Research

Engineering Mechanics

I am currently an assistant professor at Marquette University, Milwaukee, WI, USA, in the Mechanical Engineering Department 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 use the discrete element method (DEM) to inform and validate micromechanics-based elastoplastic continuum constitutive models for particulate (or granular) materials (such as gravel, sand/soil, or powder), in both the elastic and plastic ranges. This was the topic of my Ph.D. thesis from the University of Wisconsin-Madison (2013), and I continue to do research in this field with my former advisors Michael Plesha and Walter Drugan.  I have performed over 3,000 DEM simulations for my Ph.D. thesis and subsequent publications using the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS), developed by Sandia National Laboratories, which I am also currently using to perform ab initio molecular dynamics (MD) simulations of crack growth in solids, to verify theories of fracture mechanics for Walter Drugan.  Moreover, the research I performed with Michael Plesha and David Malkus for my M.S. degree from UW-Madison (2001) in engineering mechanics and subsequent industry experience have made me something of an expert in 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 BernoulliJohann 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 equationPoisson’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 such names as 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 these things — and a personalized visual representation of my academic genealogy can be viewed here.

Genealogy-Academic

Of my near 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).