Saint-Venant principle

The experimental methods used to measure residual stresses are essentially the same for metals and polymers. The most widespread are mechanical methods, which can be destructive, non-destructive, and semi-destructive146. Destructive methods involve cutting off part of a sample the residual part reacts to this procedure by deformations or displacements proportional to the inherent stresses. This approach is based on the Saint-Venant principle the response in the residual part does not depend on the stress distribution in the cut part of a sample. After measuring the distribution of deformations, residual stresses in the initial sample can be calculated. 

According to the Saint Venant principle, the stresses of two statically equivalent applied loads are closely similar except near the point of application of the load. This principle, which can be empirically tested, allows the boundary conditions to be expressed in terms of a resultant force rather than an exact distribution of stresses. Obviously, this principle is of great significance in many practical problems. 

Note that the condition expressed by Eq. (16.147) is an integral instead of a z = 0 this fact represents the application of the Saint Venant principle to the z face of the cylinder. For this reason the stress state in the cylinder is only precise enough for points far from the ends of the cylinder. 

Assuming the corresponding process volumes as ellipses having, according to the Saint-Venant principle, semi-axis a — d and b — 2 d it yields... 

Saint-Venant is famous for his principle in the strength of material that states that except in the immediate vicinity of the points of application of the load, the stress distribution may be assumed independent of the acmal mode of application of the load as long as loadings are statically equivalent. This principle is conveniendy used to find out the stresses far away from the load. In the immediate vicinity of the load, the stresses can be determined using advanced theoretical or experimental methods (Beer et al. 2004). Von Karman carried out compression test on marble under high pressure and results were published in 1911. 

Horgan, C.O. (1972) On Saint-Venant s principle in plane anisotropic elasticity. /. Blast., 2(169), 335. 

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