Abstract

RAMOS-CANON, Alfonso Mariano; PRADA-SARMIENTO, Luis Felipe  and  VEGA-POSADA, Carlos Alberto. Finite Element Analysis Using a Cosserat Linear Elastic Continuum. Tecnura [online]. 2016, vol.20, n.50, pp.43-54. ISSN 0123-921X.  https://doi.org/10.14483/udistrital.jour.tecnura.2016.4.a03.

ABSTRACT Context: Experimental results show that the stress-strain behavior of granular materials depends upon the scale analysis. However, due to the intrinsic assumptions of the mechanics of a continuum medium, the analysis of finite elements based on the Boltzmann´s continuum does not allow to consider characteristic lengths in its formulation to reflect the scale effect. Method: This work presents a finite element formulation to analyze plane-strain linear problems using the Cosserat continuum. The degrees of freedom of a four-node quadrilateral finite element are presented and the differential operator is derived to obtain the deformation vector, function form, interpolation matrix, stiffness matrix and nodal load vector. Finally, the Cosserat continuum with the aforementioned element is implemented in a finite element software coded by the authors. The software is used to solve a stress-strain problem of a homogeneous layer with a linear elastic behavior. Results: The differences of the stress and shear strain responses between the conventional and the Cosserat continuum along with the moments acting at the Gauss point level are obtained. Conclusions: The derivation and implementation of the Cosserat continuum provides an alternative finite element analysis to the conventional continuum, along with the advantage of introducing a characteristic length in the formulation to account for the scale effects and rotations observed in granular materials.

Keywords : Cosserat continuum; finite element method.

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