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.

Keywords:

• Damage
• quasistatic
• random inputs
• inclusion
• elastic

AMS Subject Classifications:

• 35K61
• 35Q74
• 35M31

Notes

No potential conflict of interest was reported by the authors.