🧪Applications of Tensors in Solid Mechanics Electromagnetism and Classical Mechanics

Tensors are essential mathematical tools used to describe complex physical phenomena in various fields. In solid mechanics, they are used to define key relationships: the stress tensor ( $\sigma_{i j}$ ) describes internal forces and must be symmetric for an object to be in static equilibrium. The strain tensor ( $\epsilon_{i j}$ ) quantifies a material's deformation. These two are related by Hooke's Law, which uses the stiffness tensor ( $c_{i j k l}$ ) to characterize a material's elasticity. In electromagnetism, tensors like the Maxwell stress tensor ( $\sigma_{i j}$ ) describe forces exerted by fields, and the conductivity tensor ( $\sigma_{i j}$ ) generalizes Ohm's Law. Finally, in classical mechanics, the moment of inertia tensor ( $I_{i j}$ ) is a rank-two tensor that acts as the rotational equivalent of mass, relating angular velocity to angular momentum and kinetic energy. The concept extends to a generalized inertia tensor ( $M_{a b}$ ) for more complex systems.

Applications of Tensors in Solid Mechanics Electromagnetism and Classical Mechanics | Condensed Notesviadean on Notion