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Computational Continuum Mechanics

By Prof. Sachin Singh Gautam   |   IIT Guwahati
Learners enrolled: 163
Continuum mechanics as a full-fledged course is a very interesting but a challenging subject. Usually,its application within the nonlinear finite element codes is not clear to the student. Computational continuum mechanics tries to bridge this gap. Hence, it can be treated as an applied version of continuum mechanics course. It assumes no prior exposure to continuum mechanics. The course starts with sufficient introduction to tensors, kinematics, and kinetics. Then, the course applies these concepts to set up the constitutive relations for nonlinear finite element analysis of a simple hyperelastic material. This is followed by the linearization of the weak form of the equilibrium equations followed by discretization to obtain the finite element equations, in particular, the tangent matrices and residual vectors is discussed. Finally, the Newton-Raphson solution procedure is discussed along with line search and arc length methods to enhance the solution procedure.

INTENDED AUDIENCE
Masters student and research scholars
PREREQUISITES : Introduction to Solid Mechanics I and II, A undergraduate course in Engineering Mathematics. Exposure to undergraduate course on numerical methods will be an added advantage.
INDUSTRIES  SUPPORT            : VSSC, ISRO, Siemens India Limited, Ansys India or any firm involved in R&D involving finite element analysis
Summary
Course Status : Upcoming
Course Type : Elective
Duration : 12 weeks
Start Date : 26 Jul 2021
End Date : 15 Oct 2021
Exam Date : 24 Oct 2021
Enrollment Ends : 02 Aug 2021
Category :
  • Mechanical Engineering
  • Computational Thermo Fluids
  • Computational Mechanics
  • Advanced Mechanics
  • Advanced Dynamics and Vibration
Credit Points : 3
Level : Postgraduate



Course layout

Week 1:Introduction – origins of nonlinearity
Week 2:Mathematical Preliminaries -1: Tensors and tensor algebra
Week 3: Mathematical Preliminaries -2: Linearization and directional derivative, Tensor analysis
Week 4:Kinematics – 1: Deformation gradient, Polar decomposition, Area and volume change
Week 5:Kinematics – 2: Linearized kinematics, Material time derivative,Rate of deformation and spin tensor
Week 6:Kinetics – 1 : Cauchy stress tensor, Equilibrium equations,Principle of virtual work
Week 7: Kinetics – 2 : Work conjugacy, Different stress tensors, Stress rates
Week 8:Hyperelasticity - 1: Lagrangian and Eulerian elasticity tensor
Week 9:Hyperelasticity - 2: Isotropic hyperelasticity, Compressible Neo-Hookean material
Week 10:Linearization : Linearization of internal virtual work, Linearization of external virtual work
Week 11: Discretization: Discretization of Linearized equilibrium equations – material and geometric tangent matrices
Week 12:Solution Procedure: Newton-Raphson procedure, Line search and Arc length method

Books and references

  • Nonlinear Solid Mechanics for Finite Element Analysis : Statics by J. Bonet A. J. Gil and R. D. Wood, Cambridge University Press, 2016
  • Finite Element Procedures by K.-J. Bathe Prentice-Hall India, New Delhi, 1996.
  • Applied Mechanics of Solids by A. F. Bower, CRC Press, Boca Raton, 2010. (Also accessible through authors website: http://solidmechanics.org/)

Instructor bio

Prof. Sachin Singh Gautam

IIT Guwahati
Dr. Sachin Singh Gautam is currently an Assistant professor in the Department of Mechanical Engineering, IIT Guwahati. He obtained his M.Tech. and Ph.D. from and worked as a postdoctoral fellow in AICES, RWTH Aachen University. His area of research is in nonlinear finite element methods and computational contact-impact problems. He has carried out projects from SERB, DST and VSSC, ISRO. He currently working on the incorporation of a contact module in the ISROs structural analysis software tool FEASTSMT (Indias first commercial FE package which is under Make-In-India). He has guided students on research problems jointly with Siemens R&D and Cummins R&D. He has guided three research scholars and is currently guiding five full-time PhD students, one part-time student. He has guided 17 M.Tech students and currently guiding 7 more. His research group has received various awards and fellowships like the DAAD fellowship and best paper award. He has 15 book chapters, 24 journal papers, and over 60 conference publications.

Course certificate

The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.
The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).
Date and Time of Exams: 24 October 2021 Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.
Registration url: Announcements will be made when the registration form is open for registrations.
The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then.
Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.

CRITERIA TO GET A CERTIFICATE

Average assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course.
Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.

Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Guwahati .It will be e-verifiable at nptel.ac.in/noc.

Only the e-certificate will be made available. Hard copies will not be dispatched.

Once again, thanks for your interest in our online courses and certification. Happy learning.

- NPTEL team


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