FE design for the numerical modelling of failure induced by differential straining in meso-scale concrete: Algorithmic implementation based on operator split method

The present paper focuses on the design of FE for the numerical modelling of failure induced by differential straining in concrete at the meso-scale. The differential straining is here considered as a deformation field added to the mechanical strain field and coming from the solution of a mass transport problem for instance. This differential straining can be induced by changes in degree of saturation, drying shrinkage or fluid overpressure for example. The meso-structure is based on a two-phase 3D representation of concrete, where stiff aggregates are embedded into a mortar matrix. In order to explicitly take into account these aggregates without any mesh adaptation, a weak discontinuity is introduced into the strain field. In addition, a strong discontinuity is also added to take into account cracking. The FE implementation is performed within the Enhanced Finite Element Method (E-FEM). An operator split method equipped with a return mapping algorithm accounting for differential straining is implemented for the computation of the discontinuities values, treated as local variables. In regards to the operator split method proposed in this paper, a broad range of problems can be solved such as basic mass transport problems or failure problem induced both by mechanical loading and differential straining. This feature is an advantage for the design of FE for durability issues. Finally 1D simulations are presented to assess the FE implementation and the performance of the numerical method. We also demonstrate the capability of the method for solving and analyzing 3D mesoscale problems.