I. D. Kotchergenko
2014 Proceedings of 10th World Congress on Computational Mechanics   unpublished
Waves are represented through the superposition of the four fundamental modes of the plane areolar strain theory. This theory was presented at references [10] to [13] , with application to finite rotations, orthotropic materials and finite element models, but a summary review is here presented in order to make this paper self contained and also to disclose the areolar strain concept, which although divulged for two decades still faces with poor acceptance by the scientific community. It is
more » ... mmunity. It is shown that the areolar strain approach does not distinguish finite from infinitesimal strain due to the fact that in addition to the traditional "forward" strain it incorporates the "sidelong" strain into its imaginary part. Instead of comparing the change in distance between two contiguous points, the areolar strains presents the complete state of finite strains on an areola that surrounds a given point. Only first derivatives are used, as expected due to the physical meaning of strain and having in mind that the relative displacement between two arbitrary points of the plane should be obtained through a single line integration of the strain, along any path of integration joining these points. The areolar strain fulfils these conditions. Now, an approach for tackling with equivoluminal waves of finite rotation is presented, assuming that the gain of volume due the mathematical finite rotation is neutralized by the mathematical shrinkages due to the complex shear strain.
doi:10.5151/meceng-wccm2012-16727 fatcat:odhdnvbabrcpdbeuhb3xgx4riq