What is the state-of-the-art?computation_flow

The state-of-the-art multiscale commercial software is based on the computational homogenization approach consisting of the following steps:

  1. Compute deformation gradient at each macro-mesh quadrature point.
  2. Subject the unit cells to the macro deformation gradients and solve the boundary value problems at each macro quadrature point
  3. Compute macro-stresses (and tangent for implicit method) by averaging micro-stresses at each macro quadrature point

Why not Computational Homogenization?nonlinear_cell

  1. Computational complexity

  2. Nonlinear unit cell problem has to be solved at every macro quadrature point, macro load increment and iteration.

  3. Size effect and uncertainty

  4. size_effect

    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.

  5. Integration of Unit Cell CAD and meshing tools with component level tools

  6. mds-framework

    The salient features of Multiscale Design System (MDS) depicted above are:

    1. built-in parametric library of microstructures;
    2. various technologies (such as computational continua, phase nonlocality, dispersion, fracture mechanics based element erosion) allowing to account for size effect, softening and fragmentation;
    3. ability to coupled multiple physical processes at multiple scales;
    4. fatigue life predictions;
    5. uncertainty quantification and propagation;
    6. characterization of micro-scale model parameters (geometry and material properties) against experimental data; and
    7. systematic information reduction which makes computational cost to be independent of unit cell complexity