Accelerated time integrator for multiple time scale homogenization

Summary This manuscript presents an accelerated time domain homogenization methodology for prediction of material and structural failure under fatigue loading. The methodology is based on mathematical homogenization theory applied to the time domain. The method addresses the computational challenge associated with the scale disparity between the characteristic fatigue load period and the overall fatigue life. Cycle sensitive continuum damage mechanics modeling is used to describe the progressive damage accumulation under fatigue loading. The original initial boundary value problem is decomposed into coupled fast and slow time scale problems. A quasilinear approximation to the fast time scale problem is introduced to efficiently evaluate the response under a fatigue load cycle. The effect of the new time integrator on the thermodynamic consistency of the resulting system of discrete equations is demonstrated for a general class of continuum damage mechanics models. The proposed method is numerically verified based on a scalar damage model and a spatially multiscale damage model used for predicting fatigue life of composite materials. The proposed accelerated time integrator is shown to have reasonable accuracy and is orders of magnitude more computationally efficient when compared with previously proposed time homogenization methods. Copyright © 2015 John Wiley & Sons, Ltd.