Multi-Scale Material Modelling techniques Part-I

Name: Multi-Scale Material Modelling techniques Part-I
Rating: 5.0 (3 reviews)

Finite element method and Molecular dynamics

Created byAtasi Ghosh

Last updated 3/2025

English

English [Auto],

What you'll learn

Materials modelling and simulation principle
Quantum mechanical simulation
Finite Element Method
Techniques of improving model accuracy

Course content

2 sections • 21 lectures • 1h 54m total length

Introduction to Finite element method5:30
Apply the finite element method to obtain approximate solutions for complex engineering problems. Solve partial differential equations with boundary conditions to assess heat transfer, fluid dynamics, and solid mechanics.
Gaussian Quadrature rule7:15
Gaussian quadrature rule improves finite element method accuracy by mapping the interval to a natural coordinate system and using weights at Gaussian points to reduce integration error.
Principle of minimum potential energy6:18
Explore the finite element method: discretize into elements, apply gaussian quadrature for integrals, map to natural coordinates, and derive stiffness matrices via minimum potential energy to solve displacement.
Characteristic Equation7:38
Learn how to convert between global, local, and natural coordinates in finite element method, using Gaussian quadrature, Jacobians, and mapping to a unit cube for two-dimensional and three-dimensional elements.
Natural Coordinate system10:05
Use the natural coordinate system and shape functions to express nodal variables across 1D, 2D, and 3D elements, and classify formulations as isoparametric, subparametric, or superparametric with convergence criteria.
Element Formulation7:26
Discretize the structure into finite elements and map each to its natural coordinate system. Apply shape functions to express nodal unknowns and variations, covering linear and higher order cases.
Types of elements5:15
Explore the finite element method’s element types, including 1d line and bar elements, 2d planar elements, 3d tetrahedral elements, and passive spatial elements for gaps, springs, and contact elements.
Boundary Conditions6:29
Learn finite element analysis that builds stiffness matrices for 1d bars, beams, and 2d trusses, applies boundary conditions, and cures singular stiffness matrices with elimination, penalty, and multipoint constraint methods.
Applications of FEA6:12
The lecture explains the finite element method, from discretizing a structure into elements to applying boundary conditions. It covers stiffness matrices, the elimination method, and applications in aerospace and automotive.

Physical vs Virtual Experiment3:47
Explore how molecular dynamics simulations replace physical experiments by modeling materials in a virtual environment, using mathematical models and inputs to study their atomistic behavior.
Time and length scale4:45
Understand how molecular dynamics simulates atomistic structures time and length scales, using macro, meso, and nano models and multiscale simulation to balance speed and accuracy by solving equations of motion.
Quantum Mechanical approach5:00
Explore molecular dynamics with a quantum mechanical approach, decoupling electron and nucleus motions via Born–Oppenheimer approximation and applying classical newtonian dynamics to nuclei to simulate thermal properties.
Types of Potentials4:56
Explore molecular dynamics, where force fields and bonded and non-bonded potentials drive newtonian motion to evolve structures, compute bond lengths, angles, and dihedrals, and generate trajectories.
Classical Newtonian mechanics5:00
Examine nonbonded potentials, including van der Waals (Lennard-Jones) and electrostatic forces. Learn how total potential sums bonded and nonbonded terms in Newtonian simulations.
Position and Velocity calculation algorithm4:58
Explore molecular dynamics algorithms for position and velocity integration, including the velocity Verlet scheme, and learn how forces, temperatures, and force fields drive simulation.
Molecular Mechanics2:39
Learn molecular mechanics by applying a force field to minimize the empirical potential energy, achieving a minimum energy configuration with bond lengths, angles, and torsions at equilibrium.
Macrostate-Microstate correlation4:58
Link microstates to macroscopic properties and macrostate in MD simulations by using time- and ensemble-averaged trajectories across microcanonical, NVT, and NPT ensembles.
Types of Ensembles in MD4:47
Explore microcanonical, canonical, and grand canonical ensembles in molecular dynamics, and learn how thermostats such as velocity rescaling, Berendsen, Andersen, and Nosova regulate temperature.
Cut-off Method & Periodic Boundary Condition4:48
Explore cut off radius to reduce computation in molecular dynamics and apply periodic boundary conditions with a primary cell and image cells to model bulk materials and reduce surface effects.
Introduction2:27
Explore density functional theory as a quantum mechanical tool for modeling periodic systems, addressing the many-body challenge beyond Schrödinger's equation with Hartree–Fock and computational approaches, including ASAP software.
Many body Problem4:32
Explore density functional theory and the many-body problem in quantum mechanics. Analyze how the Schrödinger equation, Hamiltonian, kinetic and potential energies, and electron interactions challenge solvability, prompting approximations.

Requirements

The pre-requisites required are the basic knowledge of materials science, physics, chemistry and mathematics

Description

Multi-scale materials modelling is a powerful tool in bridging the gap between the different length scale and time scale of material ranging from subatomic scale to the macroscopic scale. The theoretical foundations and numerical methods of handling the multiscale modelling in solid mechanics, from atomistic techniques all the way up to the macroscopic continuum scale have been discussed. In the part-I of this course, students will learn the basic principles of Finite Element Method, discretization of the domain, and numerical solution techniques for solid mechanics problems. Emphasis is placed on solving boundary value problems, developing element matrices, and implementing various solution methods. Practical applications of FEM in engineering design and material behavior prediction are discussed. The method of handling the material behaviour at a lower scale is different from its large scale behaviour and is dealt with under a separate section on molecular dynamics. It will cover Molecular Dynamics (MD) simulations, where students will explore atomistic models and their applications to materials science. The course introduces the principles of MD, including interatomic potentials, time integration algorithms, and system initialization. By the end of the course, students will be proficient in applying FEM for macroscopic modelling and MD for atomistic simulations, enabling them to approach complex multi-scale problems in materials engineering with a deeper understanding of both methods and their integration.

Who this course is for:

Students, Research scholars, Faculty, industry professional interested in the field of materials science and engineering

Multi-Scale Material Modelling techniques Part-I

What you'll learn

Explore related topics

Course content

Finite Element Method9 lectures • 1hr 2min

Introduction to MD Simulation12 lectures • 53min

Requirements

Description

Who this course is for: