As the internal microstructure of composite materials becomes more complex, multi-scale methods are gaining strength. These are based on obtaining the response of a system dividing its solution in several nested analyses, each one located in a different scale. In the case of composite structures, multiscale methods are commonly used by obtaining the material performance in the macro-structure from the solution of a numerical model of a Representative Volume Element (RVE) or micro-structure of th...

As the internal microstructure of composite materials becomes more complex, multi-scale methods are gaining strength. These are based on obtaining the response of a system dividing its solution in several nested analyses, each one located in a different scale. In the case of composite structures, multiscale methods are commonly used by obtaining the material performance in the macro-structure from the solution of a numerical model of a Representative Volume Element (RVE) or micro-structure of the composite. In other words, the stresses in the macro-structure are obtained from a numerical model of the micro-structure, which boundary conditions are defined from the macro-model. However, despite the increase of nowadays computational capabilities, performing a multiscale analysis of a real structure, taking into account material non-linearities, is still chimeric due to its computational cost. Acknowledging this problem, current work presents four different strategies that can be used to conduct non-linear multiscale analyses.
The first approach can be defined as a Full-Mulsticale procedure and consists in solving the RVE for all gauss points and all load steps. This approach is equivalent to the one followed with a constitutive equation. The main drawback of this approach is its computational cost, which is equivalent to solving a full microstructural problem, as it is proved in [1].
The second approach is the Simulation to Failure procedure. In this case the macro-structure is simulated linearly using a material stiffness tensor obtained from an initial analysis of the RVE. Once the macro-simulation has finished, the elements with larger strain-stress fields can be located and the RVE can be analyzed under those conditions. This analysis will provide the load in which failure occurs. The main advantage of this approach is that in most engineering fields the main interest is to obtain the failure load, and not the performance of the structure after failure. With a Simulation to Failure analysis it is possible to perform this calculation with an affordable computational cost.
The third approach considered is the one proposed by Otero et al. in [2] based on the definition of a Non-Linear Activation Function (NLAF). In it, the authors define a threshold function, based on the strain energy required by the RVE to reach its failure load. The procedure requires a first analysis of the different RVEs of the structure, under the different loads applied to them. The computational cost of this operation is reduced thanks to a Smart First Step (SFS) algorithm. Afterwards the method only analyses the RVEs that become non-linear. The main advantage of this approach is that it allows conducting the non-linear analysis of the structure, with an affordable computational cost. In [2] it is proved that it can reduce the computational cost of the analysis in more than a 98% compared to a Full Multiscale procedure.
Finally, the fourth approach that can be used is the Multiscale Constituve Database (MCD) procedure, currently under development by the authors. This procedure consists in analyzing the RVE under several load paths before conducting the macro-analysis. The mechanical response of the RVE is stored in a database for its further use, when the material analyzed wants to be used in a large macro-structure model. The main advantage of this approach is that, once a given RVE has been characterized, it can be used in as many macro-analysis as wanted, with a minimal computational cost.
Each one of the procedures proposed have advantages and drawbacks. Acknowledging them, as well as the level of accuracy required by the simulation and the computational capabilities available, will define the most adequate procedure to be used for each numerical analysis.