BENDING SIMULATION OF PRE-GELLED COMPOSITES USING AN EXPLICIT COSSERAT CONTINUUM MODEL

Forming simulation of uncured pre-preg can be made more efficient with the use of dedicated finite elements tailored for soft, layered media. These elements are based on the Cosserat continuum theory that introduces a rotational degree of freedom at each node within standard solid elements. In this study, a Cosserat element is developed within a 2D non-linear explicit finite element framework that uses the Carrera Unified Formulation for its spatial discretization. Two benchmark case studies involving bending deformations are presented as the verification of the developed model. It is demonstrated that similar accuracy of predictions can be achieved with much coarser meshes of Cosserat elements than the equivalent classical finite element models consisting of multi-layer stacks of solid elements.

Elastohydrodynamic Lubrication Modeling by a Cosserat Continuum Theory for Small Polymer Journal Bearings

Recent experiments have shown that the elastic deformation behaviors of a polymeric material are consistent with the Cosserat elasticity under nonuniform deformation at a millimeter scale. Thus, an elastohydrodynamic lubrication model in the framework of the Cosserat continuum theory is proposed to explore the lubrication performance that deviates from the classical elastohydrodynamic lubrication theory for the small polymer journal bearings with millimeter size. The elastic deformation of the bearing sleeve made of polymeric material and the pressure distribution in a lubricating film are obtained through an iterative solution of the equation of the Cosserat elasticity and the modified Reynolds’ equations with considering the boundary slippage. The effect of bearing size and Cosserat characteristic lengths for torsion and bending on the lubrication performance of the small polymer journal bearings is studied using the proposed Cosserat elastohydrodynamic lubrication model. It was found that the small changes in film thickness due to the Cosserat effect can result in large changes in film pressure. The Cosserat characteristic length of bending possesses a significant effect on the lubrication behaviors of the journal bearings, because the size effect is mainly caused by the increased apparent modulus due to the bending elastic deformation of the bearing sleeve. The boundary slip behaviors dependent on the Cosserat characteristic length are also studied using the Cosserat elastohydrodynamic model, and the numerical results show that the Cosserat characteristic length changes the optimal geometric parameters of the slip zone in terms of load carrying capacity for the small polymer journal bearings.

Three Dimensional Cosserat Continuum Model and its Application to Analysis for the Cantilever Beam

A basic 3D Cosserat continuum theory and corresponding finite element formulations are deduced. The deflections of a cantilever beam are analyzed by the 20-nodes solid elements based on the classical continuum theory and Cosserat continuum theory respectively. Compared with analytical solution brought forward by Timoshenko and Goodier, it illustrates that the numerical results based on Coseerat FEM are effective and more accurate and closer to the analytical solutions by choosing an appropriate value of the characteristic internal length, which also testifies the capability of reflecting the intrinsic property of the cantilever beam.

A Coupled Model of Two-Phase Diffusion and Flow through Deforming Porous Cosserat Media

Simulation of mining induced rock deformation, rock fracture enhanced permeability and fluid and gas diffusion and flow process is a complex task. A new three dimensional coupled mechanical two-phase double porosity desorption and diffusion finite element code called COSFLOW has been recently developed by CSIRO Exploration and Mining to service the mining industry’s need. A unique feature of COSFLOW is the incorporation of Cosserat continuum theory in its formulation. In the Cosserat model, inter-layer interfaces (joints, bedding planes) are considered to be smeared across the mass, i.e. the effects of interfaces are incorporated implicitly in the choice of stress-strain model formulation. An important feature of the Cosserat model is that it incorporates bending rigidity of individual layers in its formulation and this makes it different from other conventional implicit models. The Cosserat continuum formulation has a major advantage over conventional continuum models in that it can efficiently simulate rock breakage and slip as well as separation along the bedding planes. Any opening/closure along a bedding plane may introduce a strong anisotropy in fluid flow properties of the porous medium. This, in turn, will impact on the fluid/gas flow behaviour of the porous medium. This paper will briefly describe the Cosserat continuum theory, the treatment of permeability changes with rock deformation and the coupling of the two-phase dual porosity fluid diffusion- flow model and present a number of examples highlighting the capability of the developed code in simulating the mining induced rock deformation, permeability changes and fluid diffusion and flow will be presented.