Continuum Damage Mechanics-Based Model of Stochastic Damage Growth

Abstract

Structural damage accumulation is an intrinsically random phenomenon. Continuum damage mechanics seeks to express the aggregate effect of microscopic defects present within a material in terms of macroscopically defined quantities; this makes continuum damage mechanics well-suited to deal with random damage growth in the prelocalization stage. Growth of damage is a thermodynamically irreversible process where the evolution of the Helmholtz free energy is described by a random process. Under fairly general thermodynamic conditions, a set of stochastic differential equations are derived for random isotropic damage growth prior to the onset of localization. The notion that the current state of damage encapsulates the history of the entire process imparts a Markovian characteristic to the damage growth process. The stochastic differential equations are solved to assess damage growth and reliability for uniaxial ductile deformation, high-temperature creep, and fatigue cycling. The models are validated with available experimental results.