Mesoscopic modelling of masonry using weak discontinuities in the partition of unity framework

Abstract

Modelling of masonry has been a popular topic within computational mechanics for some years now. Three major groups of modelling approaches exist: macroscopic, mesoscopic and microscopic. In this contribution a two dimensional mesoscopic model will be developed, in which 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 PhD research 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. A 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. Both governing equations and algorithmic aspects will be discussed. The performance of the developed masonry model will be demonstrated by the simulation and validation of three-point-bending tests and shear wall analysis.