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Fundamentals of Continuum Mechanics 1st Edition by John W Rudnicki ISBN 1118479912 9781118479919

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Fundamentals of Continuum Mechanics 1st Edition John W. Rudnicki Digital Instant Download

Author(s): John W. Rudnicki
ISBN(s): 9781118479919, 1118479912
Edition: 1
File Details: PDF, 1.70 MB
Year: 2014
Language: english
SKU: EB-4916116 Category: Tag:

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ISBN 10: 1118479912 
ISBN 13: 9781118479919
Author: John W Rudnicki

A concise introductory course text on continuum mechanics

Fundamentals of Continuum Mechanics focuses on the fundamentals of the subject and provides the background for formulation of numerical methods for large deformations and a wide range of material behaviours. It aims to provide the foundations for further study, not just of these subjects, but also the formulations for much more complex material behaviour and their implementation computationally. 

This book is divided into 5 parts, covering mathematical preliminaries, stress, motion and deformation, balance of mass, momentum and energy, and ideal constitutive relations and is a suitable textbook for introductory graduate courses for students in mechanical and civil engineering, as well as those studying material science, geology and geophysics and biomechanics.  

  • A concise introductory course text on continuum mechanics
  • Covers the fundamentals of continuum mechanics
  • Uses modern tensor notation
  • Contains problems and accompanied by a companion website hosting solutions
  • Suitable as a textbook for introductory graduate courses for students in mechanical and civil engineering

Fundamentals of Continuum Mechanics 1st Table of contents:

Part One: Mathematical Preliminaries

vectors
examples
inverse
orthogonal tensor
principal values
nth-order tensors
examples
exercises
reference

tensors
cartesian coordinates
base vectors
summation convention
tensor components
dyads
tensor and scalar products
examples
exercises
reference

vector (cross) product
properties of the cross product
triple scalar product
triple vector product
applications of the cross product
velocity due to rigid body rotation
moment of a force p about o
non-orthonormal basis
example
exercises

determinants
cofactor
inverse
example
exercises

change of orthonormal basis
change of vector components
definition of a vector
change of tensor components
isotropic tensors
example
exercises
reference

principal values and principal directions
example
exercises

gradient
example: cylindrical coordinates
exercises

Part Two: Stress

traction and stress tensor
types of forces
traction on different surfaces
traction on an arbitrary plane (cauchy tetrahedron)
symmetry of the stress tensor
exercise
reference

principal values of stress
deviatoric stress
example
exercises

stationary values of shear traction
example: mohr–coulomb failure condition
exercises

mohr’s circle
exercises
reference

Part Three: Motion and Deformation

current and reference configurations
example
exercises

rate of deformation
velocity gradients
meaning of d
meaning of w
exercises

geometric measures of deformation
deformation gradient
change in length of lines
change in angles
change in area
change in volume
polar decomposition
example
exercises
references

strain tensors
material strain tensors
spatial strain measures
relations between d and rates of eg and u
relation between Ė and d
relation between d and u
exercises
references

linearized displacement gradients
linearized geometric measures
stretch in direction n
angle change
volume change
linearized polar decomposition
small-strain compatibility
exercises
reference

Part Four: Balance of Mass, Momentum, and Energy

transformation of integrals
exercises
references

conservation of mass
reynolds’ transport theorem
derivative of an integral over a time-dependent region
example: mass conservation for a mixture
exercises

conservation of momentum
momentum balance in the current state
linear momentum
angular momentum
momentum balance in the reference state
linear momentum
angular momentum
momentum balance for a mixture
exercises

conservation of energy
work-conjugate stresses
exercises

Part Five: Ideal Constitutive Relations

fluids
ideal frictionless fluid
linearly viscous fluid
non-steady flow
exercises
reference

elasticity
nonlinear elasticity
cauchy elasticity
green elasticity
elasticity of pre-stressed bodies
linearized elasticity
material symmetry
linear isotropic elastic constitutive relation
restrictions on elastic constants
more linearized elasticity
uniqueness of the static problem
pressurized hollow sphere

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Tags: John W Rudnicki, Continuum Mechanics