Multiscale Mechanics
From nano to macro scale
Multiscale Mechanics
Multi-scale mechanics consist in understanding, through both experimental methods and models (theoretical, numerical), the response of materials when submitted to external loading by accounting for phenomena occurring through the hierarchy of scales.
Comparison of the experimentally observed crack propagation with that numerically predicted. At an applied displacement of ud = 1.5 mm, which corresponds approximately to the failure load, both the experiment and the simulation present some damage at the crack tip. At ud = 2.0 mm, the crack propagated from both sides of the hole in the experiment. However, the simulation features a shorter crack present only at the top of the first hole.
Schematic flowchart of the dual-scale FFf-homogenization. (a) μCT imaging data of physical specimen, performed with large field of view for the mesoscale, and at high resolution for the microscale. (b) Constituent extraction using specialized software OpenFiberSeg. (c) The result of FFT-homogenization at the microscale serves as input for the mesoscale homogenization.
The discipline requires, on one hand, understanding material behaviour at different length scales through experimental methods. The challenge lies in developing experimental methods to mechanically load materials at the scale of their microstructure and measure strains at these scales.
On the other hand, the discipline encompasses modelling techniques that bridge the models developed and each individual scale to yield an homogeneously equivalent prediction. The main challenge lies in developing models that capture the most important features while remaining computationally-efficient.
Result of the FFT homogenization procedure on a subvolume of a specimen made with the D = 0.25 mm nozzle and the 0°-0° printing pattern. (a) Tomographic data in the plane of the printing bed. (b) Von Mises strain field, mainly present in the vicinity of pores. (c) Von Mises stress field, concentrating inside fibers.
The up-scale procedure used by Trofimov et al. [6] to simulate the RTM process. The experimentally measured polymer viscoelastic behavior, CTE and CCS using DMA, TMA and PvT-HADDOC, correspondingly, were utilized to compute the polymer’s constitutive theory parameters presented in Section 2.2 (S1). The developed constitutive theory was used in the homogenization procedure to determine the effective constitutive model parameters of the tows at the micro-scale (S2). The obtained tows and the polymer’s constitutive theories were used in the homogenization procedure to determine the effective constitutive model parameters of the ply at the mesa-scale (S3). The computed ply constitutive model was utilized to simulate the RTM process (S4).
Optimized FO geometry in Example #5; (a-e) the optimized FO, (f-j) the optimized and modified FO, (k-o) the homogenized model of the optimized and modified FO. In the optimized PO, each sub-domain features a different height and relative density which come from the optimized solution. The holes in the first layer correspond to hexagonal patterns. Thus, in each sub-domain, the holes pattern is different. The optimized FO had to be modified due to the discontinuity between the sub-domains having different honeycomb cells topologies and, correspondingly, due to the difficulties in meshing the geometry. In the modified FO, the holes at the first layer were removed. Moreover, the borders between the sub-domains have been filled with solid bars with a thickness of 2 mm. In the same way, in the corresponding homogenized FO, the first layer was considered as an in-filled layer and the borders were added whose mechanical properties were the bulk mechanical properties.
The resolved-scale procedure followed to compute the internal pressure evolution during the in-mold but after the injection stage of the RTM process. The process parameters including temperature and pressure profiles were applied as solution-independent boundary conditions to simulate the RTM process at the macro-scale computing the pressure and the strain fields in the part (S1). The strain fields were input as boundary conditions to the meso-scale RVE for the simulation of the pressure in the polymer matrix and the strain fields in the tows (S2). The strain responses in the tows were input as boundary conditions to the micro-scale RVE for the computation of the pressure in the polymer matrix (S3).
