Non-Equilibrium Mechanics Laboratory

MEAM 6640: Multiscale Modeling of Nonequilibrium Material Behavior (Graduate)

Taught Spring 2025

 

This course discusses a wide range of strategies aimed at integrating modeling and simulation techniques at various length and time scales with the goal of achieving a compromise between physical fidelity and computational cost. Our focus lies on the bridge between atomistic simulations, described by Hamiltonian or Langevin dynamics, and continuum material descriptions, as well as the coarse-graining of mesoscopic continuum models. Topics covered include: statistical mechanics and thermodynamics, the GENERIC formalism, FE   methods, the quasi-continuum method, diffusive molecular dynamics, stochastic thermodynamics and fluctuation theorems, and machine learning approaches to coarse-graining.

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ENM 5200: Principles and Techniques of Applied Mathematics (Graduate)

Taught Spring and Fall 2024

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This course is targeted to engineering Ph.D. students in all areas. It focuses on the study of linear spaces (both finite and infinite dimensional) and of operators defined on such spaces. Some examples of techniques that are studied include Fourier series, Green’s functions for ordinary and partial differential operators, eigenvalue problems for ordinary differential equations, and singular value decomposition of matrices.

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MEAM 5190: Elasticity and Micromechanics of Materials (Graduate)

Taught Spring Semester 2014 and Fall Semesters 2014-2021, 2025

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The first half of this course is devoted to the formulation of the theory of elasticity (kinematics, balance laws and constitutive relations) from basic principles such as Newton’s law and simple geometric arguments. Next, in the second half, we apply this theory to analytically solve simple two-dimensional problems and introduce a wide range of special topics, including the effective behavior of composites, homogenization, variational principles, finite element theory, thermoelasticity and plasticity.

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MEAM 3210: Vibrations of Mechanical Systems (Undergraduate)

Taught Spring Semesters 2016-2020

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This course teaches the fundamental concepts underlying the dynamics of vibrations of single and multi-degree of freedom systems, which are broadly applicable to mechanical systems. In particular, the course introduces a variety of methods for analyzing problems in vibrations and dynamics, including, Newton's method, Lagrange's equations of motion, and the principle of virtual work; and analyzes transient, steady state and forced motion of such systems. A brief introduction to numerical strategies to solve and analyze nonlinear systems is also provided.