Continuum Mechanics

Numbering Code U-ENG25 35020 LJ71 Year/Term 2021 ・ Second semester
Number of Credits 2 Course Type Lecture
Target Year Target Student
Language Japanese Day/Period Tue.3
Instructor name ADACHI TAIJI (Institute for Frontier Life and Medical Sciences Professor)
Outline and Purpose of the Course This lecture provides an introduction to the theory of continuum mechanics for its application to the fields of bioengineering and biomedical engineering.
Course Goals Students will be able to understand tensor analysis and continuum mechanics, and to apply them in modeling of living tissues and cells.
Schedule and Contents 1)Introduction to continuum mechanics

2)Mathematical preliminaries
Matrix algebra, Index notation, Summation convention, Eigenvalues and eigenvectors

3,4)Vectors and tensors
Cartesian tensors, Scalar and vector products, Dyadic product, Coordinate transformation,Invariants, Nabla operator, Divergence theorem

Bodies and configurations, Displacement, Strain tensor, Compatibility, Material time derivative

7,8)Stress and equilibrium
Force and stress, Stress tensor, Traction, Cauchy stress, Principal stresses, Equation of equilibrium

9,10)Conservation Laws and governing equations
Mass conservation, Linear and angular momentum, The first law of thermodynamics for continua

11,12)Constitutive models
Constitutive equations, Stress-strain relationship, Linear elasticity, Newtonian viscous fluids,Material symmetry, Biological tissues

13,14)Boundary value problems
Differential equations with a set of boundary conditions, Navier-Stokes equation, Navier's equation

Application of continuum mechanics to the analyses of biological tissues, Introduction to biomechanics
Evaluation Methods and Policy Exam 100 (+ Reports max 10)
Course Requirements None
Study outside of Class (preparation and review) .
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