Mixed FEM for solving a plate type model intended for analysis of pavements with discontinuities

Abstract

This paper aims at presenting the development of a numerical tool dedicated to the computation of the mechanical response of pavements incorporating vertical cracks and/or interlayer debonding. In this tool, the structure is modelled as a pilling of “plate” elements of type M4-5n (Multi-Particle Model for Multilayer Materials) which considers 5 equilibrium equations per layer (n stands for the number of layer). Here we focus on the development of a mixed Finite Element (FE) method dedicated to the solving of M4-5n. This method relies on the derivation of a variational principle based on the complementary energy theorem. Expressing stationarity of the functional obtained with respect to all its fields leads to the mixed formulation. Special attention is paid to the discretization process of this formulation in order to avoid ill-conditioned system of algebraic equations after discretization and to insure stability of the solution. The developed method is implemented in a FreeFem++ script. The advantage of the method is twofold: (i) the initial 3D problem can be handled through 2D FE simulations and (ii) finite values of the generalised efforts are obtained at crack and interlayer debonding locations. This approach is thus particularly adapted to parametric studies and, in the future, might be considered for crack growth in layered structures such as pavements. This paper ends with the analysis by means of M4-5n of a 3D structure incorporating cracks, representative of a pavement tested under full-scale conditions during an accelerated fatigue test performed at IFSTTAR. Several scenarios of cracking are analysed and compared to experimental results.