Specific shear-dependent viscoelastic third-grade fluid model

A specific modified constitutive equation for a third-grade fluid is proposed so that the model be suitable for applications where shear-thinning or shear-thickening may occur. For that, we use the Cosserat theory approach reducing the exact three-dimensional equations to a system depending only on time and on a single spatial variable. This one-dimensional system is obtained by integrating the linear momentum equation over the cross-section of the tube, taking a velocity field approximation provided by the Cosserat theory. From this reduced system, we obtain the unsteady equations for the wall shear stress and mean pressure gradient depending on the volume flow rate, Womersley number, viscoelastic coefficient and flow index over a finite section of the tube geometry with constant circular cross-section.

A staggered approach for the coupling of Cahn–Hilliard type diffusion and finite strain elasticity

We develop an algorithm and computational implementation for simulation of problems that combine Cahn–Hilliard type diffusion with finite strain elasticity. We have in mind applications such as the electro-chemo- mechanics of lithium ion (Li-ion) batteries. We concentrate on basic computational aspects. A staggered algorithm is pro- posed for the coupled multi-field model. For the diffusion problem, the fourth order differential equation is replaced by a system of second order equations to deal with the issue of the regularity required for the approximation spaces. Low order finite elements are used for discretization in space of the involved fields (displacement, concentration, nonlocal concentration). Three (both 2D and 3D) extensively worked numerical examples show the capabilities of our approach for the representation of (i) phase separation, (ii) the effect of concentration in deformation and stress, (iii) the effect of Electronic supplementary material The online version of this article (doi:10.1007/s00466-015-1235-1) contains supplementary material, which is available to authorized users. B P. Areias pmaa@uevora.pt 1 Department of Physics, University of Évora, Colégio Luís António Verney, Rua Romão Ramalho, 59, 7002-554 Évora, Portugal 2 ICIST, Lisbon, Portugal 3 School of Engineering, Universidad de Cuenca, Av. 12 de Abril s/n. 01-01-168, Cuenca, Ecuador 4 Institute of Structural Mechanics, Bauhaus-University Weimar, Marienstraße 15, 99423 Weimar, Germany strain in concentration, and (iv) lithiation. We analyze con- vergence with respect to spatial and time discretization and found that very good results are achievable using both a stag- gered scheme and approximated strain interpolation.