Abstract :
[en] Simulating fracture in realistic engineering components is computationally expensive. In the context
of early-stage design, or reverse engineering, such simulations might need to be performed for a large
range of material and geometric parameters, which makes the solution to the parametric problem of
fracture unaffordable. Model order reduction, such as the proper orthogonal decomposition (POD),
is one way to reduce significantly the computational time by reducing the number of spatial unknowns.
The solution is searched for in a reduced space spanned by a few well-chosen basis vectors only. In the
context of solid mechanics involving structural softening, the strong topological changes in the zone
where damage localises are extremely sensitive to variations of the parameters, which requires reduced
spaces of prohibitively large dimensions in order to approximate the solution with a sufficiently high
degree of accuracy. Introduced in [1], partitioned model order reduction is an alternative to global
model order reduction that essentially divides up the problem into smaller regions. Each region can
then be tackled using a reduced model of appropriate size, if at all, depending on the local material
non-linearities in the region. In the context of multiscale homogenization, simulations of representative
volume elements (RVE) have to be performed to obtain the material properties in the different elements
of a coarse mesh. When considering a nonlinear material, those multiple RVE simulations can be com-
putationally very expensive. They however only differ by the history of boundary conditions applied.
This contribution proposes to apply partitioned model order reduction to those RVEs with reduced bases
parametrized by the boundary conditions.
REFERENCES
[1] P. Kerfriden, O. Goury, T. Rabczuk, S. Bordas, A partitioned model order reduction approach
to rationalise computational expenses in nonlinear fracture mechanics, Computer Methods in
Applied Mechanics and Engineering, 256:169–188, 2013.
