The [[Stress|stresses]] shown in the following diagram can occur for a particle under general [[Force|loading]] conditions. The first subscript denotes the direction of the face, whereas the second subscript denotes the direction of applied force. ![[general_stress.png|center|500]] The general loading condition of a particle can be summarized using a matrix known as a [[Tensor|tensor]]. Tensors provide a useful mathematical framework which is compatible with [[Vector|vectors]]. $\sigma_{ij}=\dfrac{F_j}{A_i}=\begin{bmatrix}\sigma_{xx}&\tau_{xy}&\tau_{xz}\\\tau_{yx}&\sigma_{yy}&\tau_{yz}\\\tau_{zx}&\tau_{zy}&\sigma_{zz}\end{bmatrix}$ To ensure that the particle is static the following relations must be true: $\tau_{xy}=\tau_{yx}$ $\tau_{xz}=\tau_{zx}$ $\tau_{yz}=\tau_{zy}$ As such, there are only six independent stressors for any static particle.