Theses Doctoral

Data-physics Driven Reduced Order Homogenization

Yu, Yang

A hybrid data-physics driven reduced-order homogenization (dpROH) approach aimed at improving the accuracy of the physics-based reduced order homogenization (pROH), but retain its unique characteristics, such as interpretability and extrapolation, has been developed. The salient feature of the dpROH is that the data generated by a high-fidelity model based on the direct numerical simulations with periodic boundary conditions improve markedly the accuracy of the physic-based model reduction. The dpROH consist of the offline and online stages. In the offline stage, dpROH utilized surrogate-based Bayesian Inference to extract crucial information at the representative volume element (RVE) level. With the inferred data, online predictions are performed using a data-enhanced reduced order homogenization. The proposed method combines the benefits of physics-based reduced order homogenization and data-driven surrogate modeling, striking a balance between accuracy, computational efficiency, and physical interpretability.

The dpROH method, as suggested, has the versatility to be utilized across different RVE geometries (including fibrous and woven structures) and various constitutive models, including elasto-plasticity and continuum damage models. Through numerical examples that involve comparisons between different variants of dpROH, pROH, and the reference solution, the method showcases enhanced accuracy and efficiency, validating its effectiveness for a wide range of applications. A novel pseudo-nonlocal eight-node fully integrated linear hexahedral element, PN3D8, has been developed to accelerate the computational efficiency of multiscale modeling for complex material systems.

This element is specifically designed to facilitate finite element analysis of computationally demanding material models, enabling faster and more efficient simulations within the scope of multiscale modeling. The salient feature of the PN3D8 is that it employs reduced integration for stress updates but full integration for element matrices (residual and its consistent tangent stiffness). This is accomplished by defining pseudo-nonlocal and local stress measures. Only the pseudo-nonlocal stress is updated for a given value of mean strain or mean deformation measure for large deformation problems. The local stress is then post-processed at full integration points for evaluation of the internal force and consistent tangent stiffness matrices. The resulting tangent stiffness matrix has a symmetric canonical structure with an identical instantaneous constitutive matrix at all quadrature points of an element. For linear elasticity problems, the formulation of the PN3D8 finite element coincides with the classical eight-node fully integrated linear hexahedral element. The procedure is illustrated for small and large deformation two-scale quasistatic problems.


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More About This Work

Academic Units
Civil Engineering and Engineering Mechanics
Thesis Advisors
Fish, Jacob
Ph.D., Columbia University
Published Here
August 2, 2023