From SEM images to elastic responses: A stochastic multiscale analysis of UD fiber reinforced composites

A micromechanics‐based inverse study for stochastic order reduction of elastic UD fiber reinforced composites analyses

“…With a proper microstructure generation scheme, which keeps the spatial characteristics of microstructures, an adequate number of virtual samples (here, the SVEs) can be generated for virtual tests (here, homogenizations). In this section, we briefly summarize the SVE generation process built from SEM images statistical analysis as developed in the work of Wu et al 25 and the computational homogenization theory. Stochastic homogenization is then applied on the generated SVEs, and, using the obtained probabilistic behavior of the homogenized mesoscale material, a classical statistical procedure, the PCA, is performed.…”

“…However, stochastic homogenization can also be applied to capture the variation in the homogenized response with a view of upscaling the resulting uncertainties. In this context, computational homogenization performed on SVEs results in statistical homogenized properties of heterogeneous materials, ie, the homogenized behavior of random two-phase elastic composites was described by a transverse isotropic law with resultant Young's modulus and Poisson ratio, [22][23][24] an orthogonal anisotropic law was adopted in the work of Wu et al 25 for the same material system, and in the work of Lucas et al 26,27 for polysilicon elastic behavior and thermoelastic damping. In the context of nonlinear materials, a complete statistical analysis combining Monte Carlo resolutions of SVEs to multiscale analyses would require a huge series of preoffline computations on SVEs.…”

“…42 However, conducting a reliable stochastic multiscale structural analysis by SFEM requires the stochastic description of the material properties to be defined accounting for the size of the stochastic FEs, 26 ie, the SVEs used to define the mesoscale random material property fields should have a comparable size to the FE size in the composite structure analysis. Since there exists a huge length gap between the computationally affordable SVEs size to the FE size of structural analysis in UD fiber reinforced composites, the multilevel computational stochastic homogenization developed in the work of Wu et al 25 is considered to define the random vector  M-T . However, no ROM was developed in the work of the aforementioned authors, 25 which is the purpose of the present work through the development of an inverse stochastic identification of the M-T model.…”

“…Since there exists a huge length gap between the computationally affordable SVEs size to the FE size of structural analysis in UD fiber reinforced composites, the multilevel computational stochastic homogenization developed in the work of Wu et al 25 is considered to define the random vector  M-T . However, no ROM was developed in the work of the aforementioned authors, 25 which is the purpose of the present work through the development of an inverse stochastic identification of the M-T model. This paper is organized as follows.…”

“…This paper is organized as follows. In Section 2, the stochastic homogenization of UD SVEs is conducted, using as input the statistical description obtained from scanning electron microscope (SEM) images in the work of Wu et al 25 In particular, the statistical convergence of the homogenized apparent elastic properties is studied. The stochastic M-T model is developed in linear elasticity in Section 3.…”