Abstract:
Under repeated external loads, engineering structures or objects may fail by large plastic deformation or fatigue. Shakedown will occur when the accumulation of plastic deformation ceases under repeated loads; the response of the system is then purely elastic. Fatigue and shakedown have been individually studied for decades and no attempt has been made to couple these two mechanisms in the mechanics analysis. In this study, an attempt is made to couple shakedown and fatigue in pavement mechanics analysis using numerical simulation. The study covers three main areas: fatigue, static shakedown, and kinematic shakedown analysis. A numerical approach to fatigue analysis is proposed based on elastic-plastic fracture mechanics. The amount of the crack growth during each load cycle is determined by using the J-integral curve and $\rm R\sb{-}curve.$ Crack propagation is simulated by shifting the $\rm R\sb{-}curve$ along the crack growth direction. Fatigue life is predicted based on numerically estabiished fatigue equation. The numerical results indicate that the algorithm can be applied to fatigue analyses of different materials. A numerical algorithm based on the finite element method coupled with the nonlinear programming is proposed in static shakedown analysis. In this algorithm, both the inequality and equality constraints are included in the pseudo-objective function. These constraints are normalized by the material yield stress and the reference load, respectively. A multidirectional search algorithm is used in the optimization process. The influence of finite element mesh on shakedown loads is investigated. An algorithm that utilizes eigen-mode to construct the arbitrary admissible plastic deformation path is proposed in kinematic shakedown analysis. This algorithm converts the shakedown theorem into a convex optimization problem and can be solved by using a multidirectional search algorithm. Fatigue behavior of a two-layer full-depth pavement system of asphalt concrete is analyzed using the proposed numerical algorithm. Fatigue crack growth rate is estimated and fatigue life is predicted for the system. Shakedown analyses are also carried out for the same pavement system. The comparison between the shakedown load and the fatigue failure load with respect to the same crack length indicates that the shakedown dominates the response of the pavement system under traffic load.
