## Research

**Engineering Mechanics**

I am currently an Assistant Professor at Marquette University, Milwaukee, WI, USA, with a joint appointment in the Mechanical Engineering and Civil Engineering Departments, in the Structural Engineering and Structural Mechanics (SESM) group, of the Opus College of Engineering. In this capacity, I perform and publish research in the following fields:

- Computational Mechanics;
- Multiscale- and Micro- Mechanics;
- Computational Multibody Dynamics;
- Frictional Contact Mechanics;
- Discrete Element Methods (DEM);
- Finite Element Methods (FEM).

I was formerly an Assistant Scientist at the Simulation Based Engineering Laboratory (SBEL) at the University of Wisconsin-Madison. In that capacity, I contributed to the development of a scalable physics-based high performance computing (HPC) software infrastructure, including modeling, simulation, and visualization capabilities, to support the analysis of ground vehicle mobility on deformable terrain.

I currently have ongoing research projects in the following four (general) directions:

**Virtual Testing Environments for Autonomous Vehicles**: The use of so-called virtual testing environments for the design and subsequent exhaustive testing of autonomous vehicles is becoming increasingly common, to the extent that it has received a significant amount of attention in popular media, as well as in technical articles. Most of the current virtual testing environments, however, are limited to on-road driving, since the interactions between tires and pavement are relatively well understood. Less well understood, however, and more difficult to simulate accurately, is the interaction between tires and off-road terrain, such as loose soil, sand, or gravel. This environment is of great importance, however, to military applications in particular, as for example in the NATO reference mobility model (NRMM). The restriction of the majority of virtual testing environments to rigid or on-road scenarios is mirrored in the majority of current autonomous vehicle controllers as well. For example, the Model Predictive Control (MPC) Algorithm used by Liu, Jayakumar, Stein, and Ersal (2016) to develop a LIDAR-based constant speed local obstacle avoidance controller for autonomous ground vehicles (AGVs) was designed for rigid terrain only. In the work of Nick Haraus (M.S., 2017, Marquette University), this controller was tested on a complex multibody physics offroad vehicle (HMMWV) model in a virtual testing environment using Chrono, a multibody physics API, on both rigid flat and granular terrain, to examine the robustness of the control method, and it was found that the control method worked well only when the granular terrain was modeled with severely limited degrees of freedom. However, if the particles of the granular terrain were allowed full rotational degrees of freedom, with no rolling resistance, then the HMMWV tires spun in place, and the MPC failed. We hypothesize that this was due to a combination of two factors: (1) failure of the constant-speed (rigid-terrain model) MPC algorithm that was being tested to perform well on loose, dry sand; and (2) failure of the granular terrain model used in our virtual testing environment to properly account for particle shape effects, including rolling resistance. The resolution of these two failures, as well as related problems associated with the development of high-fidelity models of granular terrain on the scale needed to produce a useful off-road virtual testing environment for AGVs, is the two-fold objective of this research project.**Multiscale Analysis of Soil-Strap Interactions in Mechanically Stabilized Earth Retaining Walls**: Approximately 9 million square feet of mechanically stabilized earth (MSE) retaining walls with precast facing are constructed every year in the United States, which may represent more than half of all retaining wall usage for transportation applications (Berg, et. al, 2009). MSE walls are relatively simple to construct, are tolerant to deformations and are cost effective to heights approaching 100 ft. For many years, engineers have designed MSE walls using allowable stress design (ASD) methods, whereby all uncertainty in applied loads and material resistance are combined into factors of safety for pullout and rupture of the embedded reinforcing straps. In recent years, load resistance factors for design (LRFD) has replaced ASD methods, whereby uncertainty in load and material resistance are accounted for separately. More importantly, the resistance factor is a function of the method used to estimate the resistance and thus the model uncertainty is also included in the design process. The uncertainty inherent in the LRFD method can be minimized with a more fundamental understanding of the microscale interactions between the discrete soil particles within the select backfill materials and the reinforcing straps, which depend on material type, strap geometry, and particle arrangement. To this end, this research project involves a detailed microscale analysis of soil-strap interaction using the discrete element method (DEM), performed by Max Willingham (M.S. expected, 2018, Marquette University). This research project also includes laboratory validation studies using pull-out tests on various strap and soil combinations, performed by Kathlyn Videkovich (Ph.D. expected, 2019, Marquette University). This research is performed in collaboration with Dr. James Crovetti.**Multi-scale Models for Large-scale Granular Mechanics**: Granular materials are ubiquitous, both in nature and in industry. Natural examples include sand, silt, soil, gravel, and forest ground-cover. Industrial examples include abrasives, metallic and ceramic powders, cereals, and pharmaceuticals. Given the increasing availability of high-performance computing resources, there is a growing desire to use numerical simulation tools to model the mechanical behavior of large-scale processes involving granular materials either directly or indirectly. Examples include product handling and evolution over entire production lines, and the movement of entire convoys of ground vehicles over off-road terrain. Realistically, the granular materials involved in such simulations include many billions of individual particles. This presents serious challenges to numerical modeling, which arise from the large range of scales present (e.g., micron in the case of sand particles to meter in the case of vehicles). This research project seeks to understand and address these challenges on all fronts, from the physical modeling of micro-scale (i.e., particle-scale) contact mechanics, and the emergent macro-scale (i.e., continuum-scale) mechanics of bulk granular materials, to the efficient handling of interactions between objects with granular materials, in the context of very large-scale numerical simulations supported by high-performance computing resources. The intellectual merit of this project stems from the following three research thrusts: First, this project seeks to understand how physics-based, analytical and numerical micro-scale inter-particle contact models influence the emergent macro-scale mechanical properties of bulk granular or particulate materials. Second, this project seeks to understand how such micro-scale contact models can be optimally coupled with continuum (macro-scale) representations of bulk granular materials, both analytically (e.g., via processes of homogenization) and computationally (e.g., by coupling discrete and finite element methods). These first two research thrusts involve the use of the discrete element method (DEM) to inform and validate micromechanics-based elastoplastic continuum constitutive models, as in my own Ph.D. work, as well as more advanced continuum constitutive models, such as hypoplasticity, as in the work of Yufei Zhou (M.S. expected, 2018, Marquette University), for particulate or granular materials in both the elastic and plastic ranges. Third, this project seeks to understand how best to implement these multi-scale computational models to efficiently perform large-scale simulations of physical phenomena involving granular materials (e.g., with millions or even billions of particles), while leveraging high-performance computing resources (e.g., shared-memory parallel and hybrid computing).**Atomistic and Coupled CFD-DEM Modeling of Suspended Particulate Matter**: This research project involves both molecular dynamics (MD) and coupled computational fluid dynamics and discrete element method (CFD-DEM) modeling of particulate matter suspended in air. Current research thrusts in this project include the modeling of soot evolution in combustion, as well as dry powder aerosol behavior, including the effects of agglomeration and deagglomeration. This research is performed in collaboration with Dr. Somesh Roy, and is spearheaded by Tamanna Tasnim (M.S. expected, 2020, Marquette University).

All of these research directions involve the use and optimization of the computational resources available at my newly-formed **Multiscale Mechanics and Simulation (MMaS) laboratory**, which is housed in the Academic Data Center at Marquette University, Milwaukee, WI. This MMaS lab currently includes a single high-performance shared-memory parallel CPU-GPU computing node. This computing node has 20 physical (plus an additional 20 virtual) 3.1 GHz Intel Xeon E5-2687Wv3 CPU cores and 256 GB DDR4 RAM on the motherboard, as well as approximately 15,000 GPU cores and a total of 72 GB GDDR5 RAM on three NVIDIA Tesla K80 accelerator cards, and 15 TB of RAID-controlled high-speed permanent data storage.

I have performed over 3,000 DEM simulations, both for my Ph.D. thesis and for subsequent publications, using the open-source Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS), developed by Sandia National Laboratories, as well as its derivative LIGGGHTS (LAMMPS Improved for General Granular and Granular Heat Transfer Simulations), and its derivative open-source coupled CFD-DEM code (CFDEM). Moreover, the research I performed for my M.S. degree from UW-Madison (2001), in engineering mechanics, as well as my subsequent industry experience, have made me something of an expert in the programming and development of the finite element method (FEM). My M.S. research focused on optimizing the finite element method for modeling thin-film compressible airflow under air bearing sliders in computer hard disk drives. It was funded by Seagate Technology and the National Science Foundation (NSF). After my M.S. degree in engineering mechanics, I worked for about a year (until 2003) as a computational mechanics engineer for Third Wave Systems, which develops and sells an explicit large-deformation Lagrangian finite element code (AdvantEdge) with coupled heat flow, optimized for modeling high speed metal cutting and machining processes. In this role, I successfully designed and implemented an algorithm for bonding disparate finite element meshes (similar to a feature in Abaqus FEA) used to model laminate composite materials, and I worked on algorithms for adaptive mesh refinement. I maintain an active research interest in all of these subjects.

**Mathematical Logic**

I also continue to perform research related to my M.S. thesis from Marquette University (2008) in formal Intuitionistic logic, specifically Intuitionistic model theory. As a mathematical discipline, I tend to favor the definition of model theory given by Chang and Keisler (model theory = universal algebra + logic), rather than the “more modern” definition given by Hodges (model theory = algebraic geometry – fields). Model theory is also related to set theory. In this field, I often work with Ben Ellison, Dan McGinn, and my former advisor Wim Ruitenburg.

**Mariology**

Though I have no formal qualifications to do so, I perform research and frequently publish articles on the topic of Mariology, which is a special topic of Roman Catholic theology. In this field, I depend heavily on the input and direction of one who has been gracious enough to be both my mentor and my spiritual director, Peter Damian Mary Fehlner, FI. I am particularly fascinated by the role of the Blessed Virgin Mary — Mother of Jesus Christ and Mother of God, most perfect Daughter of the Eternal Father, and Spouse of the Holy Spirit — in the so-called “Franciscan Thesis” of the Absolute Primacy of Christ (cf. Eph. 1:3-10; Rom. 8:29; Col. 1:15-20) and the joint predestination of Jesus and Mary, which holds that “from the very beginning, and before time began, the eternal Father […], by one and the same decree, had established the origin of Mary and the Incarnation of Divine Wisdom [Jesus Christ].” (Pope Pius IX, *Ineffabilis Deus*) I am also fascinated by the relationship between formal logic and “performative contradiction” as it appears in the so-called “ontological proof” of Anselm of Canterbury, which has distinct similarities to the proof of countable incompleteness in mathematical logic. I am a great fan of the “Marian maximalism” of Maximilian Maria Kolbe, the metaphysics of John Duns Scotus, and the Illative logic of John Henry Newman (in particular his distinctions between evidence, inference, and assent). I am honored to be an invited member of the Theological Commission of the International Marian Association.

**Academic-Genealogy**

Remarkably, I am an “academic descendant” — following doctoral advisors — of some very distinguished mathematicians and engineers, including Jacob Bernoulli, Johann Bernoulli, Leonhard Euler (who developed the theory of rigid body dynamics, among many other things), Joseph Lagrange (e.g., Lagrangian mechanics), Jean d’Alembert (e.g., D’Alembert’s principle), Pierre-Simon Laplace (e.g., Laplace transform, Laplace’s equation), Simeon Poisson (e.g., Poisson’s equation, Poisson’s ratio), Jean-Baptiste Fourier (e.g., Fourier analysis), Gustav Dirichlet (e.g., Dirichlet boundary conditions), Rudolf Lipschitz (e.g., Lipschitz continuous functions), Carl Friedrich Gauss (the “Prince of Mathematicians”), Felix Klein (who gave his name to the Klein four-group, among other things), William Prager (whose yield criterion for pressure-dependent and particulate materials is among those considered in my doctoral dissertation), and Ted Belytschko (whose name is now attached to the Ted Belytschko Applied Mechanics Award given annually by the ASME). Even more remarkably, my “academic lineage” also includes Gottfried Wilhelm Leibniz, Nicolaus Copernicus, Desiderius Erasmus, Thomas à Kempis, and (Saint) Gregory Palamas! My academic genealogy can be found here — courtesy of the American Mathematical Society (AMS), which, most remarkably, keeps track of all these things — and a personalized visual representation of my academic genealogy can be viewed here.

**Genealogy-Academic**

Of my “actual” family relations, those who have also completed doctoral dissertations include my brothers Elmer Fleischman and Jay Fleischman, my brother-in-law Clemens Cavallin, and my father-in-law Samuel Cavallin (and many others on my wife Clara’s side of the family)…