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A mixed finite element (FE) procedure of the gradient Cosserat continuum for the second-order computational homogenisation of granular materials is presented. The proposed mixed FE is developed based on the Hu---Washizu variational principle. Translational displacements, microrotations, and displacement gradients with Lagrange multipliers are taken as the independent nodal variables. The tangent stiffness matrix of the mixed FE is formulated. The advantage of the gradient Cosserat continuum model in capturing the meso-structural size effect is numerically demonstrated. Patch tests are specially designed and performed to validate the mixed FE formulations. A numerical example is presented to demonstrate the performance of the mixed FE procedure in the simulation of strain softening and localisation phenomena, while without the need to specify the macroscopic phenomenological constitutive relationship and material failure model. The meso-structural mechanisms of the macroscopic failure of granular materials are detected, i.e. significant development of dissipative sliding and rolling frictions among particles in contacts, resulting in the loss of contacts.

SUMMARY Today multiphysics problems applied to various fields of engineering have become increasingly important. Among these, in the areas of civil, environmental and nuclear engineering, the problems related to the behaviour of porous media under extreme conditions in terms of temperature and/or pressure are particularly relevant. The mathematical models used to solve these problems have an increasing complexity leading to increase of computing times. This problem can be solved by using more effective numerical algorithms, or by trying to reduce the complexity of these models. This can be achieved by using a sensitivity analysis to determine the influence of model parameters on the solution. In this paper, the sensitivity analysis of a mathematical/numerical model for the analysis of concrete as multiphase porous medium exposed to high temperatures is presented. This may lead to a reduction of the number of the model parameters, indicating what parameters should be determined in an accurate way and what can be neglected or found directly from the literature. Moreover, the identification parameters influence may allow to proceeding to a simplification of the mathematical model (i.e. model reduction). The technique adopted in this paper to performing the sensitivity analysis is based on the automatic differentiation (AD), which allowed to develop an efficient tool for the computation of the sensitivity coefficients. The results of the application of AD technique have been compared with the results of the more standard finite difference method, showing the superiority of the AD in terms of numerical accuracy and execution times. From the results of the sensitivity analysis, it follows that a drastic simplification of the model for thermo-chemo-hygro-mechanical behaviour of concrete at high temperature, is not possible. Therefore, it is necessary to use different model reduction techniques in order to obtain a simplified version of the model that can be used at industrial level. Copyright © 2012 John Wiley & Sons, Ltd.

SUMMARY The aim of this paper is to present a three-dimensional (3D) finite element modeling of heat and mass transfer phenomena in partially saturated open porous media with random fields of material properties. Randomness leads to transfer processes within the porous medium that naturally need a full 3D modeling for any quantitative assessment of these processes. Nevertheless, the counterpart of 3D modeling is a significant increase in computations cost. Therefore, a staggered solution strategy is adopted which permits to solve the equations sequentially. This appropriate partitioning reduces the size of the discretized problem to be solved at each time step. It is based on a specific iterative algorithm to account for the interaction between all the transfer processes. Accordingly, a suitable linearization of mass convective boundary conditions, consistent with the staggered algorithm, is also derived. After some validation tests, the 3D numerical model is used for studying the drying process of a cementitious material with regard to its intrinsic permeability randomness. Copyright © 2011 John Wiley & Sons, Ltd.

The paper analyses the interaction between two internal length scales during dynamic strain localization in multiphase porous materials. The first internal length is introduced in the mathematical model by the gradient-dependent plasticity for the solid skeleton, while the second one is naturally contained in the multiphase model and is due to the seepage process of the water via Darcy's law, which induces a rate-dependent behaviour of the solid skeleton. Numerical results of a one-dimensional example of water saturated porous medium demonstrate the competing effect between these two length scales. The porous medium is here treated as a multiphase continuum, with the pores filled by water and air, the last one at constant atmospheric pressure. Copyright © 2005 John Wiley & Sons, Ltd.

The paper presents a fully-coupled numerical model for the analysis of fracture initiation and propagation in a two dimensional non-homogeneous elastic medium driven by mechanical loads and transient thermal fields. Cohesive crack behaviour is assumed for the solid. The solution of the coupled problem is obtained by using the finite element method without using special approximation techniques nor interface elements. Evolution of the process zone results in continuous changes of the domain topology. This is accounted for by updating the boundary geometry and successive remeshing of the domain. Optimality of the shape of the finite elements generated is controlled and the mesh density is adjusted adaptively on the basis of an error estimator. Two numerical applications are presented, which demonstrate the effectiveness of the proposed procedure. In the first, comparison is made with a laboratory experiment, whereas the second handles a problem with crack path completely unknown.

Non-linear deformable porous media with sorption (capillary condensation) hysteresis are considered. An arti cial neural network with two hidden layers is trained to interpolate the sorption hysteresis using a set of experimental data. The performance of the ANN, which is applied as a procedure in the FE code, is investigated, both from numerical, as well as from physical viewpoint. The ANN-FE code has been developed and tested for 1-D and 2-D problems concerning cyclic wetting–drying of concrete elements. In general, the application of the ANN procedure inside the classical FE program does not have any negative e ect on the numerical performance of the code. The results obtained indicate that the sorption isotherm hysteresis is of importance during analysis of hygrothermal and mechanical behaviour of capillary-porous materials. The most distinct di erences are observed for the saturation and displacement solutions. The ANN-FE approach seems to be an e cient way to take into account the in uence of hysteresis during analysis of hygro-thermal behaviour of capillary-porous materials. Copyright ? 2001 John Wiley & Sons, Ltd.

In this paper, a multi-frontal parallel algorithm is developed to solve fully coupled heat, water and gas flow in deformable porous media. The mathematical model makes use of the modified e⁄ective stress concept together with the capillary pressure relationship and takes phase change and latent heat transfer into account. The chosen macroscopic field variables are displacement, capillary pressure, gas pressure and temperature. The parallel program is developed on a cluster of workstations. The PVM (Parallel Virtual Machine) system is used to handle communications among networked workstations. The multi-frontal method has advantages such as numbering of the finite element mesh in an arbitrary manner, simple programming organization, smaller core requirements and shorter computation times. An implementation of this parallel method on workstations is discussed. The speedup and eƒciency of this method is demonstrated and compared with a general domain decomposition method based on band matrix methods by numerical examples. ( 1998 John Wiley & Sons, Ltd.

Dynamic strain localisation theory together with a multiphase material model is used to simulate shear band dominated processes in fully saturated sand samples. The fluid-saturated medium is viewed as multi-phase continuum consisting of a solid skeleton and pores filled by fluids. The governing equations are based on the general framework of averaging theories. A generalised plasticity constitutive model for fully saturated soils is adopted in the computational process. Both samples of medium-loose and dense sands are studied. Negative water pressures, which are important in localisation phenomena of fully saturated dilatant geomaterials, are obtained for dense sands, while positive water pressures result for medium-loose sands.

SUMMARY A fully coupled numerical model has been developed which describes multiphase fluid flow through soil: namely gas, water and a non-aqueous phase liquid (NAPL) in a deforming porous media for subsurface systems. A multiphase flow model, based on the two-phase flow model of Brooks and Corey, is presented to express the dependence of saturation and relative permeability on the capillary pressure. Non-linear saturation and relative permeability functions are incorporated into a Galerkin finite element model which is subsequently used to simulate multiphase immiscible fluid flow under saturated and unsaturated conditions in porous media. The governing partial diAerential equations, in terms of soil displacements and fluid pressures, which are coupled and non-linear, are solved by the finite element method. Numerical implementation of the formulation is discussed, and example problems demonstrate the model and solution procedure. #1998 John Wiley & Sons, Ltd. Commun. Numer. Meth. Engng, 14, 135‐149 (1998).

SUMMARY It is recalled that negative water pressures are of importance in localisation phenomena of fully saturated undrained samples of dilatant geomaterials. A model to simulate cavitation phenomena connected with such pore water tractions is developed and implemented in a simplified form in a dynamics code for partially saturated porous media. A case of localisation is studied from the onset of the instability up to the full developed shear band. The weak mesh dependence of the maximum effective plastic strain, due to the employed physical model, is also shown.

This paper presents a general model for the analysis of coupled thermo-hydro-mechanical problems in porous media with possible pollutant transport. The governing equations are described and discrete solution techniques using the finite element method in space and finite differences in time are shown. Emphasis is put on a direct solution procedure, where the coupled system of equations is solved without use of matrix partitioning. Both the Newton-Raphson method and fixed point method are employed. Application examples involving pollutant transport, heat and mass transfer in partially saturated geomaterials, dynamic strain localization and durability of concrete show the range of applicability of this model in the field of evironmental engineering.

The solution of contact problems involves great numerical efforts to satisfy non-penetration conditions. The search for numerical efficiency hence has limited the modelling of the real physical interface behaviour. Up to now mainly simple laws, usually formulated using constant coefficients, have been available to study contact problems in uncoupled from. Here a thermomechanically coupled contact element is presented which accounts for the real microscopic shape of the surfaces, the microscopic mechanism of force transmission and heat exchange. The contact element geometrical behaviour has been put together with experimental and theoretical well founded micro-mechanical and micro-thermal laws adapted to Finite Element Method (FEM) necessities. Based on these laws the macroscopic related stiffnesses are calculated and continuously updated taking into account changes in significant parameters. The linearization of the set of equations has been obtained using a consistent technique which implies computational efficiency.

The modeling of the effects of bending on single Nb3Sn strand DC performance (IC, n index) is presented for a bronze-route strand subjected to the same loading conditions as in an experiment performed at JAEA Naka, Japan [Y. Nunoya, et al., IEEE TAS 14 (2004) 1468–1472]. The strand is discretized in strand elements (SE) representing groups of twisted filaments in the bronze matrix, and in portions of the outer Cu annulus, electro-magnetically coupled in the THELMA code. The 3-D strain map in the filament region is computed with a newly developed, detailed thermo-mechanical model accounting for non-linear, temperature dependent material characteristics. With respect to our previous analysis [P.L.Ribani, et al., IEEE TAS 16 (2006) 860–863] several new updated ingredients, besides the new thermo-mechanical model, are used here, including more accurate thermal and mechanical properties for the materials, a jacket-like model for the outer Cu layer, IC and n index (interpolative) scaling from Durham University. The simulation results show an improved agreement with the experiments, in the degradation of the single-strand performance due to bending.

The behaviour of all geomaterials, and in particular of soils, is governed by their interaction with the pore fluid. The mechanical model of this interaction when combined with suitable constitutive discription of the solid phase and with efficient, discrete, computation procedures, allows most transient and static problems involving deformations to be solved. This paper describes the basic procedures and the development of a general purpose computer program (SWANDYNE-X). The results of the computations are validated by comparison with experimental results obtained on physical models tested in the Cambridge Centrifuge.

In this paper a 3D beam-to-beam contact element is presented, to deal with contact problems in the coupled electric mechanical fields. The beams are supposed to get in contact in a pointwise manner, the detection of the contact points and the computation of all contributions are carried out using a fully symmetric treatment of the two beams. Concerning the mechanical field, Hertz theory of contact for elastic bodies is considered. The contact area is varying according to the beamto-beam angle, being circular only in the case of perpendicular beams. This variation of the shape is taken into account too. The problem is semi-coupled: the mechanical field influences the electric one because of the dependence of the voltage distribution on the contact area. Within the finite element discretization, the mechanical and the electric treatment of the beam element is formulated in the usual way, considering nodal displacements and voltages as main unknowns. The electromechanical contact constraints are enforced with the penalty method. Starting from the virtual work equation the consistent linearization of all contributions is computed to achieve the quadratic convergence within the Newton-Raphson iterative scheme. The complete set of equations arranged in a matrix form suitable for the finite element implementation is solved with a monolithic approach. Finally some numerical examples are discussed to show the effectiveness of the model. 104 D.P. Boso, P. Litewka, B.A. Schrefler, and P. Wriggers

Finite element analysis of non-isothermal elasto-plastic multiphase geomaterials is presented. The multiphase material is modelled as a deforming porous continuum where heat, water and gas flow are taken into account. The independent variables are the solid displacements, the capillary and the gas pressure and the temperature. The modified effective stress state is limited by the Drucker-Prager yield surface for simplicity. Small strains and quasi-static loading conditions are assumed. Numerical results of strain localization in globally undrained samples of dense, medium dense and loose sands and isochoric geomaterial are presented. A biaxial compression test is simulated assuming plane strain condition during the computations. Vapour pressure below the saturation water pressure (cavitation) develops at localization in case of dense sands, as experimentally observed. A case of strain localization induced by a thermal load where evaporation takes place is also analysed.

Previous results indicate that fibers in ribbons are sometimes affected by systematic birefringence superimposed on the random one, their relative weights depending on fiber position in the ribbon. We report new theoretical and experimental results on stress distribution in ribbons, which is shown to depend on thermal and mechanical properties of the common coating. Numerical simulations are based on the theory of elasticity and the finite-element method (FEM). Polarization dispersion measurements vs. temperature match very well with numerical results, and indicate that central fibers in the ribbon exhibit significantly larger birefringence than lateral ones.

The progress in advanced technology fields requires more and more sophisticated formulations to consider contact problems properly. This paper is devoted to the development of a new constitutive model for electrostatic-mechanical contacts, based on a micro–macro approach to describe the contact behaviour. The electric-mechanical contact constitutive law is obtained considering the real microscopic shape of the contacting surfaces, the microscopic behaviour of force transmission and current flow. Some thermo-mechanical macroscopic models based on microscopic characterizations have already been developed to compute the normal and tangential contact stiffness and the thermal contact resistance. On the basis of such macroscopic models, a similar model, suitable for the electric-mechanical field, is developed. With reference to the thermal constriction resistance the electric contact resistance is studied, assuming a flux tube around each contacting asperity, and choosing a suitable geometry for its narrowing at the contact zone. The contact element geometry is based on well known theoretical and experimental micro-mechanical laws, suitably adapted for the FEM formulation. The macroscopic stiffness matrix is calculated on the basis of the microscopic laws and it is continuously updated as a function of the changes in the mechanical and electric significant parameters. A consistent linearization of the set of equations is developed to improve the computational speed, within the framework of implicit methods. Copyright © 2005 John Wiley & Sons, Ltd.

In the present concept of ITER fusion reactor the toroidal field and the central solenoid coils are made of Nb 3 Sn based strands with the cable-in-conduit-conductor (CICC) technology. It is well known that the critical parameters of the Nb 3 Sn strand material are strain sensitive; experimental investigations on short samples of basic strands and subsize CICC cables already demonstrated significant effects of residual strain on the critical parameters. In this paper a method is proposed to analyse in detail the thermal strain induced by the cool down from the strand reaction temperature to the coil working conditions. The superconducting strand can be regarded as a very good example of a hierarchical structure, since there is a clear distinction between the micro-scale of the Nb 3 Sn filaments, the meso-scale of the SC filament groups and the macro-scale of the strand, where it can be regarded as homogeneous. A constitutive relation for the homogenised micro- and meso-components is deduced from the knowledge of the respective internal structures, starting from an accurate description of the single representative cells. This two-scales homogenisation technique is associated with an efficient finite element procedure for computing effective material coefficients to be used with standard orthotropic 3D elements in structural codes. Finally the finite elements routines developed for the unsmearing process provide the real stress and strain values over each single material, which are essential to catch the local features needed for engineering design.

A fully coupled numerical model to simulate the complex behaviour of soil deformation, water flow, airflow, and heat flow in porous media is developed. The following thermal effects are taken into account: heat transfer through conduction and convection, flow, as well as viscosity and density variation of the fluids due to temperature gradients. The governing equations in terms of soil displacements, water and air pressures, and temperature are coupled non‐linear partial differential equations and are solved by the finite element method. Two examples are presented to demonstrate the model performances.

A systematic approach to determine conditions for convergence of partitioned staggered procedures for consolidation problems is presented. Consistency, convergence and stability is investigated for linear and nonlinear problems and a comparison of the partitioned and direct method is made. Conclusions, based also on numerical evidence, are drawn. The significance of the ratio of the time step length to the square of the finite element mesh length is shown.

A correlation is geven between two notations currently used in the formulation of geometrically non-linear analysis in a Lagrangian co-ordinate system. The first referred to as the B-notation results in the linear elastic, initial displacement and initial stress matrices, whilst the second, here called the N-notation features matrices that repeat in the total potential energy, equilibrium and incremental equilibrium equations. An explicit example of the correlation is presented for a pin-jointed bar element.