# Strain (materials science)

The strain (symbol: ε ) is an indication of the relative change in length ( lengthening or shortening ) of a body under stress, for example, by force or by a change in temperature ( thermal expansion ). If the dimension of the body is increased, one speaks of a positive elongation ( stretching), otherwise a negative elongation or compression.

## Definition

Elongation is defined as:

It is the change in length and the original length. The elongation is the dimensionless number is multiplied by 100 or specified as a percentage value.

In the technical field of the description of strain in microns per meter ( microns / m) is common. This is also the spelling, is derived from Mikroepsilon used μeps or με. 1 micron / m corresponds to 0.0001 percent, a 1 percent elongation corresponds to 10,000 microns / m.

For many materials, the strain is proportional to the force acting within certain limits, which is expressed by Hooke's law in the linear- elastic range. Due to the Poisson results also transverse to the direction of force a stretch. The ratio of the transverse and longitudinal stretching is called Poisson's ratio.

In a general scenario train load, pressure and shear forces can occur in combination. This has equally complex strains in the different spatial directions result. The complete mathematical description via tensors of force or strain. They form the basic framework for computer models of deformation simulation, as they are needed, for example, the finite element method.

### Technical elongation

When viewed from strains in response to two (or more ) consecutive force effects, two different reference systems for the calculation of the strain are used. If it is specified relative to the initial length before the first application of force, then one speaks of a technical stretch. This method is particularly simple because the initial length then is a constant. Technical strain is also called Cauchy expansion

However, it has the disadvantage of non- scaling, since the sum of the two strains is no longer equal to the total elongation:

However, as long approximately applies:

### Logarithmic strain

In contrast to the technical elongation logarithmic or "true" expansion to the current length of the body is obtained after it has been so pre-deformed by earlier force effects (and also referred to as the Hencky strain ).

It is defined by:

The technical expansion is mathematically a series expansion of the formula for the "true" expansion in a Taylor series with termination after the first term. For small strains, therefore, exists between the two definitions of the context: