Probabilistic criteria for lateral dynamic stability of bridges under crowd loading

A new analysis method of effective elastic modulus for composites has been developed by combining Eshelby’s equivalent inclusion method and self-consistent method. The equations obtained can describe the evolution of debonding damage of the composites with multi-phase particles and single-phase particles. Based on the incremental relation between particles and the matrix, the incremental constitutive relations of composite, matrix, particles and voids have been developed. Numerical analysis has been conducted for Ramburg–Qsgood function incorporating with equivalent elastic modulus obtained. The constitutive equation curves for different particle volume fractions can describe the influence of debonding damage on effective elastic modulus of the composites. Numerical results of the present study have a better agreement with the experimental results.