  Manufactured materials usually contain random imperfections due to the
fabrication process, e.g., the 3D-printing, casting, etc. These imperfections
affect significantly the effective material properties and result in
uncertainties in the mechanical response. Numerical analysis of the effects of
the imperfections and the uncertainty quantification (UQ) can be often done by
use of digital stochastic surrogate material models. In this work, we present a
new flexible class of surrogate models depending on a small number of
parameters with special focus on two-phase materials. The surrogate models are
constructed as the level-set of a linear combination of an intensity field
representing the topological shape and a Gaussian perturbation representing the
imperfections. The mathematical design parameters of the model are related to
physical ones and thus easy to interpret. The calibration of the model
parameters is performed using progressive batching sub-sampled quasi-Newton
minimization, using a designed distance measure between the synthetic samples
and the data. Then, employing a fast sampling algorithm, an arbitrary number of
synthetic samples can be generated to use in Monte Carlo type methods. In
particular, we illustrate the method in application to UQ of the elasto-plastic
response of an imperfect octet-truss lattice which plays an important role in
additive manufacturing. To this end, we study the effective material properties
of the lattice unit cell under elasto-plastic deformations and investigate the
sensitivity of the effective Young's modulus to the imperfections.
