engleski

Finite element analysis of micropolar continuum: application of the fixed-pole interpolation concept

In order to realistically describe the behaviour of a heterogeneous material and capture the phenomena that the classical (Cauchy) theory cannot, several alternative theories have been developed, one of which is the micropolar (Cosserat) continuum theory. Unlike the classical theory, where the static interaction between two particles of a body is described only by a force vector, in the micropolar theory there exists an additional moment vector field [1]. Consequently, there is an additional couple-stress tensor and both stress tensors are non-symmetric in general. The existence of a couple-stress tensor causes an additional kinematic field (microrotation), which gives an orientation to each material point and it is completely independent of the skew-symmetric part of the displacement gradient at the observed point (macrorotation). To describe a linear centrosymmetric isotropic micropolar continuum, it is necessary to know six independent material parameters [2]. The theory itself is well known, but reliable experimental methods for determining the material parameters are still not established, which prevents wider application of the theory. Alternatively, the material parameters may be obtained from experiments with the help of numerical analysis in an inversely posed problem. The development of high-quality micropolar finite elements is thus very important and for this reason, we present a detailed linear analysis of the micropolar continuum within the finite-element method using a novel interpolation based on the fixed-pole concept. The concept was first introduced in [3] where authors applied it to the geometrically nonlinear 3D beams which has proven to be particularly useful in dynamics, but so far, no attempts have been made to apply it in linear analysis, where some advantages of the concept can be expected. The new family of micropolar finite elements will be tested through patch tests and compared with existing elements [4].

Cosserat theory, micropolar continuum, finite element methods, fixed-pole concept

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