A coupled constitutive model for fracture in plain concrete based on continuum theory with non-local softening and eXtended Finite Element Method

• We investigate fracture in concrete elements.
• We use a coupled continuous and discontinuous constitutive model for concrete.
• The effective transition algorithm between non-local models and XFEM is formulated.
• We compare numerical results with experiments.

The paper presents a constitutive model for concrete which combines a continuous and discontinuous fracture description. In a continuum regime, two different constitutive laws were used. First, a plasticity model with a Rankine failure criterion and an associated flow rule was used. Second, a constitutive law based on isotropic damage mechanics was formulated. In order to capture the width of a localized zone and to obtain mesh-independent results, both models were equipped with a characteristic length of micro-structure by applying a non-local theory of an integral format. In order to describe a macro-crack as a displacement jump along/across a localized zone, the eXtended Finite Element Method (XFEM) was used. A transition algorithm between a non-local continuum model and XFEM was formulated. The implementation details of a coupled approach were given. The performance of two coupled models were numerically analysed based on several 2D benchmarks with a dominating mode-I (e.g. uniaxial tension and bending) and under mixed-mode conditions. The numerical results were compared with our experimental ones. The advantages of a continuous–discontinuous coupling in describing crack patterns were outlined.