småsträckningsteori

Småsträckningsteori, often translated as "small strain theory," is a fundamental concept in continuum mechanics used to describe the behavior of materials under deformation. It is based on the assumption that the displacements and rotations of material points are very small relative to the characteristic dimensions of the body. This simplification allows for linear approximations in the analysis of stress and strain.

Under small strain theory, the relationship between strain and displacement is linearized. This means that the square of displacement gradients is neglected. Similarly, the rotation tensor is also approximated as being negligible. This linearization significantly simplifies the mathematical equations governing material behavior, making them amenable to analytical and numerical solutions.

The applicability of small strain theory is widespread, particularly in engineering disciplines such as solid mechanics, structural analysis, and geomechanics. It is appropriate for analyzing phenomena like the elastic deformation of bridges, the bending of beams, or the settlement of soils under typical loading conditions. However, when deformations become large, such as in the necking of metals during tensile testing or the large-scale buckling of thin shells, the assumptions of small strain theory break down, and more advanced theories of large strain mechanics are required. The validity of small strain theory is often assessed by comparing the magnitude of strains to unity or to the characteristic dimensions of the problem.