Continuum and crystal strain gradient plasticity with energetic and dissipative length scales

This work, standing as an attempt to understand and mathematically model the small scale materials thermal and mechanical responses by the aid of Materials Science fundamentals, Continuum Solid Mechanics, Misro-scale experimental observations, and Numerical methods. Since conventional continuum plasticity and heat transfer theories, based on the local thermodynamic equilibrium, do not account for the microstructural characteristics of materials, they cannot be used to adequately address the observed mechanical and thermal response of the micro-scale metallic structures. Some of these cases, which are considered in this dissertation, include the dependency of thin films strength on the width of the sample and diffusive-ballistic response of temperature in the course of heat transfer. A thermodynamic-based higher order gradient framework is developed in order to characterize the mechanical and thermal behavior of metals in small volume and on the fast transient time. The concept of the thermal activation energy, the dislocations interaction mechanisms, nonlocal energy exchange between energy carriers and phonon-electrons interactions are taken into consideration in proposing the thermodynamic potentials such as Helmholtz free energy and rate of dissipation. The same approach is also adopted to incorporate the effect of the material microstructural interface between two materials (e.g. grain boundary in crystals) into the formulation. The developed grain boundary flow rule accounts for the energy storage at the grain boundary due to the dislocation pile up as well as energy dissipation caused by the dislocation transfer through the grain boundary. Some of the abovementioned responses of small scale metallic compounds are addressed by means of the numerical implementation of the developed framework within the finite element context. In this regard, both displacement and plastic strain fields are independently discretized and the numerical implementation is performed in the finite element program ABAQUS/standard via the user element subroutine UEL. Using this numerical capability, an extensive study is conducted on the major characteristics of the proposed theories for bulk and interface such as size effect on yield and kinematic hardening, features of boundary layer formation, thermal softening and grain boundary weakening, and the effect of soft and stiff interfaces

A Scalable Algorithm for Multi-Material Design of Thermal Insulation Components Under Uncertainty

This work presents a scalable computational framework for optimal design under uncertainty with application to multi-material insulation components of building envelopes. The forward model consists of a multi-phase thermo-mechanical model of porous materials governed by coupled partial differential equations (PDEs). The design parameter (material porosity) is an uncertain and space-dependent field, resulting in a high-dimensional PDE-constrained optimization under uncertainty problem after finite element discretization. The robust design framework uses a risk-averse formulation consisting of the mean and variance of the design objective to achieve target thermal and mechanical performances and mitigate uncertainty. To ensure the efficiency and scalability of the solution, a second-order Taylor approximation of the mean and variance and the low-rank structure of the preconditioned Hessian of the design objective are leveraged, which uncovers the low effective dimension of the high-dimensional uncertain parameter space. Moreover, a gradient-based optimization method is implemented using the Lagrangian formalism to derive expressions for the gradient and Hessian with respect to the design and uncertain parameters. Finally, approximated $\ell_0$ regularization functions are utilized via a continuation numerical scheme to promote sparsity in the designed porosity. The framework's accuracy, efficiency, and scalability are demonstrated with numerical examples of a building envelope insulation scenario.Comment: Preprint submitted to MS417 - Student Competition - USNCCM1

Predicting Hydraulic Fracturing in Hyttejuvet Dam

Hydraulic fracturing can occur in the clay core of earth and rockfill dams if the vertical effective stress in the core is reduced to the levels that are small enough to allow a tensile fracture to occur due to hydraulic pressure of the seeping water. This situation may arise if the total stress in the core is reduced by the “arching effect” where the core settles relative to the filter or rock-fill shell of the dam. Water pressure increase in the core which occurs on first impounding of water, may reduce effective stresses further, and if they reach low enough values, a fracture will occur. The design of earth dams (especially those with thin vertical central cores) to resist hydraulic fracture is therefore of great importance, as there have been several dam failures in the past that have been attributed to the hydraulic fracture. In this paper, the behavior of Hyttejuvet Dam, which was thought to have failed due to hydraulic fracturing, is studied. 2D coupled consolidation finite element analysis of the construction and first impounding of the rockfill dam was carried out with elasto-plastic model (Drucker-Preger/Cap model) using ABAQUS software. The result of the analysis with respect to the pore pressure and settlement in some parts of the dam are compared with the measured data from the instruments in the dam. According to the result of the comparison, the appropriate model for predicting the behavior of Hyttejuvet Dam is obtained. Also different criteria are used to predict the hydraulic fracturing of the dam. By comparing the results of the study using these criteria, one may be able to predict the hydraulic fracturing mechanism in the clay core of the studied dam

Technical Note: PDE-constrained Optimization Formulation for Tumor Growth Model Calibration

We discuss solution algorithms for calibrating a tumor growth model using imaging data posed as a deterministic inverse problem. The forward model consists of a nonlinear and time-dependent reaction-diffusion partial differential equation (PDE) with unknown parameters (diffusivity and proliferation rate) being spatial fields. We use a dimension-independent globalized, inexact Newton Conjugate Gradient algorithm to solve the PDE-constrained optimization. The required gradient and Hessian actions are also presented using the adjoint method and Lagrangian formalism

Microstructure to Macro-Scale Using Gradient Plasticity with Temperature and Rate Dependent Length Scale

AbstractGradient plasticity theory formulates a constitutive framework on the continuum level that bridges the gap between the micromechanical plasticity and classical continuum plasticity by incorporating the material length scale. A micromechanical-based model of variable material intrinsic length scale is developed in the present work which allows for variations in temperature and strain rate and its dependence on the grain size and accumulated plastic strain. The material constants of the proposed model are calibrated using the size e_ect encounter in nanohardness experiments. In this regard, two di_erent physically based models for Temperature and Rate Indentation Size E_ects (TRISE) are also developed in this work for single and polycrystalline metals by considering di_erent expressions of the geometrical necessary dislocation (GND) density. The results of indentation experiments performed on various single- and polycrystalline materials are then used here to implement the aforementioned framework in order to predict simultaneously the TRISE and variable length scale at di_erent temperatures, strain rates and various grain sizes

Adaptive Modeling of Stochastic Multiscale Material Systems: Bayesian Machine Learning to Accelerate Monte Carlo Methods

Whitepaper submitted to the 2017 DOE ASCR Applied Math Meeting<div><br></div><div>Questions on Future Research Directions:<br></div><div><div>1. Multiscale, multiphysics, multifidelity modeling research</div><div><br></div><div>Affiliation:<br></div><div><div>Institute for Computational Engineering and Sciences,</div><div>The University of Texas at Austin</div></div></div