Statistically equivalent surrogate material models and the impact of random imperfections on elasto-plastic response

• Published in: arXiv.org 2022-02
• Main Authors: Khristenko, Ustim, Constantinescu, Andrei, Patrick Le Tallec, Wohlmuth, Barbara
• Format: Article
• Language: English
• Subjects: Algorithms; Casting defects; Design parameters; Mathematical models; Monte Carlo simulation; Perturbation; Statistical methods; Three dimensional printing
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.2112.06655

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.