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§ BASIC EQUATIONS OF CONTINUUM MECHANICS
Continuum mechanics is the study of how materials behave when subjected to external influences.
External influences which affect the properties of a substance are such things as forces, temperature, chemical
reactions, and electric phenomena. Examples of forces are gravitational forces, ic forces, and
mechanical forces. Solids deform under external forces and so deformations are studied. Fluids move under
external forces and so the velocity of the fluid is studied.
A material is considered to be a continuous media which is a collection of material points interconnected
by internal forces (forces between the atoms making up the material). We concentrate upon the macroscopic
properties rather than the microscopic properties of the material. We treat the material as a body which is
homogeneous and continuous in its makeup.
In this introduction we will only consider solid media and liquid media. In general, most of the ideas
and concepts developed in this section can be applied to any type of material which is assumed to be a
collection of material points held together by some kind of internal forces.
An elastic material is one which deforms under applied forces in such a way that it will return to its
original unloaded state when the applied forces are removed. When a linear relation exists between the
applied forces and material displacements, then the material is called a linear elastic material. In contrast, a
plastic material is one which deforms under applied forces in such a way that it does not return to its original
state after removal of the applied forces. Plastic materials will always exhibit some permanent deformation
after removal of the applied forces. An elastic material is called homogeneous if it has the same properties
throughout. An isotropic material has the same properties, at a point, in all directions about the point.
In this introduction we develop the basic mathematical equa