Time-dependent mesoscopic modelling of masonry using embedded weak discontinuities

Abstract

The modelling of masonry has been a popular topic within computational mechanics for some years now. Two major groups of modelling approaches exist: macroscopic and mesoscopic models. In this contribution a two dimensional mesoscopic model (i.e. joints and bricks are modelled as separate entities) will be developed that incorporates time-dependent behaviour. Since in masonry structures the cracks often follow the joints, the potential crack paths are known in advance. Unlike classical mesoscopic models, where joints are modelled using strong discontinuities (i.e. jumps in the displacement field), the model developed in this paper uses embedded weak discontinuities. A weak discontinuity introduces a jump in the strain field, allowing for failure to localise in a zone with finite width. The thickness of this failure is in this case linked to the joint thickness. An advantage of this weak discontinuity approach is that the constitutive modelling can be performed in the general stress and strain spaces. In this work, the embedded weak discontinuity is implemented using the partition of unity concept. Within this method, nodes are locally enhanced to enrich the solution with discontinuous modes. Both the governing equations and the implementation aspects will be discussed. Special attention is given to the modelling of triple junctions and the dealing with the enhanced degrees of freedom. Within the discontinuities, a viscoplastic model is used to describe time-dependent joint degradation, e.g. the creep phenomenon. In this paper, the Perzyna viscoplastic model will be adopted in combination with several yield surfaces, e.g. modified von Mises, Drucker-Prager with compressive cap, Menetrey-William. The performance of the developed masonry model will be demonstrated by the simulation and validation of some simple tests in uniaxial compression and shear, three-point-bending tests and shear wall analysis.