Mesoscopic modelling of masonry using embedded weak discontinuities based on partitions of unity

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. The macroscopic approach homogenises the mortar joints and bricks creating one orthotropic material, whereas the mesoscopic approach models the joints and bricks as separate entities. In this contribution a two dimensional mesoscopic model will be developed, where mortar joints are modelled by embedded discontinuities using the partition of unity property of the finite element shape functions.

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 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 algorithmic aspects will be discussed. Special attention is given to the modelling of triple junctions and the dealing with the enhanced degrees of freedom.

A Drucker-Prager local damage model is used to describe the non-linear behaviour of the discontinuities. The global equilibrium path is traced using an energy release constraint function. The performance of the developed masonry model will be demonstrated by the simulation and validation of three-point-bending tests and shear wall analysis.