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CE7026 CONTINUUM MECHANICS

Course Objectives

This course aims to

• equip students with essential knowledge about nonlinear theory of continuous media.
• make students assimilate kinematics of deformable bodies at large strains.
• teach students the concept of stress and fundamental stress measures.
• provide students with the essential balance principles of continuum thermodynamics.
• give the fundamentals of constitutive theory and particularly hyperelasticity along with its algorithmic implementation. 

Course Content

Tensor algebra and calculus. Kinematics of geometrically nonlinear deformations. Tangent, volume, and area maps. Rates of deformation and strain tensors. Pull back and push forward operations. Fundamental stress measures. Conservation laws of continuum thermodynamics. Principles of material frame invariance. Objective rates. Concepts of material symmetry. Fundamental potentials of thermodynamics. Colemans exploitation method. Compressible and incompressible hyperelasticity and its algorithmic aspects. Representative constitutive models of hyperelasticity.

Course Learning Outcomes

Taking this course, the students will

• have an essential background on the nonlinear theory of continuous media.
• be able to carry out geometric pull-back and push-forward operations between Lagrangean, Eulerian, and mixed quantities through the tools of kinematics at large strains.
• understand the concept of stress and differentiate different fundamental stress measures
• have the fundamental understanding of thermodynamic consistency of a constitutive model of continuum thermodynamics.
• be qualified to derive the fundamental balance principles of continuum thermomechanics within the Lagrangean and Eulerian setting.
• be in a position to implement a hyperelastic material model algorithmically.