What is the state-of-the-art?
The state-of-the-art multiscale commercial software is based on the computational homogenization approach consisting of the following steps:
- Compute deformation gradient at each macro-mesh quadrature point.
- Subject the unit cells to the macro deformation gradients and solve the boundary value problems at each macro quadrature point
- Compute macro-stresses (and tangent for implicit method) by averaging micro-stresses at each macro quadrature point
Why not Computational Homogenization?
Nonlinear unit cell problem has to be solved at every macro quadrature point, macro load increment and iteration.
Size effect and uncertainty
Classical O(1) computational homogenization methods do not account for variation of macro-solution over unit cell domain. Results are independent of the unit cell size. Softening and localization results in mesh size dependence. Finally, the issue of uncertainty propagation from the micro-scale to the component level has to be addressed.
Integration of Unit Cell CAD and meshing tools with component level tools
The salient features of Multiscale Design System (MDS) depicted above are:
- built-in parametric library of microstructures;
- various technologies (such as computational continua, phase nonlocality, dispersion, fracture mechanics based element erosion) allowing to account for size effect, softening and fragmentation;
- ability to coupled multiple physical processes at multiple scales;
- fatigue life predictions;
- uncertainty quantification and propagation;
- characterization of micro-scale model parameters (geometry and material properties) against experimental data; and
- systematic information reduction which makes computational cost to be independent of unit cell complexity