Contribution to non-linear constitutive modelling of masonry structures in 2D

Abstract

This paper discusses a non-linear constitutive model for modelling of masonry in 2D. The model consists from two independent parts: the model for mortar and the model for bricks or stones.
The reason of using two different constitutive models is our need to be able to modell individual bricks (or stones in the case of a stone masonry) and the mortar between the bricks.
We have decided to use a smeared crack approach for the modelling fo a mortar. It is an approach that is widely and successfully used for a constitutive modelling of concrete and we assume that it can be also applied to a mortar that is very similar to a concrete.
The model of mortar is based on an equivalent one-dimensional stress-strain relation that depends also on 2D state of stress (through the Kupfer's failure criteria that is used to obtain the limit stresses for the one-dimensional stressstrain relation) and on some special material properties such is fracture energy of mortar.
Bricks are modelled in a different way, As a generally brittle, they often can't be effectively modelly by the smeared crack approach. The damage of the brick (a crack) usually goes through the whole brick and it can be assumed that its occurrence depends on a stress intenzity on an area and not on the stress size in an individual material point. Thus we have decided to use a simple approach that can be describes as a very basic non-local material model.
After the ckack on the brick is detected the material properties are changed in a moment. Unlike the model for a mortar, it is assumed that there is no unloading curve for this model.