Astronuc

Staff Emeritus

Science Advisor

- 18,543

- 1,685

## Main Question or Discussion Point

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.

http://www.science.mcmaster.ca/~geo/faculty/emeriti/middleton/index.html [Broken]," 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

Appendices

References

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.

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.

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.

http://www.science.mcmaster.ca/~geo/faculty/emeriti/middleton/index.html [Broken]," 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

Appendices

References

From the point of view of classical physics, matter is generally assumed to take one of three forms: apoint mass, arigid body, or acontinuum. All three forms represent an idealization of real matter but the level of idealization decreases as we move from a point mass to a continuum. Though the concept of a point mass is an extreme idealization of real bodies of matter, it is a simplification of the real world that works very well in some applications.

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.It was Newton himself who first showed that one does not need to know the exact distribution of mass within the earth (or other planet) in order to apply the 'universal' law of gravitation. For most purposes, one can assume the mass is concentrated at a point, the center of mass.

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.

When solids or fluids deform in response to applied forces, one must be concerned with the distribution of material properties (e.g., mass, resistance to deformation) with the material. There is still important simplying assumptions to be made, which is the 'continuum hypothesis'.

This is an important point to keep in mind, particularly at the beginning of model development.The useful range in length scale for the continuum hypothesis has two limits: the lower limit is defined by an element of volume that is much bigger than an atom or molecule, and the upper limit is defined by an element of volume that is smaller than any important spatial variation in material properties.

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 EngineeringThe reason one uses the continuum hypothesis is simply that it allows us to use differential calculus to analyze the properties of a material and its motion and deformation, i.e. its behavior. Continuous changes, or gradients, in physical properties and forces define mechanical problems, and differential calculus is the mathematical tool that treats such gradients precisely and efficiently. In using the continuum hypothesis, we are not limited to cases without abrupt boundaries between different materials. In these cases, we have to define the appropriateboundary conditionsand then we can use continuum mechanics to describe what happens within those boundaries.

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.

Last edited by a moderator: