Strain and Stress. A strain is any change of form or bulk of a portion of matter either solid or fluid. The system of forces which sustains the strain is called the stress. When a body is so strained that parallel lines remain parallel lines and parallel planes remain parallel planes, the strain is said to be homogeneous. Any cubical portion becomes a parallelopiped with angles, in general, other than right angles; and any spherical portion becomes an ellipsoid. The principal axes of this ellipsoid were originally mutually perpendicular diameters of the sphere. Clearly one of them must be the direction of greatest elongation (or least contraction), and another must be the direction of least elongation (or greatest contraction). These directions are the principal axes of the strain. A special case of the homogeneous strain is the isotropic strain, in which all lines suffer equal elongations—i.e. unit-length in any direction changes by the same amount. Here there is simple change of volume without any distortion; and the associated stress is of the type of a hydrostatic pressure. Now the most general homogeneous strain involves distortion as well as change of volume. If the strain is small we may decompose the complete strain into these two types of strain, which, as explained under Elasticity (q.v.), have to do with two quite distinct coefficients—viz. the Rigidity (q.v.) and the bulk modulus (see COMPRESSIBILITY). A distortion is a strain which involves no change of volume; and any distortion can always be decomposed into a number of shears or simple distortions. The simplest representation of a shear is given by the slight deformation of a circle into an ellipse of the same area. The major and minor axes of the ellipse are the principle axes of the shear, which is completely determined when its plane, axes, and elongations or contractions along these axes are given. A shear may also be represented by the sliding action of layer over layer which transforms a square into a parallelogram of the same area. Corresponding to a shear is the shearing stress, whose ratio to the shear is called the rigidity. It is obvious that in bending a bow or twisting a rod (see TORSION) we are producing strains which are not homogeneous; but by considering very small portions we are able to discuss the relations holding between the strains and corresponding stresses as if the strains were homogeneous.
When a body is perfectly elastic the relation between stress and strain is unchanging; in other words, to sustain the strain the same stress must be constantly applied. All solids, however, may be strained to such a degree that the strain may be supported by a weaker stress than that which produced the strain at first. Or, when a given stress is kept applied, the body may gradually alter its condition of strain as time goes on. Solids, in short, are found to possess Viscosity (q.v.), in virtue of which they yield slowly to a steady stress. Thus Tresca has caused metals to flow through ducts by application of great pressure. See STRENGTH OF MATERIALS.
Bodies may be strained by the action of other agents than mechanical forces. The most familiar example of this is the change of bulk which accompanies change of Temperature (q.v.). Electrification also produces changes of volume. Again, the magnetic metals, iron, nickel, and cobalt, undergo very complicated strains when magnetised in various ways. In all these instances there is always a reciprocal effect, a particular straining producing thermal, electric, or magnetic changes.