Jännitysinvarianttien

Jännitysinvarianttien, also known as stress invariants, are a set of scalar quantities derived from the stress tensor that are independent of the coordinate system. These invariants are fundamental in continuum mechanics and materials science for characterizing the state of stress within a material. There are typically three independent stress invariants.

The first stress invariant, often denoted as I1 or J1, is the trace of the stress tensor, which is the sum of its diagonal elements. This corresponds to the mean normal stress. The second stress invariant, denoted as I2 or J2, is related to the sum of the principal minors of the stress tensor. It provides information about the shear components of the stress. The third stress invariant, denoted as I3 or J3, is the determinant of the stress tensor. This invariant is directly related to the volume change under stress.

These invariants are particularly useful because they remain unchanged regardless of how the coordinate axes are rotated. This means that the physical state of stress at a point can be described using these invariant quantities, which simplifies the analysis and comparison of stress states across different orientations. Jännitysinvarianttien are crucial in formulating constitutive models for materials, predicting material failure, and analyzing the behavior of structures under load. They are commonly used in plasticity theory, where yield criteria are often expressed in terms of stress invariants.