Abstract: Abstract
We present a phenomenological thermodynamic framework for continuum systems exhibiting responses which may be nonlocal in space and for which short time scales may be important. Nonlocality in space is engendered by state variables of gradient type, while nonlocalities over time can be modelled, e.g. by assuming the rate of the heat flux vector to enter into the heat conduction law. The central idea is to restate the energy budget of the system by postulating further balance laws of energy, besides the classical one. This allows for the proposed theory to deal with nonequilibrium state variables, which are excluded by the second law in conventional thermodynamics. The main features of our approach are explained by discussing micropolar indeterminate couple stress elasticity and heat conduction theories. PubDate: 2014-12-17

Abstract: Abstract
A model of a mixture of bone tissue and bioresorbable material with voids was used to numerically analyze the physiological balance between the processes of bone growth and resorption and artificial material resorption in a plate-like sample. The adopted model was derived from a theory for the behavior of porous solids in which the matrix material is linearly elastic and the interstices are void of material. The specimen—constituted by a region of bone living tissue and one of bioresorbable material—was acted by different in-plane loading conditions, namely pure bending and shear. Ranges of load magnitudes were identified within which physiological states become possible. Furthermore, the consequences of applying different loading conditions are examined at the end of the remodeling process. In particular, maximum value of bone and material mass densities, and extensions of the zones where bone is reconstructed were identified and compared in the two different load conditions. From the practical view point, during surgery planning and later rehabilitation, some choice of the following parameters is given: porosity of the graft, material characteristics of the graft, and adjustment of initial mixture tissue/bioresorbable material and later, during healing and remodeling, optimal loading conditions. PubDate: 2014-12-11

Abstract: Abstract
We discuss a pure hyperbolic alternative to the Navier–Stokes equations, which are of parabolic type. As a result of the substitution of the concept of the viscosity coefficient by a microphysics-based temporal characteristic, particle settled life (PSL) time, it becomes possible to formulate a model for viscous fluids in a form of first-order hyperbolic partial differential equations. Moreover, the concept of PSL time allows the use of the same model for flows of viscous fluids (Newtonian or non-Newtonian) as well as irreversible deformation of solids. In the theory presented, a continuum is interpreted as a system of material particles connected by bonds; the internal resistance to flow is interpreted as elastic stretching of the particle bonds; and a flow is a result of bond destructions and rearrangements of particles. Finally, we examine the model for simple shear flows, arbitrary incompressible and compressible flows of Newtonian fluids and demonstrate that Newton’s viscous law can be obtained in the framework of the developed hyperbolic theory as a steady-state limit. A basic relation between the viscosity coefficient, PSL time, and the shear sound velocity is also obtained. PubDate: 2014-12-11

Abstract: Abstract
This is part II of this series of papers. The aim of the current paper was to solve the governing PDE system derived in part I numerically, such that the procedure of variant reorientation in a magnetic shape memory alloy (MSMA) sample can be simulated. The sample to be considered in this paper has a 3D cuboid shape and is subject to typical magnetic and mechanical loading conditions. To investigate the demagnetization effect on the sample’s response, the surrounding space of the sample is taken into account. By considering the different properties of the independent variables, an iterative numerical algorithm is proposed to solve the governing system. The related mathematical formulas and some techniques facilitating the numerical calculations are introduced. Based on the results of numerical simulations, the distributions of some important physical quantities (e.g., magnetization, demagnetization field, and mechanical stress) in the sample can be determined. Furthermore, the properties of configurational force on the twin interfaces are investigated. By virtue of the twin interface movement criteria derived in part I, the whole procedure of magnetic field- or stress-induced variant reorientations in the MSMA sample can be properly simulated. PubDate: 2014-12-11

Abstract: Abstract
The employment of different mathematical models to address specifically for the bubble nucleation rates of water vapour and dissolved air molecules is essential as the physics for them to form bubble nuclei is different. The available methods to calculate bubble nucleation rate in binary mixture such as density functional theory are complicated to be coupled along with computational fluid dynamics (CFD) approach. In addition, effect of dissolved gas concentration was neglected in most study for the prediction of bubble nucleation rates. The most probable bubble nucleation rate for the water vapour and dissolved air mixture in a 2D quasi-stable flow across a cavitating nozzle in current work was estimated via the statistical mean of all possible bubble nucleation rates of the mixture (different mole fractions of water vapour and dissolved air) and the corresponding number of molecules in critical cluster. Theoretically, the bubble nucleation rate is greatly dependent on components’ mole fraction in a critical cluster. Hence, the dissolved gas concentration effect was included in current work. Besides, the possible bubble nucleation rates were predicted based on the calculated number of molecules required to form a critical cluster. The estimation of components’ mole fraction in critical cluster for water vapour and dissolved air mixture was obtained by coupling the enhanced classical nucleation theory and CFD approach. In addition, the distribution of bubble nuclei of water vapour and dissolved air mixture could be predicted via the utilisation of population balance model. PubDate: 2014-12-11

Abstract: Abstract
The theory of linear micropolar elasticity is used in conjunction with a new representation of micropolar surface mechanics to develop a comprehensive model for the deformations of a linearly micropolar elastic solid subjected to anti-plane shear loading. The proposed model represents the surface effect as a thin micropolar film of separate elasticity, perfectly bonded to the bulk. This model captures not only the micro-mechanical behavior of the bulk which is known to be considerable in many real materials but also the contribution of the surface effect which has been experimentally well observed for bodies with significant size-dependency and large surface area to volume ratios. The contribution of the surface mechanics to the ensuing boundary-value problem gives rise to a highly nonstandard boundary condition not accommodated by classical studies in this area. Nevertheless, the corresponding interior and exterior mixed boundary-value problems are formulated and reduced to systems of singular integro-differential equations using a representation of solutions in the form of modified single-layer potentials. Analysis of these systems demonstrates that the classical Noether theorems reduce to Fredholms theorems leading to results on well-posedness of the corresponding mathematical model. PubDate: 2014-12-10

Abstract: Abstract
Today it is well known that the classical Cauchy continuum theory is insufficient to describe the deformation behavior of solids if gradients occur over distances which are comparable to the microstructure of the material. This becomes crucial e.g., for small specimens or during localization of deformation induced by material degradation (damage). Higher-order continuum approaches like micromorphic theories are established to address such problems. However, such theories require the formulation of respective constitutive laws, which account for the microstructural interactions. Especially in damage mechanics such laws are mostly formulated in a purely heuristic way, which leads to physical and numerical problems. In the present contribution, the fully micromorphic constitutive law for a porous medium is obtained in closed form by homogenization based on the minimal boundary conditions concept. It is shown that this model describes size effects of porous media like foams adequately. The model is extended toward quasi-brittle damage overcoming the physical and numerical limitations of purely heuristic approaches. PubDate: 2014-12-06

Abstract: Abstract
Following a suggestion by Forest and Sievert (Acta Mech 160:71–111, 2003), a constitutive frame for a general gradient elastoplasticity for finite deformations is established. The basic assumptions are the principle of Euclidean invariance and the isomorphy of the elastic ranges. Both the elastic and the plastic laws include the first and the second deformation gradient. The starting point is an objective expression for the stress power. PubDate: 2014-11-27

Abstract: Abstract
This paper presents ordered rate constitutive theories of orders m and n, i.e., (m, n) for finite deformation of homogeneous, isotropic, compressible and incompressible thermoviscoelastic solids with memory in Lagrangian description using entropy inequality in Gibbs potential Ψ as an alternate approach of deriving constitutive theories using entropy inequality in terms of Helmholtz free energy density Φ. Second Piola-Kirchhoff stress σ
[0] and Green’s strain tensor ε
[0] are used as conjugate pair. We consider Ψ, heat vector q, entropy density η and rates of upto orders m and n of σ
[0] and ε
[0], i.e., σ
[i]; i = 0, 1, . . . , m and ε
[j]; j = 0, 1, . . . , n. We choose Ψ, ε
[n], q and η as dependent variables in the constitutive theories with ε
[j]; j = 0, 1, . . . , n − 1, σ
[i]; i = 0, 1, . . . , m, temperature gradient g and temperature θ as their argument tensors. Rationale for this choice is explained in the paper. Entropy inequality, decomposition of σ
[0] into equilibrium and deviatoric stresses, the conditions resulting from entropy inequality and the theory of generators and invariants are used in the derivations of ordered rate constitutive theories of orders m and n in stress and strain tensors. Constitutive theories for the heat vector q (of up to orders m and n − 1) that are consistent (in terms of the argument tensors) with the constitutive theories for ε
[n] (of up to orders m and n) are also derived. Many simplified forms of the rate theories of orders (m, n) are presented. Material coefficients are derived by considering Taylor series expansions of the coefficients in the linear combinations representing ε
[n] and q using the combined generators of the argument tensors about a known configuration
\({{\underline{\varOmega}}}\)
in the combined invariants of the argument tensors and temperature. It is shown that the rate constitutive theories of order one (m = 1, n = 1) when further simplified result in constitutive theories that resemble currently used theories but are in fact different. The solid continua characterized by these theories have mechanisms of elasticity, dissipation and memory, i.e., relaxation behavior or rheology. Fourier heat conduction law is shown to be an over simplified case of the rate theory of order one (m = 1, n = 1) for q. The paper establishes when there is equivalence between the constitutive theories derived here using Ψ and those presented in reference Surana et al. (Acta Mech. doi:10.1007/s00707-014-1173-6, 2014) that are derived using Helmholtz free energy density Φ. The fundamental differences between the two constitutive theories in terms of physics and their explicit forms using Φ and Ψ are difficult to distinguish from the ordered theories of orders (m, n) due to complexity of expressions. However, by choosing lower ordered theorie... PubDate: 2014-11-25

Abstract: 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: 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: 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: 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: 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: 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: 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: 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: 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: 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