Quasistatic evolution of damage in an elastic body with random inputs

Abstract A model for the quasistatic evolution of the motion of an elastic body which is subject to material damage is presented and analyzed. The model takes the form of an elliptic system for the displacements coupled with a parabolic inclusion for the damage field. In both the system and the inclusion the coefficient and input functions that are present are assumed to be stochastic processes dependent on a random variable. The existence of a weak solution to the model is established using a sequence of approximate problems and passage to a limit. Moreover, the weak solution is shown to be product measurable.

[1]  E. Bonetti,et al.  An existence result for a model of complete damage in elastic materials with reversible evolution , 2017 .

[2]  Meir Shillor,et al.  Product measurability with applications to a stochastic contact problem with friction , 2014 .

[3]  Meir Shillor,et al.  Quasistatic evolution of damage in an elastic body: numerical analysis and computational experiments , 2007 .

[4]  J. J. Telega,et al.  Models and analysis of quasistatic contact , 2004 .

[5]  Michel Frémond,et al.  Damage theory: microscopic effects of vanishing macroscopic motions , 2003 .

[6]  Thermomechanical behaviour of a damageable beam in contact with two stops , 2006 .

[7]  W. Han,et al.  Quasistatic Contact Problems in Viscoelasticity and Viscoplasticity , 2002 .

[8]  W. Han,et al.  A frictionless contact problem for elastic–viscoplastic materials with normal compliance and damage , 2002 .

[9]  Michel Frémond,et al.  Damage in concrete: the unilateral phenomenon , 1995 .

[10]  Giulio Schimperna,et al.  Local existence for Frémond’s model of damage in elastic materials , 2004 .

[11]  J. Lions,et al.  Inequalities in mechanics and physics , 1976 .

[12]  L. White,et al.  Sufficient conditions for Hadamard well-posedness of a coupled thermo-chemo-poroelastic system , 2016 .

[13]  Meir Shillor,et al.  Mathematical model and simulations of MERS outbreak: Predictions and implications for control measures , 2017 .

[14]  On a rolling problem with damage and wear , 1999 .

[15]  M. Shillor,et al.  Existence and Regularity for Dynamic Viscoelastic Adhesive Contact with Damage , 2006 .

[16]  W. Han,et al.  Analysis and Approximation of Contact Problems with Adhesion or Damage , 2005 .

[17]  W. Han,et al.  Variational and numerical analysis of a quasistatic viscoelastic problem with normal compliance, friction and damage , 2001 .

[18]  W. Han,et al.  A dynamic viscoelastic contact problem with normal compliance and damage , 2005 .

[19]  Meir Shillor,et al.  Existence and Uniqueness of Solutions for a Dynamic One-Dimensional Damage Model , 1999 .

[20]  M. Frémond,et al.  Damage, gradient of damage and principle of virtual power , 1996 .

[21]  Model and Simulations of a Wood Frog Population , 2012 .

[22]  Meir Shillor,et al.  One-dimensional dynamic thermoviscoelastic contact with damage , 2002 .

[23]  J. Lions.  Quelques méthodes de résolution de problèmes aux limites non linéaires , 1969 .

[24]  M. Frémond,et al.  Non-Smooth Thermomechanics , 2001 .

[25]  H. Brezis.  Opérateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert , 1973 .

[26]  Meir Shillor,et al.  A Model for the Transmission of Chagas Disease with Random Inputs , 2014 .

[27]  KENNETH L. KUTTLER,et al.  A GENERAL PRODUCT MEASURABILITY THEOREM WITH APPLICATIONS TO VARIATIONAL INEQUALITIES , 2016 .

[28]  Meir Shillor,et al.  Quasistatic evolution of damage in an elastic body , 2006 .

[29]  Analysis of a one‐dimensional damage model , 2005 .

[30]  J. Simon.  Compact sets in the spaceLp(O,T; B) , 1986 .

[31]  Analyse numérique d'un problème de contact viscoélastique sans frottement avec adhérence et endommagement , 2005 .

[32]  E. Vrscay,et al.  Continuous evolution of equations and inclusions involving set-valued contraction mappings with applications to generalized fractal transforms , 2014 .

[33]  R. Showalter.  Monotone operators in Banach space and nonlinear partial differential equations , 1996 .