Q2. What is the advantage of the proposed method?
Considering the number of analysis needed to create the stress-strain DB, which is proportional to the discretization parameter m, it is obvious that as long as the number of integration points at the macroscale level is higher than the number of tags, the advantages of the proposed method increases.
Q3. What is the important aspect to consider in a FEM analysis?
In a FEM analysis an important aspect to consider is the mesh discretization of the structure, namely the results must be independent of the mesh size.
Q4. What is the proposed procedure for removing the dependence on macro and micro-scale mesh size?
A fracture-energy-based regularization procedure is also proposed in order to remove the dependence of the results on macro and micro-scale mesh size.
Q5. How many elements are considered in the DMTS and DMCM methods?
In order to reduce the computational cost of the numerical analysis, in case of Full Multiscale and DMTS methods, only 84 elements are considered with double scale, using elastic homogenized properties in the rest of the structure.
Q6. What is the key constraint for this class?
The key kinematical constraint for this class is that the displacement uctuation must be periodic on the di erent faces of the RVE.•
Q7. What is the json format for the data base?
To speed up the Data Base look-up and the parsing process, the information is stored in json format [24] that provides a exible, more compact, easier to parse and more human readable text.
Q8. What is the frequent scenario in DMTS and DMCM?
In order to determine if the stresses in the macro-model are below the threshold surface or to know the equivalent damage parameter associated to the stress state, in the DMTS and DMCM models respectively, the authors need to use an interpolation technique because the most frequent scenario is that the strains associated with the stress analyzed do not correspond to any of the tags previously calculated.
Q9. How can the DMCM method predict the behavior of the macrostructure at each integration point?
an additional interpolation method over the stored threshold surfaces could be performed to predict the behavior of the macrostructure at each integration point.
Q10. What is the simplest way to reduce the computational cost of the RVE?
As their interest lays in the RVE performance, to reduce the computational cost this analysis is conducted in a macroscale triangular FE element with a single gauss point, and in which the strains are imposed as xed displacement to the nodes.
Q11. What are the boundary conditions for the displacement elds?
For the displacement elds, the authors use periodic boundary conditions since they generally provide an intermediate and more exact response compared to other type of boundary conditions, as it is described in [16] [17] [18] [19] [14].
Q12. How many analyses were required to construct the stress-strain database?
In this case, the discretization parameter used to construct the stress-strain database is m = 8 that required a minimum of 114 analyses of the RVE.
Q13. what is the symmetric gradient of the microscopic strain eld?
Ωµ εµ(xµ, t)dV (1)From the Eq. [1] the microscopic strain eld can be expressed as the symmetric gradient of the microscopic displacement eld, uµ = (u x µ, u y µ):εm(xm, t) = 1Vµ ∫