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ES525 THEORY OF CONTINUOUS MEDIA I

Course Objectives

This course aims to

• equip students with essential knowledge about non-linear theory of continuous media.

• make students assimilate kinematics of continum at large strains. 

• teach students the concept of stress and fundamental stress measures. 

• provide students with the essential balance principles of continuum thermomechanics.

• give the fundamentals of constitutive theory and particularly hyperelasticity along with its algorithmic implementation.

Course Content

Review of tensor analysis and integral theorems. Kinematics of deformation, strain tensor, compatibility condition. Material derivative of tensors, deformation rate, spin and vorticity. External and internal loads, Cauchy principle and stress tensor. Balance laws of momenta and energy, entropy principle. Constitutive theory and its axioms, thermomechanical materials. Some illustrative applications.

Course Learning Outcomes

Taking this course, the students will 

• Explain the fundamental principles of continuum mechanics, including stress, strain, and kinematics of deformation.
• Formulate and derive balance laws (mass, momentum, and energy) for continuous media.
• Apply tensor analysis and indicial notation in the context of engineering mechanics problems.
• Analyze and model linear elastic material behavior and interpret constitutive relations.
• Solve basic boundary value problems using the governing equations of continuum mechanics.

Program Outcomes Matrix