Abstract: Abstract
This paper examines the indentation of an elastic body by a rigid spherical inclusion. In contrast to conventional treatments where the contact between a rigid inclusion and the elastic medium is regarded as being perfectly bonded, we examine the influence of non-classical interface conditions including frictionless bilateral contact, separation and Coulomb friction on the load–displacement behaviour of the spherical rigid inclusion. Both analytical methods and boundary element techniques are used to examine the inclusion/elastic medium interaction problems. This paper also provides a comprehensive review of non-classical interface conditions between inclusions and the surrounding elastic media. PubDate: 2015-11-25

Abstract: Abstract
Phonon cross-plane transport across silicon and diamond thin films pair is considered, and thermal boundary resistance across the films pair interface is examined incorporating the cut-off mismatch and diffusive mismatch models. In the cut-off mismatch model, phonon frequency mismatch for each acoustic branch is incorporated across the interface of the silicon and diamond films pair in line with the dispersion relations of both films. The frequency-dependent and transient solution of the Boltzmann transport equation is presented, and the equilibrium phonon intensity ratios at the silicon and diamond film edges are predicted across the interface for each phonon acoustic branch. Temperature disturbance across the edges of the films pair is incorporated to assess the phonon transport characteristics due to cut-off and diffusive mismatch models across the interface. The effect of heat source size, which is allocated at high-temperature (301 K) edge of the silicon film, on the phonon transport characteristics at the films pair interface is also investigated. It is found that cut-off mismatch model predicts higher values of the thermal boundary resistance across the films pair interface as compared to that of the diffusive mismatch model. The ratio of equilibrium phonon intensity due to the cut-off mismatch over the diffusive mismatch models remains >1 at the silicon edge, while it becomes <1 at the diamond edge for all acoustic branches. PubDate: 2015-11-04

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 theories, the difference be... PubDate: 2015-11-01

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: 2015-11-01

Abstract: 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: 2015-11-01

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: 2015-11-01

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: 2015-11-01

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: 2015-11-01

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: 2015-11-01

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: 2015-11-01

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: 2015-11-01

Abstract: Abstract
The studies of shark skin textured surfaces in flow drag reduction provide inspiration to researchers overcoming technical challenges from actual production application. In this paper, three kinds of infinite parallel plate flow models with microstructure inspired by shark skin were established, namely blade model, wedge model and the smooth model, according to cross-sectional shape of microstructure. Simulation was carried out by using FLUENT, which simplified the computation process associated with direct numeric simulations. To get the best performance from simulation results, shear-stress transport k-omega turbulence model was chosen during the simulation. Since drag reduction mechanism is generally discussed from kinetics point of view, which cannot interpret the cause of these losses directly, a drag reduction rate was established based on the second law of thermodynamics. Considering abrasion and fabrication precision in practical applications, three kinds of abraded geometry models were constructed and tested, and the ideal microstructure was found to achieve best performance suited to manufacturing production on the basis of drag reduction rate. It was also believed that bionic shark skin surfaces with mechanical abrasion may draw more attention from industrial designers and gain wide applications with drag-reducing characteristics. PubDate: 2015-10-31

Abstract: Abstract
We derive the compatibility equations of L
2 displacement gradients on non-simply connected bodies. These compatibility equations are useful for non-smooth strains such as those associated with deformations of multi-phase materials. As an application of these compatibility equations, we study some configurations of different phases around a hole and show that, in general, the classical Hadamard jump condition is not a sufficient compatibility condition. PubDate: 2015-10-16

Abstract: Abstract
Micromechanical approaches are frequently employed to monitor local and global field quantities and their evolution under varying mechanical and/or thermal loading scenarios. In this contribution, an overview on important methods is given that are currently used to gain insight into the deformational and failure behaviour of multiphase materials and complex structures. First, techniques to represent material microstructures are reviewed. It is common to either digitise images of real microstructures or generate virtual 2D or 3D microstructures using automated procedures (e.g. Voronoï tessellation) for grain generation and colouring algorithms for phase assignment. While the former method allows to capture exactly all features of the microstructure at hand with respect to its morphological and topological features, the latter method opens up the possibility for parametric studies with respect to the influence of individual microstructure features on the local and global stress and strain response. Several applications of these approaches are presented, comprising low and high strain behaviour of multiphase steels, failure and fracture behaviour of multiphase materials and the evolution of surface roughening of the aluminium top metallisation of semiconductor devices. PubDate: 2015-10-13

Abstract: Abstract
The shock structure problem for Grad 10-moment equations for an inert binary mixture is investigated: necessary conditions for the formation of sub-shocks in fields of only one gas or of both components are rigorously obtained, and a detailed comparison with the shock-wave structure of its principal sub-system (deduced assuming vanishing viscous stress tensors) and of the equilibrium Euler sub-system is performed. Some numerical simulations for a mixture of argon and helium are presented. PubDate: 2015-09-23

Abstract: Abstract
We propose a model of complex poroelastic media with periodic or locally periodic structures observed at microscopic and mesoscopic scales. Using a two-level homogenization procedure, we derive a model coherent with the Biot continuum, describing effective properties of such a hierarchically structured poroelastic medium. The effective material coefficients can be computed using characteristic responses of the micro- and mesostructures which are solutions of local problems imposed in representative volume elements describing the poroelastic medium at the two levels of heterogeneity. In the paper, we discus various combinations of the interface between the micro- and mesoscopic porosities, influence of the fluid compressibility, or solid incompressibility. Gradient of porosity is accounted for when dealing with locally periodic structures. Derived formulae for computing the poroelastic material coefficients characterize not only the steady-state responses with static fluid, but are relevant also for quasistatic problems. The model is applicable in geology, or in tissue biomechanics, in particular for modeling canalicular-lacunar porosity of bone which can be characterized at several levels. PubDate: 2015-09-04

Abstract: Abstract
Targeted energy transfer between a main oscillator with a set of parallel Saint-Venant elements and
a nonlinear energy sink with a general nonlinear and odd potential function around 1:1 resonance is studied. The complexified system has been investigated at fast and slow time scales by detecting its invariant manifold, equilibrium and singular points, which can explain bifurcation(s) and different regimes of the system. Then, we introduce an example which treats vibratory energy exchanges between a main oscillator with two parallel Saint-Venant elements and a coupled cubic nonlinear energy sink. Finally, analytical predictions are compared with results obtained by numerical integrations of system equations. PubDate: 2015-09-01

Abstract: Abstract
A model for lipid membranes with lipid distension is presented. This incorporates the conventional Helfrich-type formulation as a special case. The effects of lipid distension on the shape equation, and the required adjustments to operative edge conditions, are discussed in detail. The model is illustrated through numerical simulations. PubDate: 2015-09-01

Abstract: Abstract
We study the exterior stress field in a three-phase circular inclusion which is bonded to the surrounding matrix through an intermediate interphase layer. All three phases belong to a particular class of compressible hyperelastic materials of harmonic type. We focus on the design of a harmonic elastic inclusion which by definition, does not disturb the sum of the normal stresses in the surrounding matrix. We show that in order to make the coated inclusion harmonic, certain inequalities concerning the material and geometric parameters of the three-phase composite must first be satisfied. The corresponding remote loading parameters can then be uniquely determined while keeping the associated phase angles arbitrary. Our results allow for both uniform and non-uniform remote loading. We show that the stress field inside the inclusion is uniform when the remote loading is uniform. PubDate: 2015-09-01