spänningsvektor

A spänningsvektor, or stress vector, is a mathematical concept used in continuum mechanics and solid mechanics to describe the force acting on a surface element within a continuous material. It is a vector quantity, meaning it has both magnitude and direction. The spänningsvektor is defined as the force per unit area acting on a specific surface. The direction of the spänningsvektor is generally not perpendicular to the surface itself, but rather it is the resultant of both normal and shear stresses acting on that surface.

To understand the spänningsvektor more deeply, one must consider the stress tensor, which is a second-order tensor that fully characterizes the state of stress at a point within a material. The stress tensor relates the normal vector of any given surface passing through that point to the spänningsvektor acting on that surface. Specifically, the spänningsvektor can be calculated by multiplying the stress tensor by the outward-pointing unit normal vector of the surface.

The spänningsvektor is a crucial tool for analyzing the behavior of materials under load. It allows engineers and physicists to determine the forces acting on internal surfaces within a body, which is essential for predicting failure, deformation, and other mechanical responses. Concepts like the maximum shear stress and principal stresses are derived from the analysis of spänningsvektorer on various oriented surfaces.