Authors:R. Fechte-Heinen; A. Schlömerkemper Pages: 1601 - 1621 Abstract: Abstract
This work is concerned with different estimates of the quasiconvexification of multi-well energy landscapes of NiTi shape memory alloys, which models the overall behavior of the material. Within the setting of the geometrically linear theory of elasticity, we consider a formula of the quasiconvexification which involves the so-called energy of mixing.We are interested in lower and upper bounds on the energy of mixing in order to get a better understanding of the quasiconvexification. The lower bound on the energy of mixing is obtained by convexification; it is also called Sachs or Reuß lower bound. The upper bound on the energy of mixing is based on second-order lamination. In particular, we are interested in the difference between the lower and upper bounds. Our numerical simulations show that the difference is in fact of the order of 1% and less in martensitic NiTi, even though both bounds on the energy of mixing were rather expected to differ more significantly. Hence, in various circumstances it may be justified to simply work with the convexification of the multi-well energy, which is relatively easy to deal with, or with the lamination upper bound, which always corresponds to a physically realistic microstructure, as an estimate of the quasiconvexification. In order to obtain a potentially large difference between upper and lower bound, we consider the bounds along paths in strain space which involve incompatible strains. In monoclinic shape memory alloys, three-tuples of pairwise incompatible strains play a special role since they form so-called T
3-configurations, originally discussed in a stress-free setting. In this work, we therefore consider in particular numerical simulations along paths in strain space which are related to these T
3-configurations. Interestingly, we observe that the second-order lamination upper bound along such paths is related to the geometry of the T
3-configurations. In addition to the purely martensitic regime, we also consider the influence of adding R-phase variants to the microstructure. Adding single variants of R-phase is shown to be energetically favorable in a compatible martensitic setting. However, the combination of several R-phase variants with compatible or incompatible martensite yields significant differences between the bounds considered. PubDate: 2016-11-01 DOI: 10.1007/s00161-016-0494-1 Issue No:Vol. 28, No. 6 (2016)

Authors:Hejie Li; Andreas Öchsner; Guowei Ni; Dongbin Wei; Zhengyi Jiang Pages: 1623 - 1634 Abstract: Abstract
The stress state is an important parameter in metal forming processes, which significantly influences the strain state and microstructure of products, affecting their surface qualities. In order to make the metal products have a good surface quality, the surface stress state must be optimised. In this study, two classical methods, the upper bound method and the crystal plasticity finite element method, were investigated. The differences between the two methods were discussed in regard to the model, the velocity field, and the strain field. Then the related surface roughness is deduced. PubDate: 2016-11-01 DOI: 10.1007/s00161-016-0496-z Issue No:Vol. 28, No. 6 (2016)

Authors:Sergei Alexandrov; Robert Goldstein Pages: 1635 - 1643 Abstract: Abstract
The main objective of the present paper is to compare, by means of a problem permitting a closed-form solution, qualitative behavior of solutions based on three models of strain hardening plasticity and two models of viscoplasticity. The elastic portion of the strain tensor is neglected. The study focuses on the solution behavior near frictional interfaces. The solution behavior essentially depends on the model chosen. Such features of the solutions as nonexistence and singularity are emphasized. The key constitutive parameter that divides all the models considered into two groups is the saturation stress. In particular, under certain conditions no solution satisfying the regime of sticking exists for the models that involve the saturation stress. Qualitative comparison with numerous experimental observations is made. It is concluded that models with a saturation stress, including the models considered in the present paper, may be capable of describing the generation of a narrow layer of severe plastic deformation in the vicinity of frictional interfaces. PubDate: 2016-11-01 DOI: 10.1007/s00161-015-0486-6 Issue No:Vol. 28, No. 6 (2016)

Authors:Paolo Podio-Guidugli Pages: 1705 - 1709 Abstract: Abstract
On moving from the classic papers by Einstein and Langevin on Brownian motion, two consistent statistical interpretations are given for the thermal displacement, a scalar field formally introduced by Helmholtz, whose time derivative is by definition the absolute temperature. PubDate: 2016-11-01 DOI: 10.1007/s00161-016-0505-2 Issue No:Vol. 28, No. 6 (2016)

Authors:M. Gołąbczak; A. Gołąbczak; A. Konstantynowicz; R. Święcik Pages: 1781 - 1789 Abstract: Abstract
Titanium and its alloys are widely recognized as the hardly machinable materials, especially due to their relatively high hardness, low thermal conductivity and possible subcritical superplasticity. Then, a thorough control of the machining process parameters shall be maintained. In this paper, we have concentrated on the grinding of the Ti6Al4V titanium alloy using cBN (boron nitride) grinding wheel combined with the AEDG (abrasive electrodischarge grinding) process. The mathematical model we have dealt with has been based mainly on Jaeger model of the heat taking over between sliding bodies with substantial upgrades related to:
estimation of the frictional heat generating based on friction forces distribution,
spatial, not only planar, shape of the contact area,
generated heat partition between different parties of the grinding process,
heat transfer in the multilayered environment.
The experimental verification of the theoretical predictions has been carried out. Fundamental difficulty in such a research is placing temperature probes sufficiently close to the ground surface with possibly low space devoted for probes due to the temperature field deformation with relation to the real conditions of grinding. The temperature field in the machined workpiece has been investigated using electronic data logging and DSP methods. Obtained results exhibit clearly that distribution of heat generation in the contact zone could be of the relatively complicated shape due to the external cooling and the very specific heat transfer and accumulation in the titanium workpiece surface layer. PubDate: 2016-11-01 DOI: 10.1007/s00161-016-0509-y Issue No:Vol. 28, No. 6 (2016)

Authors:Maurizio Romeo Pages: 1807 - 1820 Abstract: Abstract
A micromorphic continuum model of a deformable electromagnetic conductor is established introducing microdensities of bound and free charges. The conductive part of electric current consists of contributions due to free charges and microdeformation. Beside the conservation of charge, we derive suitable evolution equations for electric multipoles which are exploited to obtain the macroscopic form of Maxwell’s equations. A constitutive model for electromagneto-elastic conductors is considered which allows for a natural characterization of perfect conductors independently on the form of the constitutive equation for the conduction current. A generalized Ohm’s law is also derived for not ideal conductors which accounts for relaxation effects. The consequences of the linearized Ohm’s law on the classic magnetic transport equation are shown. PubDate: 2016-11-01 DOI: 10.1007/s00161-016-0513-2 Issue No:Vol. 28, No. 6 (2016)

Authors:Fazle Mabood; Giulio Lorenzini; Nopparat Pochai; Sheikh Muhammad Ibrahim Pages: 1925 - 1932 Abstract: Abstract
A numerical treatment for axisymmetric flow and heat transfer due to a stretching cylinder under the influence of a uniform magnetic field and prescribed surface heat flux is presented. Numerical results are obtained for dimensionless velocity, temperature, skin friction coefficient and Nusselt number for several values of the suction/injection, magnetic and curvature parameters as well as the Prandtl number. The present study reveals that the controlling parameters have strong effects on the physical quantities of interest. It is seen that the magnetic field enhances the dimensionless temperature inside the thermal boundary layer, whereas it reduces the dimensionless velocity inside the hydrodynamic boundary layer. Heat transfer rate reduces, while the skin friction coefficient increases with magnetic field. PubDate: 2016-11-01 DOI: 10.1007/s00161-016-0519-9 Issue No:Vol. 28, No. 6 (2016)

Authors:Geralf Hütter Pages: 1935 - 1941 Abstract: Abstract
Within rational continuum mechanics, the Coleman–Noll procedure is established to derive requirements to constitutive equations. Aiming in particular at generalized continuum theories, the present contribution demonstrates how this procedure can be extended to yield additionally the underlying balance equations of stress-type quantities. This is demonstrated for micromorphic and strain gradient media as well as for the microforce theory. The relation between the extended Coleman–Noll procedure and the method of virtual powers is pointed out. PubDate: 2016-11-01 DOI: 10.1007/s00161-016-0506-1 Issue No:Vol. 28, No. 6 (2016)

Abstract: Abstract
If electrons (e) and holes (h) in metals or semiconductors are heated to the temperatures
\(T_{e}\)
and
\(T_{h}\)
greater than the lattice temperature
\(T_{p}\)
, the electron–phonon interaction causes energy relaxation. In the nonuniform case, a momentum relaxation occurs as well. In view of such an application, a new model based on an asymptotic procedure for solving the kinetic equations of carriers and phonons is proposed, with generation–recombination of electrons and holes, which gives naturally the displaced Maxwellian at the leading order. After that, balance equations for the electron number, hole number, energy densities, and momentum densities are constructed, which constitute now a system of eight equations for the chemical potentials (carriers), the temperatures (carriers and phonons), and the drift velocities (carriers and phonons). In the drift-diffusion approximation the constitutive laws are derived and the Onsager relations recovered. PubDate: 2016-11-01

Abstract: Abstract
This paper is concerned with the theory of thermoelastic dipolar bodies which have a double porosity structure. In contrast with previous papers dedicated to classical elastic bodies, in our context the double porosity structure of the body is influenced by the displacement field, which is consistent with real models. In this setting, we show instability of solution as the initial energy is negative while under an appropriated (and realistic) condition, we prove existence and uniqueness of solution using semi-group theory. PubDate: 2016-11-01

Abstract: Abstract
A dynamic two-scale model is developed for describing the mechanical behavior of elastomers filled with hard nanoparticles. Using nonequilibrium thermodynamics, a closed system of evolution equations is derived, coupling continuum mechanics with a fine-scale description on the level of filler particles. So doing, a constitutive stress–strain relation emerges that is applicable to transient situations. In addition to the number density of filler particles, the particle arrangement is captured by the distribution of the difference vector between two representative interacting particles, which makes this model efficient in comparison with many-particle models. The two-particle model presented here is analyzed numerically in oscillatory deformation, for two purposes. First, the nonlinearity of the model is studied in detail, in terms of the Payne effect, that compares favorably with the literature. And second, the two-particle model is compared with a corresponding many-particle model in the literature. PubDate: 2016-11-01

Abstract: Abstract
The mechanical response, serviceability, and load-bearing capacity of materials and structural components can be adversely affected due to external stimuli, which include exposure to a corrosive chemical species, high temperatures, temperature fluctuations (i.e., freezing–thawing), cyclic mechanical loading, just to name a few. It is, therefore, of paramount importance in several branches of engineering—ranging from aerospace engineering, civil engineering to biomedical engineering—to have a fundamental understanding of degradation of materials, as the materials in these applications are often subjected to adverse environments. As a result of recent advancements in material science, new materials such as fiber-reinforced polymers and multi-functional materials that exhibit high ductility have been developed and widely used, for example, as infrastructural materials or in medical devices (e.g., stents). The traditional small-strain approaches of modeling these materials will not be adequate. In this paper, we study degradation of materials due to an exposure to chemical species and temperature under large strain and large deformations. In the first part of our research work, we present a consistent mathematical model with firm thermodynamic underpinning. We then obtain semi-analytical solutions of several canonical problems to illustrate the nature of the quasi-static and unsteady behaviors of degrading hyperelastic solids. PubDate: 2016-11-01

Abstract: Abstract
The main objective of this work is the contribution to the study of the piezoelectric structures which contain preexisting defect (crack). For that, we consider a Griffith crack located at the interface of two piezoelectric materials in a semi-infinite plane structure. The structure is subjected to an anti-plane shearing combined with an in-plane electric displacement. Using integral Fourier transforms, the equations of piezoelectricity are converted analytically to a system of singular integral equations. The singular integral equations are further reduced to a system of algebraic equations and solved numerically by using Chebyshev polynomials. The stress intensity factor and the electric displacement intensity factor are calculated and used for the determination of the energy release rate which will be taken as fracture criterion. At the end, numerical results are presented for various parameters of the problem; they are also presented for an infinite plane structure. PubDate: 2016-11-01

Abstract: Abstract
A novel kind of lightweight integrated thermal protection system, named pyramidal core sandwich panel, is proposed to be a good safeguard for hypersonic aircrafts in the current study. Such system is considered as not only an insulation structure but also a load-bearing structure. In the context of design for hypersonic aircrafts, an efficient optimization should be paid enough attention. This paper concerns with the homogenization of the proposed pyramidal sandwich core panel using two-dimensional model in subsequent research for material selection. According to the required insulation performance and thermal–mechanical properties, several suitable material combinations are chosen as candidates for the pyramidal core sandwich panel by adopting finite element analysis and approximate response surface. To obtain lightweight structure with an excellent capability of heat insulation and load-bearing, an investigation on some specific design variables, which are significant for thermal–mechanical properties of the structure, is performed. Finally, a good balance between the insulation performance, the capability of load-bearing and the lightweight has attained. PubDate: 2016-11-01

Abstract: Abstract
Within the spatial description, it is customary to refer thermodynamic state quantities to an elementary volume fixed in space containing an ensemble of particles. During its evolution, the elementary volume is occupied by different particles, each having its own mass, tensor of inertia, angular and linear velocities. The aim of the present paper is to answer the question of how to determine the inertial and kinematic characteristics of the elementary volume. In order to model structural transformations due to the consolidation or defragmentation of particles or anisotropic changes, one should consider the fact that the tensor of inertia of the elementary volume may change. This means that an additional constitutive equation must be formulated. The paper suggests kinetic equations for the tensor of inertia of the elementary volume. It also discusses the specificity of the inelastic polar continuum description within the framework of the spatial description. PubDate: 2016-11-01

Abstract: Abstract
The nonextensive thermodynamic relations are expressed under the assumption of temperature duality, endowing the “physical temperature” and the “Lagrange temperature” in different physical senses. Based on this assumption, two sets of parallel Legendre transform structures are given. One is called “physical” set, and the other is called “Lagrange” set. In these two formalisms, the thermodynamic quantities and the thermodynamic relations are both liked through the Tsallis factor. Application of the two sets of the thermodynamic relations to the self-gravitating system shows that the heat capacity defined in the classical thermodynamics has no relevance to the stability of the system. Instead, the newly defined heat capacity can determine the stability of the system. PubDate: 2016-11-01

Abstract: Abstract
It is assumed that any free energy function exhibits strict periodic behavior for histories that have been periodic for all past times. This is not the case for the work function, which, however, has the usual defining properties of a free energy. Forms given in fairly recent years for the minimum and related free energies of linear materials with memory have this property. Materials for which the minimal states are all singletons are those for which at least some of the singularities of the Fourier transform of the relaxation function are not isolated. For such materials, the maximum free energy is the work function, and free energies intermediate between the minimum free energy and the work function should be given by a linear relation involving these two quantities. All such functionals, except the minimum free energy, therefore do not have strict periodic behavior for periodic histories, which contradicts our assumption. A way out of the difficulty is explored which involves approximating the relaxation function by a form for which the minimal states are no longer singletons. A representation can then be given of an arbitrary free energy as a linear combination of the minimum, maximum and intermediate free energies derived in earlier work. This representation obeys our periodicity assumption. Numerical data are presented, supporting the consistency of this approach. PubDate: 2016-11-01

Abstract: Abstract
The theory of phenomenological non-equilibrium thermodynamics is extended by including stochastic processes in order to account for recently derived thermodynamical relations such as the Jarzynski’s equality. Four phenomenological axioms are postulated resulting in a phenomenological interpretation of Jarzynski’s equality. In particular, considering the class of Jarzynski processes Jarzynski’s equality follows from the axiom that the statistical average of the exponential work is protocol independent. PubDate: 2016-11-01

Abstract: Abstract
The kinematics of generalized continua is investigated and key points concerning the definition of overall tangent strain measure are put into evidence. It is shown that classical measures adopted in the literature for micromorphic continua do not obey a constraint qualification requirement, to be fulfilled for well-posedness in optimization theory, and are therefore termed redundant. Redundancy of continua with latent microstructure and of constrained Cosserat continua is also assessed. A simplest, non-redundant, kinematic model of micromorphic continua, is proposed by dropping the microcurvature field. The equilibrium conditions and the related variational linear elastostatic problem are formulated and briefly discussed. The simplest model involves a reduced number of state variables and of elastic constitutive coefficients, when compared with other models of micromorphic continua, being still capable of enriching the Cauchy continuum model in a significant way. PubDate: 2016-11-01