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Continuum Mechanics - Solids and Fluids

  1. Jan 19, 2007 #1


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    Staff: Mentor

    I started reading a great textbook and thought I would share some of its finer points. It is a great introduction to mechanics of solids and liquids, although the title explicitly states Earth and Environmental Sciences.

    Gerard V. Middleton (Prof. Emeritus, McMaster Univ) and Peter R. Wilcock (Johns Hopkins), "Mechanics in the Earth and Environmental Science," Cambridge University Press, 1994.

    1. Introduction
    2. Review of elementary mechanics
    3. Dimensional analysis and theory of models
    4. Stress
    5. Pressure, buoyancy and consolidation
    6. Flow through porous media
    7. Strain
    8. Elasticity
    9. Viscous fluids
    10. Flow of natural materials
    11. Turbulence
    12. Thermal convection

    This is the case for a central body force (gravity). In reality, variations in density (e.g. granite or basalt compared to water) or elevation (mountains) cause perturbations in the gravitational force field.

    For many other problems concerned with solid bodies, one must be concerned with the size and shape of the material, as well as its mass. For example, a boulder moved by water or a round object rolling down an incline.

    This is an important point to keep in mind, particularly at the beginning of model development.

    The issue of element size is more complicated when significant thermal gradients are present since properties like density and strength, or solubility of different phases may be significantly affected by temperature (internal energy). When a radiation field is imposed on a material, the modeling can be even more complex.

    There are relevant topics in the other tutorials in this section and the physics tutorials sections, as well as the forums Mechanical & Aerospace Engineering and Materials & Chemical Engineering

    Some definitions:

    Statics - study of equilibrium of forces, i.e. there is no acceleration because the net forces and net moments are null.

    Kinematics - study of motion, exclusive of masses and forces.

    Dynamics - study of the relationship of motion and forces

    All three are included within mechanics.
  2. jcsd
  3. Mar 23, 2007 #2


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    Staff: Mentor

    So notes on Mechanics of Solids

    Advanced Mechanics of Solids

    These notes were written by Prof. A. F. Bower during the fall semesters of 1998 and 1999, and updated during the Fall semester of 2005. The notes are intended for individual study in Engineering 175, Advanced Mechanics of Solids at Brown University. Please seek the author's permission before reproducing the notes for any other purpose.

    Division of Engineering
    Brown University
    Providence RI 02912

    More advanced courses

    EN224: Linear Elasticity

    It is very kind of Professor Bower and Brown University to make these notes available.

    Bower's own site - http://solidmechanics.org/contents.htm
    Last edited: Mar 6, 2012
  4. May 15, 2007 #3


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  5. May 16, 2007 #4
    Astronuc, i had a look in my university library, and i found two books on continuum mechanics:
    1. schaum outline.
    2. a four volumes book by ivanovich sedov, which is called a course on continuum mechanics.
    i think that the second is more advanced than the first book, have you tried any of them?
  6. May 16, 2007 #5


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    Staff: Mentor

    I may have Schaum's outline on Continuum Mechanics, but I'd have to dig through my library.

    Leonid Ivanovich Sedov (b. 1907 - d. 2000) is a big name in Continuum Mechanics. I am sure the text, Course on CM is very involved, although I am not familiar with it.
  7. Aug 4, 2007 #6
    Mase's Continuum Mechanics is really a good book. It gives concise concepts before showing concrete examples plus extra exercises. Other good texts are Malvern, Fung, Eringen,...

    Currently, not many people are writing continuum mechanics books. Three reasons for this maybe. 1: The old texts were good enough so that there is no need for any updating. 2: Not many people are doing related research so that the speed of the updating is too slow.3: Classical Continuum mechanics
    do not have many applications (at least the theory is not necessary) or even some theory are out of date.

    On the contrary, fluid mechanics as a part of continuum mechancis, has been a hot topic now.
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