Abstract: Ageing of polymers becomes more and more important. This can be seen by the increasing number of research projects dealing with this topic. However, the influence of oxygen on changes in the mechanical performance is undisputable and important with respect to the lifetime of polymer products. Therefore, a respirometer offers the potential to detect the smallest amounts of oxygen changes in the polymers’ ambient air. It will be used to analyse the oxygen consumption of rubber which is exposed for different times to elevated temperatures. In this contribution, virgin rubber samples are aged for various times in a sealed chamber at temperatures of 60, 80 and 100°C. The decline of the oxygen concentration in the ambient air is measured by flushing the chamber with dried and cleaned air which is conducted into the respirometer. The oxygen concentration is compared with that in a reference chamber, which is exposed to the same ageing conditions as the sample under investigation. The absorbed oxygen is relevant for ageing and a considerable factor for further investigations. For this reason, an experimental set-up using a differential oxygen analyser is developed, which allows for ageing several samples simultaneously in external climate chambers. The comparison of the change in the mechanical material behaviour after ageing can provide an important contribution for improving constitutive models or ongoing researches on the fatigue strength of polymers. This work shows the development of an improved method for combining mechanical testing and the measurement of oxygen consumption. PubDate: 2014-11-23

Abstract: In this paper, the energy-type terms such as the stress power, the rate of the heat transferred to the system and the rate of the specific internal energy are presented in the Lagrangian, Eulerian and two-point descriptions for thermoelastic continua. In order to solve a problem based on the energy viewpoint, the mechanical, thermal and thermo-mechanical tensors conjugate to the Seth–Hill strains, and a general class of Lagrangian, Eulerian and two-point strain tensors are determined. Also, the energy pairs for thermoelastic continua are simplified for special cases of isentropic and isothermal deformation processes as well as the so-called entropic elastic materials (rubber-like materials and elastomers). At the end, a strain energy density function of the Saint Venant–Kirchhoff type in terms of different strain measures and temperature is considered for modeling the thermo-mechanical behavior of the rubber-like materials and elastomers. It is shown that this constitutive modeling can give results which are in good agreement with the experimental data. PubDate: 2014-11-22

Abstract: We present and analyse a thermodynamical theory of rheology with single internal variable. The universality of the model is ensured as long as the mesoscopic and/or microscopic background processes satisfy the applied thermodynamical principles, which are the second law, the basic balances and the existence of an additional—tensorial—state variable. The resulting model, which we suggest to call the Kluitenberg–Verhás body, is the Poynting–Thomson–Zener body with an additional inertial element or, in other words, is the extension of Jeffreys model to solids. We argue that this Kluitenberg–Verhás body is the natural thermodynamical building block of rheology. An important feature of the presented methodology is that nontrivial inequality-type restrictions arise for the four parameters of the model. We compare these conditions and other aspects to those of other known thermodynamical approaches, like Extended Irreversible Thermodynamics or the original theory of Kluitenberg. PubDate: 2014-11-20

Abstract: SMA pseudo-elastic hysteresis with tension–compression asymmetry at finite deformation may be simulated by finite elastoplastic J
2-flow models with nonlinear combined hardening, in a direct, explicit sense with no reference to any phase variables. To this goal, a novel method of treating tension–compression asymmetry is proposed, and the hardening moduli are determined directly from any two given pairs of single-variable functions shaping non-symmetric hysteresis loops in uniaxial tension and compression so that the combined hardening model thus established can automatically exactly give rise to any given shapes of non-symmetric hysteresis loops. Numerical examples show good agreement with test data. PubDate: 2014-11-18

Abstract: We consider ionic transport by diffusion and migration through microstructured solid electrolytes. The assumed constitutive relations for the constituent phases follow from convex energy and dissipation potentials which guarantee thermodynamic consistency. The effective response is determined by homogenizing the relevant field equations via the notion ofmulti-scale convergence. The resulting homogenized response involves several effective tensors, but they all require the solution of just one standard conductivity problem over the representative volume element. A multi-scale model for semicrystalline polymer electrolytes with spherulitic morphologies is derived by applying the theory to a specific class of two-dimensional microgeometries for which the effective response can be computed exactly. An enriched model accounting for a random dispersion of filler particles with interphases is also derived. In both cases, explicit expressions for the effective material parameters are provided. The models are used to explore the effect of crystallinity and filler content on the overall response. Predictions support recent experimental observations on doped poly-ethylene-oxide systems which suggest that the anisotropic crystalline phase can actually support faster ion transport than the amorphous phase along certain directions dictated by the morphology of the polymeric chains. Predictions also support the viewpoint that ceramic fillers improve ionic conductivity and cation transport number via interphasial effects. PubDate: 2014-11-08

Abstract: This paper intends to summarize the scientific production of Angelo Luongo on the occasion of his Sixtieth Birthday, focusing on his main contributions in the field of Mechanics. The task will not be easy because of the breadth of his scientific production, only apparently attributable to a restricted number of keywords. In fact, even when the work seems purely algorithmic, speculation on the physical and mechanical aspects of the problem is always present, providing new interpretations and innovative openings to a careful reader. Similarly, also the works, which apparently seem to be high-level applications, always reserve methodological aspects that are not negligible. The editorial choice to divide his papers through a small number of keywords is certainly simplistic, but offers the possibility to better highlight all the connections among his variegated production. The most original contributions of Angelo Luongo in the context of perturbation methods, linear and nonlinear dynamics and control, elastic buckling and structural analysis, bifurcation and stability of non-conservative systems, are discussed in detail. Finally, the Angelo Luongo’s central role in the creation and development of activities of the international research center M&MoCS is pointed out. PubDate: 2014-11-05

Abstract: The nonaxisymmetric problem of natural vibrations of a hollow sphere made of functionally gradient piezoelectric material is solved based on 3D electroelasticity. The properties of the material change continuously along a radial coordinate according to an exponential law. The external surface of the sphere is free of tractions and either insulated or short-circuited by electrodes. After separation of variables and representation of the components of the displacements and of the stress tensor in terms of spherical functions, the initially three-dimensional problem is reduced to a boundary-value problem for the eigenvalues expressed by ordinary differential equations. This problem is solved by a stable discrete-orthogonalization technique in combination with a step-by-step search method with respect to the radial coordinate. Moreover, a numerical investigation is performed based on the algorithm used for solving the problem. In particular, we investigate the influence of the geometric and electric parameters on the frequency spectrum at the nonaxisymmetry of natural vibrations of an inhomogeneous piezoceramic thick-walled sphere. PubDate: 2014-11-01

Abstract: We consider a viscoelastic–viscoplastic continuum damage model for polycrystalline ice. The focus lies on the thermodynamics particularities of such a constitutive model and restrictions on the constitutive theory which are implied by the entropy principle. We use Müller’s formulation of the entropy principle, together with Liu’s method of exploiting it with the aid of Lagrange multipliers. PubDate: 2014-11-01

Abstract: We consider a constitutive model for polycrystalline ice, which contains delayed-elastic and viscous deformations, and a damage variable. The damage variable is coupled to the delayed-elastic deformation by a fiber bundle ansatz. We construct an isotropic theory, which can be calibrated with experimental data. Furthermore, we generalize the theory to a damage model in terms of rank-four tensors. This general model allows the evolution of anisotropic damage. PubDate: 2014-11-01

Abstract: Based on the Müller–Liu entropy principle and the axioms of constitutive theory, a continuum model for reacting ionic mixtures is presented. The influence of microscopic structure on the mixture dynamics is taken into account through the thermodynamics of polar materials. Moreover, mechanical balance laws for classical mixtures under influence of electromagnetic fields and quasi-electrostatic Maxwell’s equations are briefly shown. With an appropriate constitutive model for a diluted and isotropic mixture of non-volatile solutes and by considering the same temperature field for all constituents, constraints on constitutive quantities are imposed, and the conditions for the thermodynamic equilibrium are established from the entropy principle. Furthermore, the nonlinear nature of chemical reactions as well as the reciprocal nature of some irreversible processes is highlighted. Unlike the classical approach for electrolyte solutions, the current constitutive model incorporates thermoelectric and electro-kinetic phenomena into the phenomenological equations, providing a more comprehensive approach of electrolyte solutions dynamics. PubDate: 2014-11-01

Abstract: The impressive properties of shape memory alloys are produced by means of solid-to-solid phase transformations where thermal effects play an important role. In this paper, we present a model for polycrystalline shape memory alloys which takes full thermo-mechanical coupling into account. Starting from the equations of the first and the second law of thermodynamics, we derive evolution equations for the volume fractions of the different martensitic variants and a related equation for heat conduction. A thermodynamic analysis allows to formulate a complete expression for the dissipation caused by phase transformation and heat flux. This allows to model the experimentally well-documented transformation fronts in tension tests by a finite element scheme without further assumptions. Additionally, the number of required model parameters is very small in comparison with phenomenological approaches. Numerical examples are presented which show a good agreement with experimental observations. PubDate: 2014-11-01

Abstract: This paper presents an energetic framework for the study of the macroscopic evolution of shape memory alloys (SMA) with softening behavior. It is written for a class of standard rate-independent materials with an internal variable derived from the Drucker–Ilyushin work property. This one-dimensional model is defined by three material functions of the internal variable and one material parameter. The quasi-static evolution is formulated for a one-dimensional bar under traction and is based on two physical principles: a stability criterion which consists in selecting the local minima of the total energy and an energy balance condition which requires the absolute continuity of the total energy. The stability criterion aims to overcome the non-uniqueness issue associated with the intrinsic softening character of SMA while the energy balance condition accounts for evolutions even with possible time discontinuities. While being consistent with the classical Kuhn–Tucker formulation of the phase transformations, such energetic formulation proved to be more suitable than this latter for the study of stress-softening SMA. Both homogeneous and non-homogenous solutions are investigated with respect to this variational evolution problem. Specifically, we show the instability of the homogeneous states for softening materials and construct, in this latter case, a non-homogeneous stable evolution that follows a transformation stress line which corresponds to the Maxwell line of the softening intrinsic behavior. PubDate: 2014-11-01

Abstract: The lattice Boltzmann method (LBM) for simulating fluid phases was coupled with the discrete element method (DEM) for studying solid phases to formulate a novel solver for fast discrete particle simulation (DPS) of particle–fluid flows. The fluid hydrodynamics was obtained by solving LBM equations instead of solving the Navier–Stokes equation by the finite volume method (FVM). Interparticle and particle–wall collisions were determined by DEM. The new DPS solver was validated by simulating a three-dimensional gas–solid bubbling fluidized bed. The new solver was found to yield results faster than its FVM–DEM counterpart, with the increase in the domain-averaged gas volume fraction. Additionally, the scalability of the LBM–DEM DPS solver was superior to that of the FVM–DEM DPS solver in parallel computing. Thus, the LBM–DEM DPS solver is highly suitable for use in simulating dilute and large-scale particle–fluid flows. PubDate: 2014-11-01

Abstract: A new version of rate-independent generalized plasticity, suitable for the derivation of general thermomechanical constitutive laws for materials undergoing phase transformations, is proposed within a finite deformation framework. More specifically, by assuming an additive decomposition of the finite strain tensor into elastic and inelastic (transformation induced) parts and by considering the fractions of the various material phases as internal variables, a multi-phase formulation of the theory is developed. The concepts presented are applied for the derivation of a three-dimensional thermomechanical model for shape memory alloy materials. The ability of the model in simulating several patterns of the extremely complex behavior of these materials, under both monotonic and cyclic loadings, is assessed by representative numerical examples. PubDate: 2014-11-01

Abstract: A phenomenological model for the coupled thermo-electro-magneto-mechanical and phase-transformation behaviour of magnetic shape-memory alloys is advanced in small strains and eddy current approximation. The corresponding system of strongly nonlinear relations is tackled via a suitable enthalpy-like transformation. A fully implicit regularized time-discretization scheme is devised and proved to be stable and convergent. In particular, the convergence proof for discrete solutions entails that a suitably weak, energy-conserving solution to the continuous nonlinear system exists. Moreover, several particular models as e.g. ferro/paramagnetic transformation in ferromagnetic materials, martensitic transformation in shape memory allows, or just a simple thermistor problem are covered just as special cases. PubDate: 2014-11-01

Abstract: In this work, the effects of inherent variability of the geometric properties of dimer granular chains on their capacity to passively attenuate propagating pulses are investigated. Numerical studies are performed for both the nominal model and the system with uncertainty. The deterministic system is governed by a single parameter (the ratio of the radii of “heavy” and “light” beads of the dimer) and is fully rescalable with energy. The effects of uncertainty, i.e., of the spatial variability of the radii of the light (odd) beads of the granular chain, on the transmitted force at its boundary are investigated. Reliability analysis through Monte Carlo simulations and sensitivity analysis of the dimer with uncertain properties are carried out, and a deeper insight for improved bead configurations is provided. It is shown that the optimal level of force attenuation achieved with a deterministically predicted optimal parameter can be further increased when certain spatial variations in the parameter, based on specific wave number content, are introduced. PubDate: 2014-10-30

Abstract: On the example of two-phase continua experiencing stress-induced solid–fluid phase transitions, we explore the use of the Euler structure in the formulation of the governing equations. The Euler structure guarantees that solutions of the time evolution equations possessing it are compatible with mechanics and with thermodynamics. The former compatibility means that the equations are local conservation laws of the Godunov type, and the latter compatibility means that the entropy does not decrease during the time evolution. In numerical illustrations, in which the one-dimensional Riemann problem is explored, we require that the Euler structure is also preserved in the discretization. PubDate: 2014-10-12

Abstract: Exact solutions of elastic Kirchhoff plates are available only for special geometries, loadings and kinematic boundary constraints. An effective solution procedure, based on an analogy between functionally graded orthotropic Saint-Venant beams under torsion and inhomogeneous isotropic Kirchhoff plates, with no kinematic boundary constraints, is proposed. The result extends the one contributed in Barretta (Acta Mech 224(12):2955–2964, 2013) for the special case of homogeneous Saint-Venant beams under torsion. Closed-form solutions for displacement, bending–twisting moment and curvature fields of an elliptic plate, corresponding to a functionally graded orthotropic beam, are evaluated. A new benchmark for computational mechanics is thus provided. PubDate: 2014-10-04