småsträckningsteorin

Småsträckningsteorin, or "small strain theory" in English, is a fundamental concept in continuum mechanics that simplifies the analysis of deformation. It applies when the displacements and rotations within a material are very small compared to the characteristic dimensions of the object. This assumption allows for significant mathematical simplifications, making the analysis of many engineering problems tractable.

The core idea behind small strain theory is that the deformation of the material does not significantly alter the geometry of the body during the deformation process. This means that the original undeformed configuration can be used for calculations of forces, stresses, and strains, rather than needing to consider the continuously changing deformed state. This approximation is valid for a wide range of materials and applications, including most structural engineering problems, elasticity, and many fluid mechanics scenarios.

Mathematically, small strain theory implies that the strain tensor can be approximated by a linear relationship between displacement gradients. Higher-order terms that account for changes in geometry are neglected. This linearization is crucial as it transforms complex non-linear equations into more manageable linear ones, which can be solved using standard analytical or numerical techniques. While powerful, it's important to recognize the limitations; when deformations become large, such as in rubber elasticity or large plastic deformations, small strain theory is no longer applicable, and non-linear theories must be employed.