New Definitions of Piola Stress Tensors Based on Some Geometrical Characterization of Cuachy traction

F.S. BUEZAS; C.P. FILIPICH; R. SAMPAIO

Huston

Congreso; PACAM 2013; 2013

The American Academy of Mechanics

Traditional de_nitions of the _rst and second Piola stress tensor can be extended. In this paper, based on a geometric characterization of the Cauchy traction with the corresponding Piola traction, diverse alternatives are introduced. Of course they could not be unique, but the spectrum of possibilities expands. In eventual applications one can use any of them, especially if a Lagrangian reference is handled. These properties can be such as to maintain the parallelism of vectors of Piola and Cauchy acting on elements of di_erent areas (_rst Piola stress tensor). Cauchy traction being tangent to some _ber gives rise to the correponding Piola vector according to the transformation between _ber material elements (second Piola tensor). Among others,by considering the relationship that governs the normals to surface elements a new Piola vector is found.(and lets say a third Piola tensor). These new de_nitions are supplemented by the cor- responding stress tensors, the balance equations of linear momentum and the unique power conjugate pairings.