Theses Doctoral

Multiscale Modeling with Meshfree Methods

Xu, Wentao

Multiscale modeling has become an important tool in material mechanics because material behavior can exhibit varied properties across different length scales. The use of multiscale modeling is essential for accurately capturing these characteristics and predicting material behavior. Mesh-free methods have also been gaining attention in recent years due to their innate ability to handle complex geometries and large deformations. These methods provide greater flexibility and efficiency in modeling complex material behavior, especially for problems involving discontinuities, such as fractures and cracks. Moreover, mesh-free methods can be easily extended to multiple lengths and time scales, making them particularly suitable for multiscale modeling.

The thesis focuses on two specific problems of multiscale modeling with mesh-free methods. The first problem is the atomistically informed constitutive model for the study of high-pressure induced densification of silica glass. Molecular Dynamics (MD) simulations are carried out to study the atomistic level responses of fused silica under different pressure and strain-rate levels, Based on the data obtained from the MD simulations, a novel continuum-based multiplicative hyper-elasto-plasticity model that accounts for the anomalous densification behavior is developed and then parameterized using polynomial regression and deep learning techniques. To incorporate dynamic damage evolution, a plasticity-damage variable that controls the shrinkage of the yield surface is introduced and integrated into the elasto-plasticity model. The resulting coupled elasto-plasticity-damage model is reformulated to a non-ordinary state-based peridynamics (NOSB-PD) model for the computational efficiency of impact simulations. The developed peridynamics (PD) model reproduces coarse-scale quantities of interest found in MD simulations and can simulate at a component level. Finally, the proposed atomistically-informed multiplicative hyper-elasto-plasticity-damage model has been validated against limited available experimental results for the simulation of hyper-velocity impact simulation of projectiles on silica glass targets.

The second problem addressed in the thesis involves the upscaling approach for multi-porosity media, analyzed using the so-called MultiSPH method, which is a sequential SPH (Smoothed Particle Hydrodynamics) solver across multiple scales. Multi-porosity media is commonly found in natural and industrial materials, and their behavior is not easily captured with traditional numerical methods. The upscaling approach presented in the thesis is demonstrated on a porous medium consisting of three scales, it involves using SPH methods to characterize the behavior of individual pores at the microscopic scale and then using a homogenization technique to upscale to the meso and macroscopic level. The accuracy of the MultiSPH approach is confirmed by comparing the results with analytical solutions for simple microstructures, as well as detailed single-scale SPH simulations and experimental data for more complex microstructures.


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More About This Work

Academic Units
Applied Physics and Applied Mathematics
Thesis Advisors
Fish, Jacob
Spiegelman, Marc W.
Ph.D., Columbia University
Published Here
November 8, 2023