A new description of the stress state at a point with applications

Summary

The concept of base forces is introduced in order to replace various stress tensors for the description of the stress state at a point. Basic equations are written in terms of the base forces. The elastic law is given that can directly express the base forces by strain energy. The Cauchy and Piola stresses are expressed through base forces by dyadic vectors. Further, a purely physical expression of stress tensors is obtained without using a coordinate system. Finally, as examples, the potential energy principle of elasticity for the case of large strain is re-stated in a simple manner and the explicit expressions of stiffness and compliance matrices of the finite element method for linear elasticity are obtained.