Keywords: masonry modelling, plasticity, Chen criteria, crack band model, smeared cracks.

This paper discusses an elasto-plastic constitutive modelling for masonry. The non-linear numerical modelling of masonry is one of the most frequently discussed problems. There is a large number of possible approaches that differ both in the complexity and in the accuracy of the results [1].

The proposed approach is one of these less complicated - it is based on use of experimental data or detailed non-linear numerical model to recognize a structural sample behaviour and on use of homogenous elasto-plastic models for actual computational analysis of structure.

The detailed models presented will be discussed for plane stress problems. However, the Chen--Chen criteria is defined for three dimensions (it can also be simplified for two dimensions) so three-dimensional problems will also be discussed here.

The constitutive model for mortar is based on some principles of non-linear fracture mechanics [2]. It is based on the use of a smeared crack approach and uses an equivalent one-dimensional stress-strain (or stress-crack width) relation. Effects of a two-dimensional state of stress are included in the computation through modifications to the limits of an equivalent one-dimensional relationship in the dependence of a current two-dimensional stress state during a computational process. For this purpose Chen-Chen or Kupfer conditions for two-dimensional stresses are used.

The constitutive model for bricks is defined in a different way. It is based on a simplified non-local approach and it is designed for a simulation of a failure of a material that is much more brittle than the mortar.

The Chen-Chen [3] plasticity (and failure) criteria have been selected for elasto-plastic modelling. It was originally derived for the non-linear constitutive modelling of concrete and its use for a modelling of masonry has several disadvantages.

The Chen-Chen condition allows different material strengths for different stress states to be respected but it is not able to respect the anisotropic properties of masonry that are caused by the position of bricks and mortar. To respect the anisotropy at least partially (it is usually simplified and described as orthotropic) a more complicated material condition must be used (for example a combination of Rankine and Hill failure conditions that is proposed by Lourenço [1] can be used).

1

G. Milani, P.B. Lourenço, "Modelling Masonry with Limit Analysis Finite Elements: Review, Applications and New Directions", in B.H.V. Topping, Editor, "Civil Engineering Computations: Tools and Techniques", Saxe-Coburg Publications, UK, 2007. doi:10.4203/csets.16.10

2

M. Jirásek, Z.P. Bazant "Inelastic Analysis of Structures", John Willey and Sons, Chichester, USA, 2002.

3

A.C.T. Chen, W.F. Chen, "Constitutive Relations for Concrete", Journal of the Engineering Mechanics Division ASCE, 1975.

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