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In order to understand how hardening of the binder phase in particulate reinforced metal matrix composites (PRMMC) influences the effective strength, we present in this work a numerical framework consisting of the direct method (DM) and statistical models. Using this approach we created a large number of statistically equivalent representative volume element (SERVE) models to represent an exemplary PRMMC material WC-20 Wt.% Co and predicted its effective strengths using DM. After the global strength was calculated from each SERVE sample all derived data are interpreted by Bayesian network and diagnostic testing. By doing so the relationship between material strength and few selected characteristics have been clarified. The study shows the formulated approach as a novel means for investigating how the overall mechanical properties of random heterogeneous materials react to a certain constituent. Meanwhile, the study also demonstrates how statistical models, in particular the Bayesian network, can be used as a powerful supplement to micromechanical models for result analysis and knowledge discovery.

In this paper, a numerical technique is presented for evaluating the influence of particle size in particulate reinforced metal matrix composites (PRMMCs) on two critical material parameters, namely, the ultimate strength and endurance limit. To demonstrate this technique a representative PRMMC material, tungsten carbide–cobalt hard metal (WC–Co), was selected. As a typical random heterogeneous material, WC–Co demonstrates a noteworthy randomness in its composite structure. In order to take this characteristic into consideration, a novel numerical approach is adopted in this work, which is a conjunction between so-called direct methods (DMs) and statistical analyses. As the approach requires a large number of samples to be evaluated, numerical efficiency in solving optimization problems resulted from DM is a critical issue. For the purpose of comparison with the lower bound formulation, a numerical scheme formulated from the upper bound method is selected in this work. Overall, the study clarifies how the material strength of WC–Co with a fixed binder content is influenced by the reinforcement WC particle size and shows how the proposed approach can be used as a viable means for investigating the relationship between properties and structural characteristics of PRMMC materials.

This paper introduces a numerically-based methodology for determining the load-bearing capacity of particulate reinforced metal matrix composites (PRMMC) under both monotonic and cyclic loading. A multi-scale approach combining shakedown analysis with homogenization was used to evaluate the influence exerted by the composite structure on the global behavior of PRMMCs. The results were interpreted using statistical methods in order to take account of the randomness associated with the composite structure of the material. The general work flow of the approach can be summarized as follows: first, a large number of representative volume elements (PRMMC) were constructed from real material images using an in-house code. Next, lower bound limit and shakedown problems were solved via the interior-point method. Finally, results were converted to their corresponding macro quantities and evaluated statistically. With this approach we investigated a representative PRMMC structure, WC/Co, with two different binder contents and scrutinized the contribution of the composite structure over composite strength.

A numerical approach is presented to determine the load bearing capacity of structural elements made of heterogeneous materials subjected to variable loads. Melan’s lower-bound shakedown theorem is applied to representative volume elements. Combined with the homogenization technique, the material effective properties are determined through transformation from the mesoscopic to macroscopic admissible loading domains. For the numerical applications, finite element method and large-scale nonlinear optimization, based on an interior-point-algorithm, are used. The methodology is illustrated by the application to regular and random heterogeneous materials. This way, the proposed method provides a direct numerical approach to evaluate the macroscopic strength of heterogeneous structures as a useful tool for the design of structures.

Particulate reinforced metal matrix composites (PRMMCs) are typical random heterogeneous materials whose global behavior depends on the microstructural characterisics. Recently a numerical approach was developed (Hachemi et al., Int J Plast 63:124–137, 2014 [1], Chen et al. Direct methods for limit and shakedown analysis of structures, 2015 [2]), by applying it to a typical PRMMC material WC/Co, we presented how the ultimate strength and endurance limit can be predicted from the material microstructures. Due to the randomness in the microstructures of PRMMCs, size of the representative volume element (RVE) has a nontrivial influence over the predicted effective behaviors. In order to understand how size of RVEs contribute to the result and based on that to eliminate its influence, a numerical investigation is performed in the present study. In this study, a large number of representative volume element (RVE) samples representing a representative PRMMC material, WC-20 Wt% Co, were built from artificial microstructures. The samples are obviously different in size, and by deploying the established numerical approach to these samples, ultimate strength and endurance limit were calculated. Afterwards, the derived material strengths were analyzed by multiple inferential statistical models. The statistical study reveals how strength and other effective material properties react to the change of the RVE size. On that basis, the study proposed a feasible and computationally inexpensive solution to minimize the size effect.

The load-bearing capacity of cylindrical pressure vessels closed by Klopperboden torispherical drumheads with piping nozzle connections placed in the head's knuckle region is determined by using shakedown analysis. The pressure vessels under consideration are subjected to internal pressure, an axial force in the direction of the nozzle, in-plane bending moment at the nozzle, and temperature loading, all of which may vary independently. In particular, the interactions are investigated in several combinations of two and three of these loads, leading to two- and three-dimensional loading domains. The corresponding elastic and shakedown limits are computed based on Melan's statical shakedown theorem. The obtained results are compared to those taken from literature where available.

Propagation of nonlinear strain waves through a layered composite material is considered. The governing macroscopic wave equation for the long-wave case was obtained earlier by the higher-order asymptotic homogenization method (Andrianov et al., 2013). Non-stationary dynamic processes are investigated by a pseudo-spectral numerical procedure. The time integration is performed by the Runge–Kutta method; the approximation with respect to the spatial co-ordinate is provided by the Fourier series expansion. The convergence of the Fourier series is substantially improved and the Gibbs–Wilbraham phenomenon is reduced with the help of Pade approximants. As result, we explore how fast and under what conditions the solitary strain waves can be generated from an initial excitation. The numerical and analytical solutions (when the latter can be obtained) are in good agreement.

Predicting strengths and understanding how these values related to the underlying composite structure is essential for the design and application of particulate reinforced metal matrix composites (PRMMCs). In order to investigate how ultimate strength and endurance limit of an exemplary PRMMC material, WC-20 wt% Co, are related to other structural and mechanical characteristics, an integrated numerical approach consisting of direct methods (DM) and artificial neural network (ANN) is presented in this work. Using few features obtained from elastic and DM analyses as inputs, multiple regression and classification ANNs were established to predict global material strengths. With this approach, the study implied that the distribution pattern of the stress field, in particular the one pertained to the binder phase, has a nontrivial influence over global composite strengths.

Lower-bound shakedown analysis leads to nonlinear convex optimization problems with large numbers of unknowns and constraints, the solution of which can be obtained efficiently by interior-point algorithms. The performance of these algorithms strongly depends on the choice of the starting point. In general, starting points should be located inside the feasible region. In addition, they should also be well centred. Although there exist several heuristics for the construction of suitable starting points, these are restricted, as long as only the mathematical procedure is considered without taking into account the nature of the underlying mechanical problem. Thus, in this article, a strategy is proposed for choosing appropriate starting points for interior-point algorithms applied to shakedown analysis. This strategy is based on both the mathematical characteristics and the physical meaning of the variables involved. The efficiency of the new method is illustrated by numerical examples from the field of powe...

SUMMARY Determining the load-bearing capacity of engineering structures is essential for their design. In the case of varying thermo-mechanical loading beyond the elastic limit, the statical shakedown analysis constitutes a particularly suitable tool for this. The application of the statical shakedown theorem, however, leads to a nonlinear convex optimization problem, which is typically characterized by large numbers of variables and constraints. In the present work, this optimization problem is solved by a primal–dual interior-point algorithm, which shows a remarkable performance due to its problem-tailored formulation. Nevertheless, the solution procedure remains still a demanding task from computational point of view. Thus, the aim of this paper is to tackle the task of solving large-scale problems by use of a new so-called selective algorithm. This algorithm detects automatically the plastically most affected zones within the structure, which have the highest influence on the solution. The entire system is then reduced to a substructure consisting of these zones, based upon which a new optimization problem can be set up, which is solved with significantly less effort. Consequently, the running time decreases drastically, as is shown by application to numerical examples from the field of power plant engineering. Copyright © 2013 John Wiley & Sons, Ltd.

Wave propagation in nonlinear elastic media with microstructure is studied. As an illustrative example, a 1D model of a layered composite material is considered. Geometrical nonlinearity is described by the Cauchy–Green strain tensor. For predicting physical nonlinearity the expression of the energy of deformation as a series expansion in powers of the strains is used. The effective wave equation is derived by the higher-order asymptotic homogenization method. An asymptotic solution of the nonlinear cell problem is obtained using series expansions in powers of the gradients of displacements. Analytical expressions for the effective moduli are presented. The balance between nonlinearity and dispersion results in formation of stationary nonlinear waves that are described explicitly in terms of elliptic functions. In the case of weak nonlinearity, an asymptotic solution is developed. A number of nonlinear phenomena are detected, such as generation of higher-order modes and localization. Numerical results are presented and practical significance of the nonlinear effects is discussed.

This paper is devoted to the numerical analysis of the various continuum models of a 1D discrete media. Namely, we consider intermediate, quasi-continuum, and improved quasi-continuum models. The analysis of various receptions of continualization in a linear case is carried out. For this purpose, we consider the solution in the form of a traveling wave caused by the initial perturbation. The solution is obtained by Fourier transformation inverted numerically. Then we compare solutions of discrete and continuum models for wave velocity. Numerical calculations show that all the above described nonlocal theories qualitatively equally well describe the propagation of waves in a discrete media. The disadvantage of intermediate continuum model is the high order of differential equation. For finite chain this leads to the need for the formulation of boundary conditions that do not follow naturally from the source of the problem. The quasi-continuum approximation yields results practically identical with those obtained on the basis of improved quasi-continuum approximation. The most accurate approximation of a discrete medium gives improved quasi-continuum approximation. The advantage of improved quasi-continuum approximation is manifested in those cases where you need to describe the high modes of oscillation of the discrete finite chain.

We present a numerical method for the computation of shakedown loads of engineering structures with limited kinematical hardening under thermo-mechanical loading. The method is based on Melan’s statical shakedown theorem, which results in a nonlinear convex optimization problem. This is solved by an interior-point algorithm recently developed by the authors, specially designed for lower bound shakedown analysis of large-scale problems. Limited kinematical hardening is taken into account by use of a two-surface model, such that both alternating plasticity and incremental collapse can be captured. For the yield surface as well as for the bounding surface the von Mises criterion is used. The proposed method is validated by two examples, where numerical results are compared to those of literature where available.

A finite element model of gradient-enhanced damage viscoplasticity for dynamic analysis of thin-walled shell structures is proposed. To take void nucleation and growth into account, the free-energy function is enhanced by introducing a non-local damage term, which is defined in terms of a new non-local variable and a local damage parameter. Local constitutive laws considering viscoplastic behavior, isotropic hardening and isotropic ductile damage leading to softening are used. The performance of the proposed model is demonstrated through numerical simulations of several examples including shock-wave loaded plates.

A numerical method for the computation of shakedown loads of structures subjected to varying thermal and mechanical loading is proposed for the case of multidimensional loading spaces. The shakedown loading factors are determined based on the lower bound direct method using the von Mises yield criterion. The resulting nonlinear convex optimization problem is solved by use of the interior-point method. Although the underlying theory allows for the consideration of arbitrary numbers of loadings in principle, until now applications have been restricted to special cases, where either one or two loads vary independently. In this article, former formulations of the optimization problem are generalized for the case of arbitrary numbers of loadings. The method is implemented into an interior-point algorithm specially designed for this method. For illustration, numerical results are presented for a three-dimensional loading space applied to a square plate with a central circular hole.

We propose a numerical method for the computation of shakedown loads of engineering structures subjected to varying thermo-mechanical loading. The method is based on Melan’s lower bound shakedown theorem using the von Mises yield criterion. The resulting nonlinear convex optimization problem is presented in a generalized formulation and then solved by an interior-point algorithm, which is characterized by a problem-tailored solution strategy, particularly suitable for application to large-scale engineering structures. Theoretical and numerical issues of the algorithm are described. It’s efficiency is shown by application to thermo-mechanical problems from power plant engineering. The results are compared to those found in literature as well as to calculations with other optimization codes lancelot , ipopt and ipdca .

Here, we study a relation between discrete and continuum models on an example of the sine-Gordon and Φ4 equations. The analysis of various receptions of continualization in a linear case is carried out. The best approach allowing describing all spectrum of the discrete one-dimensional medium is chosen. Also, the nonlinear discrete sine-Gordon and Φ4 models are analyzed. The possibility of improvement of the known continuum approximations of these equations is shown.

In this paper we study wave propagation through a composite material built up of a periodically repeated one-dimensional structure of coated inclusions and matrix material by the application of the asymptotic homogenization method. We take into account geometrical nonlinearity, which is described by the Cauchy-Green strain tensor and physical nonlinearity by the Murnaghan elastic potential. We take into account structural nonlinearity by considering the bonding between two materials to be imperfect. As a result we obtain homogenized equations for the low-frequency range.

The present paper provides details on the application of asymptotic homogenization techniques to the analysis of viscoelastic-matrix fibrous composites with square-lattice reinforcement and their effective properties. The correspondence principle allows transformation of the governing boundary value problems to quasi-static ones. Thereafter, the homogenization procedure is used. To solve the cell problem, modified boundary shape perturbation procedure is proposed. The resulting Laplace transforms are inverted by the effective and accurate Gaver algorithm. The proposed approach, however, yields a computationally intense solution.

Imperfect bonding between the constitutive components can greatly affect the properties of the composite structures. An asymptotic analysis of different types of imperfect interfaces arising in the problem of 2D fibrereinforced composite materials are proposed. The performed study is based on the asymptotic reduction of the governing biharmonic problem into two harmonic problems. All solutions are obtained in a closed analytical form. The obtained results can be used for the calculation of pull-out and pushout tests, as well as for the investigation of the fracture of composite materials.

A novel asymptotic approach to the problem of laminated fibrous composites with free edges is proposed in this article. Commonly, this type of composites is modeled on the assumption of homogenized individual plies. In the presence of free edges, the elastic fields in the individual plies need additional investigation. Our approach is based on the asymptotic splitting of the governing biharmonic problem into two harmonic problems. All solutions are obtained in the closed analytical form. In particular, the obtained results can be used in the analysis of fracture of composite materials as well as for the analytical modeling of the pull-out and push-out tests.

The paper focuses on the development of 2D continuous models for a theoretical prediction of dynamic properties of discrete microstructures. A new continualization procedure, which refers to nonlocal interactions between variables of the discrete media, is proposed and the corresponding continuous model is obtained. The performed study is based on the application of composite equations. The developed approach is suitable for the dynamic analysis of 2D lattices of micro- and nanoparticles oscillating with arbitrary frequencies.

Based on the static theory of strain-gradient viscoplasticity proposed by Anand et al. (2005) , a one-dimensional dynamic analysis is derived for finite element computation of isotropic hardening materials. The kinetic energy is assumed to be composed of the conventional and internal kinetic energy. The internal energy is described phenomenologically in terms of the equivalent plastic strain in order to capture the heterogeneity of plastic flow. Herein the microscopic density is assumed to be related to the macroscopic one through a microscopic-inertia parameter. The macroscopic-force balance and microscopic-force balance including inertia effects are derived. The performance of the proposed formulation is illustrated through the numerical simulation of a one-dimensional dynamic problem. A parameter study to find the microscopic-inertia parameter is carried out. At last, suitable microscopic boundary conditions and dynamic effects are discussed through comparison with the conventional plasticity.

Many studies in the theory of composite materials are based on the homogenization approach, which consists of the substitution of the original heterogeneous medium by a homogeneous one with certain effective properties. Though this procedure works well for the entire composite solid, it cannot be applied in the vicinity of the outer boundary. The transmission of an external load applied at the boundary to the inner domain of the material occurs by a redistribution of stresses between the constitutive components (inclusions and matrix) and involves strong singularities in the local stress field, which may result in microscopic failure of the composite structure. In the present paper, we propose an approximate analytical procedure, allowing determination of the stress–strain field in the vicinity of the outer boundaries of fibre-reinforced composite materials. It is also shown that controlled decrease in bonding between the components leads to a more uniform redistribution of local stresses, which can essentially reduce the risk of failure.

Imperfect bonding between the constitutive components can greatly affect the properties of composite structures. We propose an asymptotic analysis of different types of imperfect interfaces arising in the problem of conduction through a simple cubic array of spherical inclusions. The performed study is based on the two-scale asymptotic homogenization method. The microscopic problem on the unit cell is solved using the underlying principles of the boundary-shape perturbation technique. The influence of the interface properties on the effective conductivity and on the local potential and flux fields is studied.

Based on the lower-bound direct methods, namely limit and shakedown analysis, it is shown in this paper how these methods can be used in a constructive manner for structural industrial design. The proposed methods are based on finite element analyses and numerical optimization to determine the admissible loading. Numerical applications are presented and compared with existing results in literatures.

An asymptotic approach is proposed to describe the load-transfer from a periodical system of fibres to a transversally isotropic elastic layer. To start with we simplified the input boundary value problem by using ratios of the elastic constants as small parameters. The interactions between neighbouring fibres are predicted using the composite cylinder assemblage model. The simplified boundary value problem is solved using finite integral transforms. The inverse transforms are expressed through the elementary and special functions. We also analysed the interface between the fibres and the matrix. The obtained results can be used for the investigation of the fracture of composites. In Civil Engineering, the proposed solution can describe the behaviour of piles or piers embedded in soil media that exhibit linear elastic response in the working-load range.

In A fibre-reinforced 2D composite material with elastic fibres and viscoelastic, isotropic matrix is studied. Starting from the solution of a reference-problem with elastic matrix material the elastic matrix parameters are substituted by their viscoelastic correspondents in the Laplace domain. For simplification the time-dependent solution is approximated by using limiting value theorems that give information about the time-dependent solution for t → 0 and t → ∞. Then the method of asymptotically equivalent functions is used and illustrated with examples of a steel fibre in a PMMA matrix. The analytical solutions are compared with their numerical counterparts. In summary it can be stated that this paper is a further contribution to the vast literature about the application of the correspondence principle to the solution of special problems of the linear viscoelasticity.

SUMMARY Based on the lower-bound shakedown theorem by Melan, a method to analyse pavements under cyclic, in particular, rolling contact loading is presented. Repeated sliding/rolling line contact as well as repeated stationary contact is considered. The material is assumed to be rate-independent elastic–plastic. As yield conditions, the rounded Mohr–Coulomb and von Mises yield criteria are used, assuming associated flow rules. The proposed numerical method is based on finite elements, and the inherent optimization problem to determine the shakedown factors is solved using the interior-point method. Several numerical results are presented and compared with the existing results in literatures. Copyright q 2008 John Wiley & Sons, Ltd.

Cold drawing of bimetallic wires is an efficient technology for fabrication of filamentary composite materials. In the present paper an analytical approach to the plastic flow of a two-component mono-filamentary wire through a converging conical die is proposed. Developed solution is based on a number of simplified assumptions concerning the radial flow pattern, the perfectly plastic materials’ behavior, and the perfect bonding conditions between the components. The stress and the strain-rate fields are determined. Obtained results for the drawing stress show a good agreement with available experimental data. Examination of the interfacial stresses localized at the boundary between the components allows to identify the range of the input parameters in which the pure radial flow can exist.

Improved bounds for effective transport properties of a random non-percolated composite with cylindrical fibres are developed by means of the security-spheres approach. The key point of the method is to obtain a solution for a regular composite that can be valid for all values of the volume fractions and properties of the components. For this aim we use the asymptotic homogenization method; a cell problem is solved by a modified version of the boundary shape perturbation technique.

The phenomenon of the load diffusion from a fibre to a surrounding matrix is analysed for the 2D case. We use an approximate analytical approach based on the asymptotic reduction of the governing biharmonic problem into two harmonic problems. The comparison of the obtained solutions with known results of other authors shows an acceptable accuracy of the proposed asymptotic simplifications. All solutions are obtained in closed analytical form. The case of perfect bonding between fibre and matrix for a single fibre and for a periodic system of fibres is firstly considered. Then we study the influence of the interface stiffness. In the case when only a single fibre is loaded, the influence of all other fibres is predicted by means of a three-phase model. The proposed approach gives a possibility to solve the problems for a broken fibre and for a broken matrix, as well as for partly debonded fibres. The important problem of infinite matrix cracks is also solved in the present paper. The obtained results can be used for the calculation of pull-out and push-out tests, as well as for the investigation of the fracture of composite materials.

We present an application of the higher order asymptotic homogenization method (AHM) to the study of wave dispersion in periodic composite materials. When the wavelength of a travelling signal becomes comparable with the size of heterogeneities, successive reflections and refractions of the waves at the component interfaces lead to the formation of a complicated sequence of the pass and stop frequency bands. Application of the AHM provides a long-wave approximation valid in the low-frequency range. Solution for the high frequencies is obtained on the basis of the Floquet–Bloch approach by expanding spatially varying properties of a composite medium in a Fourier series and representing unknown displacement fields by infinite plane-wave expansions. Steady-state elastic longitudinal waves in a composite rod (one-dimensional problem allowing the exact analytical solution) and transverse anti-plane shear waves in a fibre-reinforced composite with a square lattice of cylindrical inclusions (two-dimensional problem) are considered. The dispersion curves are obtained, the pass and stop frequency bands are identified.

The method of matched asymptotic expansions is applied to construct an asymptotic model for the Eshelby inhomogeneity problem in the case of a slender sufficiently rigid inhomogeneity. On the basis of the obtained asymptotic model, it is shown that the only infinitesimal perturbations of the elongated ellipsoid that preserve constancy of stresses inside the inhomogeneity are those into another elongated ellipsoid.

An asymptotic approach for simulation of the imperfect interfacial bonding in composite materials is proposed. We introduce between the matrix and inclusions a flexible bond layer of a volume fraction c(3) and of a non-dimensional rigidity λ(3), derive a solution for such three-component structure, and then set c(3)→0, λ(3)→0. In the asymptotic limit depending on the ratio λ(3)/c(3) different degrees of the interface's response can be simulated. A problem of the axial shear of elastic fibre-reinforced composites with square and hexagonal arrays of cylindrical inclusions is considered. The performed analysis is based on the asymptotic homogenization method, the cell problem is solved using the underlying principles of the boundary shape perturbation technique. As a result, we obtain approximate analytical solutions for the effective shear modulus and for the stress field on micro level depending on the degree of the interfacial debonding. Developed solutions are valid for all values of the components’ volume fractions and properties. In particular, they work well in cases of rapid oscillations of local stresses (e.g., in the case of densely packed perfectly rigid inclusions), while many of other commonly used methods may face computational difficulties.

The paper reports on recent progress in numerical shakedown and limit analysis based on Melan's lower bound shakedown theorem. After explaining the theoretical foundations of their approach, the authors describe in detail the numerical scheme, in particular the underlying optimization via interior point methods. Numerous examples mostly related to pressure vessel technology are presented, illustrating the potential of the method.

Shakedown analysis is currently implemented by the coupling of finite element methods with techniques of computational optimization. Engineering structures problems contain a large number of variables and constraints, leading to large-scale nonlinear programming problems, since, usually, nonlinear yield criteria are preferred. The respective algorithms use iterative techniques to solve the problem at hand and the selection of a starting point is of crucial importance for their performance. To this goal the elastic limit solution could be applied, which yields a feasible point, since the zero residual stress identically satisfies the null space conditions. The present study proposes a mechanically motivated, simple technique to obtain an initial feasible point with nonzero residual stresses starting from the plastic shakedown analysis. The residual stresses obtained by this problem are generally infeasible and they are projected into the null space of the equilibrium conditions in order to yield a feasible set of self-equilibrating nonzero stresses. Next, this feasible point is completed by a safety factor, obtained from a one-dimensional optimization problem of elastic limit type. The applicability and appropriateness of this approach is studied by numerical comparisons.

In this paper we present a numerical methodology to determine the load bearing capacity of a random heterogeneous material. It is applied to a particulate reinforced metal matrix composite (PRMMC), WC-30 Wt.% Co, to predict its strength against both monotonic and cyclic loads. In this approach, limit and shakedown analysis based on Melan’s static theorem [30] is performed on representative volume element (RVE) models generated from real material microstructure and the obtained results are converted to macroscopic load domains through homogenization. To evaluate microstructure’s impact on the overall material strength, the relationship between strength and composite structure is investigated by means of statistics. Meanwhile, several numerical issues, e.g. the impact of RVE’s size, mesh density, as well as the discrepancy between 2D and 3D models, are studied.

This paper reports on recent developments in the field of direct methods, in particular shakedown analysis (SA) from theoretical and numerical points of view. Emphasis is placed on problems connected with the failure of fibre-reinforced periodic composites under variable loads where special attention is paid to the problem of interface debonding between fibre and matrix materials. The approach is based on a local SA in a representative volume element of the composite and the use of averaging techniques to study the influence of each component (matrix, fibre and interface) on the macroscopic response of such composite. For numerical applications, the interior-point difference-of-convex-functions algorithm (IPDCA) is proposed as an efficient method for solving large-scale problems.

The thermo-mechanical behaviour of a fluid-filled metal foam is influenced by the characteristics of the solid skeleton and the pore-fluid. During the deformation process both constituents exchange momentum and energy. Based on the theory of porous media a fluid-filled foam is modeled as a binary mixture consisting of a metal skeleton and a pore-gas. The porous solid skeleton is assumed to behave thermo-elasto-plastically. The pore-gas is considered as an ideal gas. For both constituents different phase temperatures and thermo-mechanical coupling mechanisms are taken into account. The resulting system of differential equations is solved using the finite element method. An example demonstrates the applicability and validity of this approach.

In this paper, the theoretical background for the failure analysis of fibre-reinforced composites under variable repeated loads in the framework of direct methods is presented. It is based on a local shakedown analysis in a representative volume element of the composite and the use of averaging techniques to study the influence of each component (matrix, fibre and interface) on the macroscopic response of such composite.

An experimental study of hot spots occurrence in railway disc brakes is reported on. The aim of this study was to better classify and to explain the thermal gradients appearance on the surface of the disc. Thermographic measurements with an infrared camera have been carried out on the rubbing surface of brake discs on a full-scale test bench. Based on thermography, a classification of hot spots observed in disc brakes is proposed. A detailed investigation of the most damaging thermal gradients, called macroscopic hot spots (MHS) is given. From these experimental researches, a scenario of hot spots occurrence is suggested step by step. Influence of parameter such as pad stiffness and pad contact length on hot spots developments is studied. Observations give new highlights on the conditions of hot spots appearance. Discussion of the theoretical approaches compared to experimental observations is proposed.