Multiscale Modeling with Meshfree Methods

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

Review of Methods to Solve Desiccation Cracks in Clayey Soils

This paper reviews numerical methods used to simulate desiccation cracks in clayey soils. It examines five numerical approaches: Finite Element (FEM), Lattice Boltzmann (LBM), Discrete Element (DEM), Cellular Automaton (CAM), and Phase Field (PFM) Methods. The paper presents a simplified description of the methods, including their basic numerical formulations. Several factors such as the multiphase nature of soils, heterogeneity, nonlinearities, coupling, scales of analysis, and computational aspects are discussed. The review highlights the characteristics, strengths, and limitations of each method. FEM shows a good capacity to deal with the thermo-hydromechanical behavior of clays when drying that complement well with the ability of DEM to deal with particle interactions as well as LBM, PFM, and CAM to deal with complex crack patterns. The article concludes by reviewing the integration of multiple numerical methods to enhance the simulation of desiccation cracks in clayey soils and proposing what is the best option to continue improving the study of this problem

Contribution to the Non-Lagrangian Formulation of Geotechnical and Geomechanical Processes

Numerical simulations of geomechanical and geotechnical processes, such as vibro-injection pile installation, require suitable algorithms and sufficiently realistic models. These models have to account for large deformations, the evolution of material interfaces including free surfaces and contact interfaces, for granular material behavior in different flow regimes as well as for the interaction of the different materials and phases. Although the traditional Lagrangian formulation is well-suited to handling complex material behavior and maintaining material interfaces, it generally cannot represent large deformation, shear and vorticity. This is because in Lagrangian numerical methods the storage points (nodes resp. material points) move with the local material velocity, which may cause mesh tangling resp. clustering of points. The present contribution addresses the development of models for geotechnical and geomechanical processes by utilizing Eulerian and Arbitrary Lagrangian-Eulerian (ALE) formulations. Such non-Lagrangian viewpoints introduce additional difficulties which are discussed in detail. In particular, we investigate how to track interfaces and to model interaction of different materials with respect to an arbitrarily moving control volume, and how to validate non-Lagrangian numerical models by small-scale experimental tests

Progress in particle-based multiscale and hybrid methods for flow applications

This work focuses on the review of particle-based multiscale and hybrid methods that have surfaced in the field of fluid mechanics over the last 20 years. We consider five established particle methods: molecular dynamics, direct simulation Monte Carlo, lattice Boltzmann method, dissipative particle dynamics and smoothed-particle hydrodynamics. A general description is given on each particle method in conjunction with multiscale and hybrid applications. An analysis on the length scale separation revealed that current multiscale methods only bridge across scales which are of the order of O(102)−O(103) and that further work on complex geometries and parallel code optimisation is needed to increase the separation. Similarities between methods are highlighted and combinations discussed. Advantages, disadvantages and applications of each particle method have been tabulated as a reference

A Particle Model for Prediction of Cement Infiltration of Cancellous Bone in Osteoporotic Bone Augmentation.

PMC3693961Femoroplasty is a potential preventive treatment for osteoporotic hip fractures. It involves augmenting mechanical properties of the femur by injecting Polymethylmethacrylate (PMMA) bone cement. To reduce the risks involved and maximize the outcome, however, the procedure needs to be carefully planned and executed. An important part of the planning system is predicting infiltration of cement into the porous medium of cancellous bone. We used the method of Smoothed Particle Hydrodynamics (SPH) to model the flow of PMMA inside porous media. We modified the standard formulation of SPH to incorporate the extreme viscosities associated with bone cement. Darcy creeping flow of fluids through isotropic porous media was simulated and the results were compared with those reported in the literature. Further validation involved injecting PMMA cement inside porous foam blocks - osteoporotic cancellous bone surrogates - and simulating the injections using our proposed SPH model. Millimeter accuracy was obtained in comparing the simulated and actual cement shapes. Also, strong correlations were found between the simulated and the experimental data of spreading distance (R2 = 0.86) and normalized pressure (R2 = 0.90). Results suggest that the proposed model is suitable for use in an osteoporotic femoral augmentation planning framework.JH Libraries Open Access Fun

Particle Dynamics Simulation toward High-Shear Mixing Process in Many Particle Systems

Granular materials appear in a broad range of industrial processes, including mineral processing, plastics manufacturing, ceramic component, pharmaceutical tablets and food products. Engineers and scientists are always seeking efficient tools that can characterize, predict, or simulate the effective material properties in a timely manner and with acceptable accuracy, such that the cost for design and develop novel composite granular materials could be reduced. The major scope of this dissertation covers the development, verification and validation of particle system simulations, including solid-liquid two-phase particle mixing process and foaming asphalt process. High shear mixing process is investigated in detail with different types of mixers. Besides particle mixing study, one liquid-gas two phase foaming asphalt simulation is studied to show the broad capacity of our particulate dynamics simulation scheme. Methodologies and numerical studies for different scenarios are presented, and acceleration plans to speed up the simulations are discussed in detail. The dissertation starts with the problem statement, which briefly demonstrates the background of the problem and introduces the numerical models built from the physical world. In this work, liquid-solid two-phase particle mixing process is mainly studied. These mixing processes are conducted in a sealed mixer and different types of particles are mixed with the rotation of the mixer blades, to obtain a homogeneous particle mixture. In addition to the solid-liquid particle mixing problem, foaming asphalt problem, which is a liquid-gas two phase flow problem is also investigated. Foaming asphalt is generated by injecting a small amount of liquid additive (usually water) to asphalt at a high temperature. The volume change during this asphalt foaming process is studied. Given the problem statement, detailed methodologies of particle dynamics simulation are illustrated. For solid-liquid particle mixing, Smoothed Particle Hydrodynamics (SPH) and Discrete Element Method (DEM) are introduced and implemented to simulate the dynamics of solid and liquid particles, respectively. Solid-liquid particle interactions are computed according to Darcy`s Law. Then the proposed SPH coupling DEM model is verified by three classical case studies. For foaming asphalt problems, a SPH numerical model for foaming asphalt simulation is proposed, and simulations with different water contents, pressures and temperatures are conducted and the results agree with the experiments well. The coupled SPH-DEM method is applied to the particle mixing process, and several particle mixing numerical studies are conducted and these simulations are analyzed in multiple aspects. For the solid-liquid particle mixing problem, liquid plays an important role in the mixing performance. The effects of liquid content and liquid viscosity on mixing performance are studied. The mixing indexes of the mixture are applied to analyze the mixing quality, and the differences between three kinds of mixing indexes are discussed. Then mixers commonly used in industry such as Double Planetary Mixer (DPM) are modeled in mixing simulation and their results are compared with the experiments. Similar to other numerical simulation problems, the scale of the model and the accuracy of the simulation results are constrained by the computational capacity. Our in-house software package Particle Dynamics Parallel Simulator(PDPS) has been used as a platform to implement the algorithms above and conduct the simulations. Two parallel computing methods of Message Passing Interface (MPI) parallel computing and Graphics Processing Unit (GPU) acceleration have been used to accelerate the simulations. Speedup results for both MPI parallel computing and GPU methods are illustrated in the case studies. In summary, a comprehensive approach for particle simulation is proposed and applied to particle mixing process and asphalt foaming simulation. The simulation results are analyzed in various aspects to provide valuable insights to the problems studied in this work. Given the improvement of computational capacity, particle dynamics in higher resolution and simulations in more complex configurations can be obtained. This particle simulation platform is general and it can be straightforwardly extended to many-particle systems with more particle phases and solid-liquid-gas dynamics problems

Dissipative Particle Dynamics and Other Particle Methods for Multiphase Fluid Flow in Fractured and Porous Media

Particle methods are much less computationally efficient than grid based numerical solution of the Navier Stokes equation, and they have been used much less extensively, particularly for engineering applications. However, they have important advantages for some applications. These advantages include rigorous mast conservation, momentum conservation and isotropy. In addition, there is no need for explicit interface tracking/capturing. Code development effort is relatively low, and it is relatively simple to simulate flows with moving boundaries. In addition, it is often quite easy to include coupling of fluid flow with other physical phenomena such a phase separation. Here we describe the application of three particle methods: molecular dynamics, dissipative particle dynamics and smoothed particle hydrodynamics. While these methods were developed to simulate fluids and other materials on three quite different scales – the molecular, meso and continuum scales, they are very closely related from a computational point of view. The mesoscale (between the molecular and continuum scales) dissipative particle dynamics method can be used to simulate systems that are too large to simulate using molecular dynamics but small enough for thermal fluctuations to play an important role. Important examples include polymer solutions, gels, small particle suspensions and membranes. In these applications inter particle and intra molecular hydrodynamic interactions are automatically include