Computational mechanics of materials

Lectures: 2 sessions / week, 1.5 hours / session

Recitations: 1 session / week, 1.5 hours / session

16.225 is a graduate level course on Computational Mechanics of Materials. The primary focus of this course is on the teaching of state-of-the-art computational methods for the modeling and simulation of the mechanical response of engineering materials used in aerospace as well as in other branches of engineering including mechanical and civil engineering, material science and biomechanics. The range of material behavior considered includes: finite deformation elasticity and inelasticity, contact, friction and coupled problems. Numerical formulation and algorithms include: Variational formulation and variational constitutive updates, finite element discretization, mesh generation, error estimation, constrained problems, time discretization and convergence analysis. There will be a strong emphasis on the (parallel) computer implementation of algorithms in programming assignments. At the beginning of the course, the students will be given the source of a base code with all the elements of a finite element program which constitute overhead and do not contribute to the learning objectives of this course (assembly and equation-solving methods, etc.). Each assignment will consist of formulating and implementing on this basic platform, the increasingly complex algorithms resulting from the theory given in class, as well as in using the code to numerically solve specific problems. The application to real engineering applications and problems in engineering science will be stressed throughout. 16.225 has a specific set of learning objectives. Students graduating from 16.225 will be able to:

The achievement of the learning objectives in 16.225 will be measured through the students' ability to:

Undergraduate mechanics background or permission of the instructor, some programming experience in any of the following languages: Python, C++, C or Fortran.

There will be two lectures of one and a half hours a week. Student attendance is necessary to maximize the learning experience.

Recitations will be used for answering questions related to the homework assignments, explanations of the computer software sumMIT developed for this course, software issues on the athena cluster.

The course work involved in 16.225 includes homework assignments.

A total of approximately six (6) problem sets and computer assignments will be given on Wednesdays and on a bi-weekly basis. The due date for submission of assignments is at the beginning of class two Wednesdays after the assignment is given. Late submission of assignments is not accepted. The assignments will consist of specific exercises of algorithm formulation on paper, their computer implementation in programming exercises and their testing in specific applications. At the beginning of the course, the students will be given the source of a base code sumMIT with all the elements of a finite element program which constitute overhead and do not contribute to the learning objectives of this course (assembly and equation-solving methods, etc.). Electronic homework submissions are strongly recommended. Students are strongly encouraged to discuss homework problems in groups, since this is expected to help the learning process. However, homework assignments are also used for performance assessment and, therefore, the material that is turned in must represent the student's own understanding of the material.

Students are strongly encouraged to discuss homework problems with each other, since this is expected to help the learning process. However, homework assignments are also used for performance assessment and, therefore,the material that is turned in must represent the student's own understanding of the material. The final letter grades will be assigned according to the rules and regulations of the Faculty.

Textbooks on Continuum Mechanics and Mathematical Theory of Elasticity:

Textbooks on the finite element method:

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