under Creep with Strain History Taken into Account, and Long-Term Strength Modelling,” Izv. Ross. Akad. Nauk, Mekh. Tverd. Tela, No. 4, 121–135 (2009) [Mech. Solids 44 (4), 596–607 (2009)].Google Scholar
  8. 8.
    S. E. Duenwald, R. Vanderby, and R. S. Lakes, “Constitutive Equations for Ligament and Other Soft Tissue: Evaluation by Experiment,” Acta Mech. 205, 23–33 (2009).CrossRefMATHGoogle Scholar
  9. 9.
    R. S. Lakes, Viscoelastic Materials (Cambridge Univ. Press, Cambridge, 2009).CrossRefMATHGoogle Scholar
  10. 10.
    D. Tscharnuter, M. Jerabek, Z. Major Z., et al., “On the Determination of the Relaxation Modulus of PP Compounds from Arbitrary Strain Histories,” Mech. Time-Dependent Mater. 15 (1), 1–14 (2011).ADSCrossRefGoogle Scholar
  11. 11.
    R. M. Guedes and J. L. Morais, “A Simple and Effective Scheme for Data Reduction of Stress Relaxation Incorporating Physical-Aging Effects: An Analytical and Numerical Analysis,” Polymer Testing 32 (5), 961–971 (2013).CrossRefGoogle Scholar
  12. 12.
    M. Di Paola, V. Fiore, F. Pinnola, and A. Valenza, “On the Influence of the Initial Ramp for a Correct Definition of the Parameters of Fractional Viscoelastic Materials,” Mech. Mater. 69 (1), 63–70 (2014).CrossRefGoogle Scholar
  13. 13.
    V. A. Fernandes and D. S. De Focatiis, “The Role of Deformation History on Stress Relaxation and Stress Memory of Filled Rubber,” Polymer Testing 40, 124–132 (2014).CrossRefGoogle Scholar
  14. 14.
    D. Mathiesen, D. Vogtmann, and R. Dupaix, “Characterization and Constitutive Modeling of Stress-Relaxation Behavior of Polymethyl Methacrylate (PMMA) across the Glass Transition Temperature,” Mech. Mater. 71, 74–84 (2014).CrossRefGoogle Scholar
  15. 15.
    J. Sweeneya, M. Bonnerb, and I. Ward, “Modelling of Loading, Stress Relaxation and Stress Recovery in a Shape Memory Polymer,” J. Mech. Behav. Biomed. Mater. 37, 12–23 (2014).CrossRefGoogle Scholar
  16. 16.
    B. Babaei, A. Davarian, K. M. Pryse, et al., “Efficient and Optimized Identification of Generalized Maxwell Viscoelastic Relaxation Spectra,” J. Mech. Behav. Biomed. Mater. 55, 32–41 (2015).CrossRefGoogle Scholar
  17. 17.
    A. V. Khokhlov, “Specific Features of Stress-Strain Curves at Constant Stress Rate or Strain Rate Yielding from Linear Viscoelasticity,” Probl. Prochnosti Plastichnosti 77 (2), 139–154 (2015).Google Scholar
  18. 18.
    A. V. Khokhlov, “Asymptotic Commutativity of Creep Curves at Piecewise-Constant Stress Produced by the Linear Viscoelasticity Theory,” Mashinostroenie Inzhener. Obrazovanie, No. 1, 70–82 (2016).Google Scholar
  19. 19.
    A. V. Khokhlov, “The Qualitative Analysis of Theoretic Curves Generated by Linear Viscoelasticity Constitutive Equation,” Nauka Obrazovanie, No. 5, 187–245 (2016).Google Scholar
  20. 20.
    A. V. Khokhlov, “Properties of Creep Curves Families Generated by the Linear Viscoelasticity Theory at Ramp Stress Histories,” Probl. Prochnosti Plastichnosti 78 (2), 164–176 (2016).MathSciNetGoogle Scholar
  21. 21.
    A. V. Khokhlov, “Creep and Relaxation Curves Produced by the Rabotnov Nonlinear Constitutive Relation for Viscoelastoplastic Materials,” Probl. Prochnosti Plastichnosti 78 (4), 452–466 (2016).Google Scholar

Copyright information

© Allerton Press, Inc. 2017

Authors and Affiliations

  1. 1.Institute of MechanicsMoscow State UniversityLeninskie Gory, MoscowRussia

Personalised recommendations