Dear Usman,

as it was suggested by Mr Ye and me, in an elastic analysis, concrete would be considered as isotropic.  This is becasue ortortropic behaviour occurs when one direction has different stiffness than another, for instance because of cracking. That is not the case of otrher materials that are orthotropic in elastic regime, like wood, composite laminates, etc.  If you are still interested in conducting an orthotropic analysis, the stiffness to assign in each direction (D1111, D2222, etc.) will depend on the type of problem you try to simulate.  The stiffness in the weakened direction (which you should also decide in your study) is not a material property in concrete (like elastic modulus or Poisson ratio), but will depend on the level of damage. Therefore, is not a simple answer.  Hence, what it is a modification of the modulus in a particular direction.  

In the direction orthogonal to the cracks, the stiffness should be something proportional to the elasticity modulus (E), reduced by cracking.  This reduction can be up to 0 for a fully cracked state, or somewhere in between 0 and the full modulus depending on the extension of the damage.  In the direction pararlell to the crackes, concrete has a higher stiffness but also with some reduction as the cracks weakens concrete in compression.  There are models accounting for that reduction, like the Modified-Compression-Field-Theory (MCFT) or the Softened-Truss-Model, among others.

I do not know what kind of problem you try to study, but I think you should analyse first why you want to study it as an ortrotropic problem and if that is the best option.

In my opinion, concrete can be treated as isotropy, and the material strength depends on the type of imposed loading.

Before cracking, concrete can be consdiered as isotropic in a messo and big scale, although it is actually an anisotropic material at a smaller scale.  Orthotropic charasteristics of concrete results after cracking and other nonlinearities take place. Therefore, those propoerties will depend on the principal directions of stresses and also will be load dependent (depending on the degree of damage, for instance).  That will require a non-linear analysis, in general, not an linear elastic one, for which there are many different porssibilities.

Nevertheless, if you want to do a simplified elastic estimation with linear analysis, you mau decide orthotropic directions after an initial estimation of the principal direction, for instance, and provide a reduced stiffness in the direction corresponding to principal tension.  That would depend on the type of analysis you want to do.

Thankyou Jesus,

The answer was pretty helpful,

Jesus, do you have any idea where can I get the values of orthotropy as shown in the figure above?

Dear Usman,

as it was suggested by Mr Ye and me, in an elastic analysis, concrete would be considered as isotropic.  This is becasue ortortropic behaviour occurs when one direction has different stiffness than another, for instance because of cracking. That is not the case of otrher materials that are orthotropic in elastic regime, like wood, composite laminates, etc.  If you are still interested in conducting an orthotropic analysis, the stiffness to assign in each direction (D1111, D2222, etc.) will depend on the type of problem you try to simulate.  The stiffness in the weakened direction (which you should also decide in your study) is not a material property in concrete (like elastic modulus or Poisson ratio), but will depend on the level of damage. Therefore, is not a simple answer.  Hence, what it is a modification of the modulus in a particular direction.  

In the direction orthogonal to the cracks, the stiffness should be something proportional to the elasticity modulus (E), reduced by cracking.  This reduction can be up to 0 for a fully cracked state, or somewhere in between 0 and the full modulus depending on the extension of the damage.  In the direction pararlell to the crackes, concrete has a higher stiffness but also with some reduction as the cracks weakens concrete in compression.  There are models accounting for that reduction, like the Modified-Compression-Field-Theory (MCFT) or the Softened-Truss-Model, among others.

I do not know what kind of problem you try to study, but I think you should analyse first why you want to study it as an ortrotropic problem and if that is the best option.

Dear Jesus!

The answer was pretty comprehensive, and yes I am modelling cracks in concrete, and simulating a 2 point loading test, I'll get back to you soon

Thanks!

concrete is isotropic material otherwise in case of modeling the brick wall as one unit by concrete model in abaqus, in this case you need to define the ortortropic behavior of concrete

Usually,  concrete is considered as an isotropic material and can give you reasonable results.