  Recent developments in the field of computational modeling of fracture have
opened up possibilities for designing structures against failure. A special
case, called interfacial fracture or delamination, can occur in loaded
composite structures where two or more materials are bonded together at
comparatively weak interfaces. Due to the potential crack growth along these
interfaces, the structural problem suffers from snap-back/snap-through
instabilities and bifurcations with respect to the model parameters, leading to
noisy and discontinuous responses. For such a case, the design optimization
problem for a selected quantity of interest is ill-posed, since small
variations in the design parameters can lead to large jumps in the structural
response. To this end, this paper presents a stochastic optimization approach
to maximize delamination resistance that is less sensitive to small
perturbations of the design and thereby leads to a robust solution. To overcome
the intractability of Monte Carlo methods for estimating the expected value of
the expensive-to-evaluate response function, a global, piecewise-constant
surrogate is constructed based on nearest-neighbor interpolation that is
iteratively refined during the optimization run. We found that by taking a
large stochastic region at the beginning of the optimization and gradually
reducing it to the desired one can help overcome poor local optima. Our results
demonstrate the effectiveness of the proposed framework using an example of
shape optimization of hard inclusions embedded in a double-cantilever beam,
which significantly enhances delamination resistance.
