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CONTENTS
Volume 7, Number 1, February 2018
 

Abstract
This special issue contains selected papers first presented in a short format at the 3rd International Conference ECCOMAS MSF 2017-Multiscale Computations for Solids and Fluids, organized in Slovenian capital Ljubljana, September 20-22, 2017.

Key Words
multiscale computations; solid mechanics; fluid mechanics

Address
Adnan Ibrahimbegovic: Universite de Technologie Compiegne – Sorbonne Universities, Laboratoire Roberval de Mecanique,
Centre de Recherche Royallieu, Compiegne, France

Abstract
A fully-coupled thermodynamic-based transient finite element formulation is proposed in this article for electric, magnetic, thermal and mechanic fields interactions limited to the linear case. The governing equations are obtained from conservation principles for both electric and magnetic flux, momentum and energy. A full-interaction among different fields is defined through Helmholtz free-energy potential, which provides that the constitutive equations for corresponding dual variables can be derived consistently. Although the behavior of the material is linear, the coupled interactions with the other fields are not considered limited to the linear case. The implementation is carried out in a research version of the research computer code FEAP by using 8-node isoparametric 3D solid elements. A range of numerical examples are run with the proposed element, from the relatively simple cases of piezoelectric, piezomagnetic, thermoelastic to more complicated combined coupled cases such as piezo-pyro-electric, or piezo-electro-magnetic. In this paper, some of those interactions are illustrated and discussed for a simple geometry.

Key Words
electromagnetic-thermomechanical coupling; elasticity; thermodynamics; finite element formulation

Address
Pablo Moreno-Navarro and Adnan Ibrahimbegovic: Sorbonne Universites-Universite de Technologie Compiegne, Laboratoire Roberval de Mécanique, Chaire de Mecanique, France
Jose L. Pérez-Aparicio: Department of Continuum Mechanics & Theory of Structures, Universitat Politecnica de Valencia, Spain

Abstract
Behavior of soil is usually described with continuum type of failure models such as Mohr-Coulomb or Drucker-Prager model. The main advantage of these models is in a relatively simple and efficient way of predicting the main tendencies and overall behavior of soil in failure analysis of interest for engineering practice. However, the main shortcoming of these models is that they are not able to capture post-peak behavior of soil nor the corresponding failure modes under extreme loading. In this paper we will significantly improve on this state-of-the-art. In particular, we propose the use of a discrete beam lattice model to provide a sharp prediction of inelastic response and failure mechanisms in coupled soil-foundation systems. In the discrete beam lattice model used in this paper, soil is meshed with one-dimensional Timoshenko beam finite elements with embedded strong discontinuities in axial and transverse direction capable of representing crack propagation in mode I and mode II. Mode I relates to crack opening, and mode II relates to crack sliding. To take into account material heterogeneities, we determine fracture limits for each Timoshenko beam with Gaussian random distribution. We compare the results obtained using the discrete beam lattice model against those obtained using the modified three-surface elasto-plastic cap model.

Key Words
discrete beam lattice model; modified three-surface elasto-plastic cap model; Timoshenko beam; Gaussian distribution; failure mechanisms

Address
Emina Hadzalic:
1) Universite de Technologie de Compiegne/Sorbonne Universites, Laboratoire Roberval de Mecanique, Centre de Recherche Royallieu, 60200 Compiegne, France
2) Faculty of Civil Engineering, University of Sarajevo, Patriotske lige 30, Sarajevo 71000, Bosnia and Herzegovina
Adnan Ibrahimbegovic: Universite de Technologie de Compiegne/Sorbonne Universites, Laboratoire Roberval de Mecanique, Centre de Recherche Royallieu, 60200 Compiegne, France
Samir Dolarevic: Faculty of Civil Engineering, University of Sarajevo, Patriotske lige 30, Sarajevo 71000, Bosnia and Herzegovina

Abstract
The presence of the pore fluid strongly influences the reponse of the soil subjected to external loading and in many cases increases the risk of final failure. In this paper, we propose the use of a discrete beam lattice model with the aim to investigate the coupling effects of the solid and fluid phase on the response and failure mechanisms in the saturated soil. The discrete cohesive link lattice model used in this paper, is based on inelastic Timoshenko beam finite elements with enhanced kinematics in axial and transverse direction. The coupling equations for the soil-pore fluid interaction are derived from Terzaghi\'s principle of effective stresses, Biot\'s porous media theory and Darcy\'s law for fluid flow through porous media. The application of the model in soil mechanics is illustrated through several numerical simulations.

Key Words
discrete beam soil; discrete beam lattice model; poroplasticity; coupling; failure mechanisms

Address
Emina Hadzalic:
1) Universite de Technologie de Compiegne/Sorbonne Universites, Laboratoire Roberval de Mecanique, Centre de Recherche Royallieu, 60200 Compiegne, France
2) Faculty of Civil Engineering, University of Sarajevo, Patriotske lige 30, Sarajevo 71000, Bosnia and Herzegovina
Adnan Ibrahimbegovic: Universite de Technologie de Compiegne/Sorbonne Universites, Laboratoire Roberval de Mecanique, Centre de Recherche Royallieu, 60200 Compiegne, France
Mijo Nikolic:
1) Universite de Technologie de Compiegne/Sorbonne Universites, Laboratoire Roberval de Mecanique, Centre de Recherche Royallieu, 60200 Compiegne, France
2) Faculty of Civil Engineering, Arhitecture and Geodesy, University of Split, Matice Hrvatske 15, 21000 Split, Croatia

Abstract
This paper establish a high concentration ratio approximation of linear elastic properties of materials with periodic microstructure with cubic inclusions. The approximation is derived using first few terms of power series expansion of the solution of the equivalent eigenstrain problem with a homogeneous eigenstrain approximation. Viability of the approximation at high concentration ratios is proved by comparison with a numerical solution of the homogenization problem. To this end some theoretical result of symmetry properties of the homogenization problem are given. Using these results efficient numerical computation on a reduced computational domain is presented.

Key Words
periodic homogenization; material symmetries; equivalent eigenstrain method; effective elastic properties; asymptotic solution

Address
George Mejak: Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia

Abstract
The process of material failure i.e. cracks development and their propagation in an experiment related to the bending collapse of cross laminated timber plate with ribs is described. Numerical simulation of such an experiment by the nonlinear finite element method is presented. The numerical model is based on Hashin failure criteria, initially developed for unidirectional composites, and on material softening concept applied by the smeared crack approach. It is shown that such a numerical model can be used for an estimation of the limit load and the limit displacement of a cross laminated timber ribbed plate.

Key Words
cross-laminated timber (CLT); ribbed timber plate; limit load analysis; Hashin failure criteria; material softening

Address
Marko Lavrencic and Bostjan Brank: University of Ljubljana, Faculty of Civil and Geodetic Engineering, Jamova c. 2,
1000 Ljubljana, Slovenia


Abstract
The relevance of turbulent mixing in estuarine numerical models for stratified two-layer shallow water flows is analysed in this paper. A one-dimensional numerical model was developed for this purpose by extending an immiscible two-layer model with an additional source term, which accounts for turbulent mixing effects, namely the entrainment of fluid from the lower to the upper layer. The entrainment rate is quantified by an empirical equation as a function of the bulk Richardson number. A finite volume method based on an approximated Roe solver was used to solve the governing coupled system of partial differential equations. A comparison of numerical results with and without entrainment is presented to illustrate the influence of entrainment on both the salt-water intrusion length and lower layer dynamics. Furthermore, one example is given to demonstrate how entrainment terms may help to stabilize the numerical scheme and prevent a possible loss of hyperbolicity. Finally, the model with entrainment is validated by comparing the numerical results to field measurements.

Key Words
turbulent mixing; entrainment; two-layer flow; finite volume method; shallow water flow; numerical model; estuaries

Address
Nino Krvavica and Nevenka Ozanic: Department of Hydrology and Hydraulic Engineering, Faculty of Civil Engineering, University of Rijeka, Radmile Matejcic 3, 51000 Rijeka, Croatia
Ivica Kozar: Department of Computer Modeling, Faculty of Civil Engineering, University of Rijeka, Radmile Matejcic 3, 51000 Rijeka, Croatia


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