The traction problem in elastodynamics

Abstract

In continuum mechanics, Cauchy’s six equations Open image in new window are incomplete[1] and the famous Cauchy’s laws of motion $$\rho \ddot x = divT + \rho b and T^T = T$$ where\(\rho \ddot x\), ρb, T anddivT are continuous are also incomplete[2]. The first six equations are incomplete because the geometrical representation of deformation at a given point is as yet incomplete[3]. and the last two laws are incomplete because, b,T anddivT are frame-indifferent, but\(\rho \ddot x\) is not, and T is a symmetric, as Cauchy interpreted himself. Therefore, we say, the last two laws can’t accommodate to the asymmetric tensor.