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Articles

Quasistatic evolution of damage in an elastic body with random inputs

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Pages 1416-1431 | Received 20 Apr 2017, Accepted 24 Sep 2017, Published online: 07 Oct 2017

References

  • Frémond M, Nedjar B. Damage in concrete: the unilateral phenomenon. Nucl Eng Design. 1995;156:323–335.
  • Frémond M, Nedjar B. Damage, gradient of damage and principle of virtual work. Int J Solids Struct. 1996;33(8):1083–1103.
  • Frémond M. Non-smooth thermomechanics. Berlin: Springer; 2002.
  • Andrews KT, Kuttler KL, Rochdi M, et al. One-dimensional dynamic thermoviscoelastic contact with damage. J Math Anal Appl. 2002;272:249–275.
  • Andrews KT, Shillor M. Thermomechanical behaviour of a damageable beam in contact with two stops. Appl Anal. 2006;85(6–7):845–865.
  • Andrews KT, Fernandez JR, Shillor M. Numerical analysis of dynamic thermoviscoelastic contact with damage of a rod. IMA J Appl Math. 2005;70(6):768–795.
  • Angelov TA. On a rolling problem with damage and wear. Mech Res Comm. 1999;26:281–286.
  • Bonetti E, Frémond M. Damage theory: microscopic effects of vanishing macroscopic motions. Comp Appl Math. 2003;22(3):313–333.
  • Bonetti E, Schimperna G. Local existence for Fré mond’s model of damage in elastic materials. Comp Mech Thermodyn. 2004;16(4):319–335.
  • Bonetti E, Freddi F, Segatti A. An existence result for a model of complete damage in elastic materials with reversible evolution. Comp Mech Thermodyn. 2017;29(1):31–50.
  • Campo M, Fernández JR, Han W, et al. A dynamic viscoelastic contact problem with normal compliance and damage. Finite Elem Anal Des. 2005;42:1–24.
  • Campo M, Fernández JR, Kuttler KL, et al. Quasistatic evolution of damage in an elastic body: numerical analyis and computational experiments. Appl Numer Math. 2007;57(9):975–988.
  • Chau O, Fernández JR, Han W, et al. A frictionless contact problem for elastic-viscoplastic materials with normal compliance and damage. Comput Meth Appl Mech Eng. 2002;191:5007–5026.
  • Fernández JR. Analysis of a one-dimensional damage model. Numer Methods Partial Differ Equ. 2005;21(6):1122–1139.
  • Fernández JR, Kuttler KL, Shillor M. Analyse numěrique d’un problème de contact viscoělastique sans frottement avec adhěrence et endommagement [Numerical analysis of a viscoelastic frictionless contact problem with adhesion and damage]. C R Math. 2005 Jul;341(1):63–68.
  • Frémond M, Kuttler KL, Nedjar B, et al. One-dimensional models of damage. Adv Math Sci Appl. 1998;8:541–570.
  • Frémond M, Kuttler KL, Shillor M. Existence and uniqueness of solutions for a one-dimensional damage model. J Math Anal Appl. 1999;229:271–294.
  • Han W, Shillor M, Sofonea M. Variational and numerical analysis of a quasistatic viscoelastic problem with normal compliance, friction and damage. J Comput Appl Math. 2001;137:377–398.
  • Kuttler KL, Shillor M. Quasistatic evolution of damage in an elastic body. Nonlinear Anal RWA. 2006;7:674–699.
  • Kuttler KL, Shillor M, Fernandez JR. Existence and regularity for dynamic viscoelastic adhesive contact with damage. Appl Math Optim. 2006;53:31–66.
  • Sofonea M, Han W, Shillor M. Analysis and approximations of contact problems with adhesion or damage. Vol. 276, Pure and applied mathematics. Boca Raton (FL): Chapman & Hall/CRC Press; 2006.
  • Kuttler KL, Shillor M. Product measurability with applications to a stochastic contact problem with friction. Electron J Differ Equ. 2014;2014(258):1–29.
  • Al-Asuoad N, Alaswad S, Rong L, et al. Mathematical model and simulations of MERS outbreak: predictions and implications for control measures. BIOMATH. 2016;5:1612141.
  • Coffield Jr DJ , Kuttler K, Qu X, et al. A model for the transmission of Chagas disease with random inputs. BIOMATH. 2014;3(2):1–16.
  • Shillor M, Al-Asuoad N, Berven K, et al. Simulations and sensitivity analysis of a model for Wood Frog population, Preprint.
  • Kuttler KL, Li J, Shillor M. A general product measurability theorem with applications to variational inequalities. Electron J Differ Equ. 2016;2016(90):1–12.
  • Duvaut G, Lions JL. Inequalities in mechanics and physics. Berlin: Springer-Verlag; 1976.
  • Han W, Sofonea M. Quasistatic contact problems in viscoelasticity and viscoplasticity. Providence (RI): American Mathematical Society-Intl. Press; 2002.
  • Shillor M, Sofonea M, Telega JJ. Models and analysis of quasistatic contact. Vol. 655, Lecture notes in physics. Berlin: Springer; 2004.
  • Brezis H. Operateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert. Vol. 5, North Holland mathematical studies. Amsterdam: Elsevier; 1973.
  • Simon J. Compact sets in the space Lp(0, T; B). Ann Mat Pura Appl. 1986;146(1):65–96.
  • Lions JL. Quelques methodes de resolution des problemes aux limites non lineaires. Paris: Junod; 1969.
  • Showalter R. Monotone operators in banach space and nonlinear partial differential equations. Vol. 49, Mathematical surveys and monographs. Providence (RI): American Mathematical Society; 1997.

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