an orthotropic continuum model for the analysis of masonry structures

TNO-95-NM-R0712 1995 15Ñ The normal stress-strain response in the x-direction shows an implicit coupling between normalstress and shear stress. This is also in opposition with the Þxed crack model, where nocoupling is found, but also characterizes the rotating crack model, though to a less extent;Ñ The normal stress-strain response in the y-direction shows the implicit coupling between normalstresses. This is also in opposition with the Þxed crack model, where no coupling isfound, but also characterizes the rotating crack model, though to a less extent. The largeramount of coupling found in the proposed model is due to the isotropic softening.2.3.2 Orthotropic material behaviourThe orthotropic behaviour of the model is now discussed in a single element test under pure uniaxialtension. The material properties given in Table 2 are assumed, in which the y-direction is penalizedby a factor 2. Two different fracture energies are considered for the y-direction: G fx /2 and500 × G fx (almost ideally plastic behaviour).Table 2 - Material properties (orthotropic - α = 1.0)Material propertiesE x 10000 N/mm 2 E y 5000 N/mm 2ν xy 0.2 G xy 3000 N/mm 2f tx 1.0 N/mm 2 f ty 0.5 N/mm 2G fx 0.0002 N.mm/mm 2 G fyCase 1 Case 20.0001 N.mm/mm 2 0.1 N.mm/mm 2The values chosen for the material properties conÞrm the fact that completely different behaviouralong the two material axes can be reproduced, see Fig. 12. In the Þrst example isotropic softeningis considered. This means that the ratio of the material strength along the material axes is constant,see Fig. 13a, during any load history. It is important that this deÞnition is not confounded with thedeÞnition of isotropy used in damaged models. Isotropic softening is related to the current yieldstrength values and, not necessarily, to all the components the current stress vector. When all thefracture energy is exhausted a no-tension material is recovered, see Fig. 14a. In the second exampleideally plastic behaviour in the y-direction is considered. This means that the ratio of the materialstrength along the material axes ( f tx / f ty) tends to zero, see Fig. 13b. The yield surface is onlyallowed to shrink along the x-axis, see Fig. 14b.