A variational multiscale computational framework for reaction-dominated thermo-chemo-mechanical process modeling in multi-constituent material systems

This dissertation develops a computational framework for modeling multi-constituent material systems characterized by the transport of reacting fluids through deformable solids, and their coupled, nonlinear, thermo-chemo-mechanical response in the reaction-dominated regime. This is accomplished through two major components of the work: (i) new robust variational multi-scale numerical methods that are consistently derived, and (ii) models for multi-physics processes in multi-constituent materials. New robust numerical methods are developed via the variational multiscale (VMS) framework. Through the concept of fine scales in VMS, unresolved physics are recovered and embedded at the coarse scale level, improving stability and accuracy of the method. Focus is placed on fine scales that do not vanish at element boundaries (so-called “edge bubbles”). Using edge bubbles and an explicit time integration algorithm, a VMS Discontinuous Galerkin (VMDG) method is derived for multi-domain problems in elastodynamics where different subdomains can be solved synchronously and concurrently with minimal sharing of information. In addition, a new VMS method is introduced for the reaction-dominated regime of the diffusion–reaction equation. The proposed fine-scale basis consists of enrichment functions that may be nonzero at element edges. The method captures sharp boundary and internal layers, suppresses spurious oscillations, and better satisfies the maximum principle as compared to other existing methods. A priori mathematical analysis of the stability and convergence of the method is presented, and optimal rates of convergence are verified numerically. The numerical methods developed in this work may be applied to many reaction-diffusion systems in mathematical models for coupled thermo-chemo-mechanical phenomena arising from different theoretical frameworks. Here, a model for thermo-chemo-mechanical response of open solid-fluid systems is presented in the context of mixture theory. Derivation starts from constituent-wise equations for balance of mass, momentum, and energy, accounting for energy in formation and breaking of chemical bonds. Interactions between different constituents are captured through interaction terms as per locally homogenized mixture theory. Satisfaction of the second law of thermodynamics is achieved by providing constitutive equations that guarantee non-negative entropy production. Resulting mathematical models yield transient diffusion-advection-reaction problems posed by systems of coupled, nonlinear, second-order partial differential equations (PDEs), whose solution require stable numerical methods. Several numerical studies are presented to highlight stability, accuracy, and other features of the newly developed variational multiscale methods and thermo-chemo-mechanical models. Tests involve hypothetical as well as realistic materials with boundary layers, advancing reaction fronts, chemical swelling, and fingering phenomena.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Civil Engineering

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2022

Author dc:creator

• Anguiano Chavez, Marcelino

Contributors dc:contributor

• Masud, Arif
• Duarte, C. Armando
• Lopez-Pamies, Oscar
• Valocchi, Albert J
• Admal, Nikhil C

• variational multiscale method
• stabilized methods
• reaction-diffusion
• thermo-chemo-mechanical response
• advancing reaction fronts
• solid-fluid interaction
• mixture theory

Statement dc:rights

• Copyright 2021 Marcelino Anguiano Chavez

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/113029

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/113029