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 Continuum Mechanics and Thermodynamics   [SJR: 0.665]   [H-I: 34]   [7 followers]  Follow         Hybrid journal (It can contain Open Access articles)    ISSN (Print) 1432-0959 - ISSN (Online) 0935-1175    Published by Springer-Verlag  [2355 journals]
• Mathematical homogenization of inelastic dissipative materials: a survey
and recent progress
• Authors: Nicolas Charalambakis; George Chatzigeorgiou; Yves Chemisky; Fodil Meraghni
Pages: 1 - 51
Abstract: Abstract In this paper, a review of papers on mathematical homogenization of dissipative composites under small strains and on the interplay between homogenization procedure and dissipation due to mechanical work is presented. Moreover, a critical survey on the links between mathematical homogenization and computational homogenization is attempted.
PubDate: 2018-01-01
DOI: 10.1007/s00161-017-0587-5
Issue No: Vol. 30, No. 1 (2018)

• Numerical simulation and experimental investigation of the elastocaloric
cooling effect in sputter-deposited TiNiCuCo thin films
• Authors: F. Welsch; J. Ullrich; H. Ossmer; M. Schmidt; M. Kohl; C. Chluba; E. Quandt; A. Schütze; S. Seelecke
Pages: 53 - 68
Abstract: Abstract The exploitation of the elastocaloric effect in superelastic shape memory alloys (SMA) for cooling applications shows a promising energy efficiency potential but requires a better understanding of the non-homogeneous martensitic phase transformation. Temperature profiles on sputter-deposited superelastic $${\mathrm {Ti_{55.2}Ni_{29.3}Cu_{12.7}Co_{2.8}}}$$ shape memory alloy thin films show localized release and absorption of heat during phase transformation induced by tensile deformation with a strong rate dependence. In this paper, a model for the simulation of the thermo-mechanically coupled transformation behavior of superelastic SMA is proposed and its capability to reproduce the mechanical and thermal responses observed during experiments is shown. The procedure for experiment and simulation is designed such that a significant temperature change from the initial temperature is obtained to allow potential cooling applications. The simulation of non-local effects is enabled by the use of a model based on the one-dimensional Müller–Achenbach–Seelecke model, extended by 3D mechanisms such as lateral contraction and by non-local interaction, leading to localization effects. It is implemented into the finite element software COMSOL Multiphysics, and comparisons of numerical and experimental results show that the model is capable of reproducing the localized transformation behavior with the same strain rate dependency. Additionally to the thermal and the mechanical behavior, the quantitative prediction of cooling performance with the presented model is shown.
PubDate: 2018-01-01
DOI: 10.1007/s00161-017-0582-x
Issue No: Vol. 30, No. 1 (2018)

• A new constitutive analysis of hexagonal close-packed metal in equal
channel angular pressing by crystal plasticity finite element method
• Authors: Hejie Li; Andreas Öchsner; Prasad K. D. V. Yarlagadda; Yin Xiao; Tsuyoshi Furushima; Dongbin Wei; Zhengyi Jiang; Ken-ichi Manabe
Pages: 69 - 82
Abstract: Abstract Most of hexagonal close-packed (HCP) metals are lightweight metals. With the increasing application of light metal products, the production of light metal is increasingly attracting the attentions of researchers worldwide. To obtain a better understanding of the deformation mechanism of HCP metals (especially for Mg and its alloys), a new constitutive analysis was carried out based on previous research. In this study, combining the theories of strain gradient and continuum mechanics, the equal channel angular pressing process is analyzed and a HCP crystal plasticity constitutive model is developed especially for Mg and its alloys. The influence of elevated temperature on the deformation mechanism of the Mg alloy (slip and twin) is novelly introduced into a crystal plasticity constitutive model. The solution for the new developed constitutive model is established on the basis of the Lagrangian iterations and Newton Raphson simplification.
PubDate: 2018-01-01
DOI: 10.1007/s00161-017-0583-9
Issue No: Vol. 30, No. 1 (2018)

• Natural convection with evaporation in a vertical cylindrical cavity under
the effect of temperature-dependent surface tension
• Authors: Danil A. Kozhevnikov; Mikhail A. Sheremet
Pages: 83 - 94
Abstract: Abstract The effect of surface tension on laminar natural convection in a vertical cylindrical cavity filled with a weak evaporating liquid has been analyzed numerically. The cylindrical enclosure is insulated at the bottom, heated by a constant heat flux from the side, and cooled by a non-uniform evaporative heat flux from the top free surface having temperature-dependent surface tension. Governing equations with corresponding boundary conditions formulated in dimensionless stream function, vorticity, and temperature have been solved by finite difference method of the second-order accuracy. The influence of Rayleigh number, Marangoni number, and aspect ratio on the liquid flow and heat transfer has been studied. Obtained results have revealed that the heat transfer rate at free surface decreases with Marangoni number and increases with Rayleigh number, while the average temperature inside the cavity has an opposite behavior; namely, it growths with Marangoni number and reduces with Rayleigh number.
PubDate: 2018-01-01
DOI: 10.1007/s00161-017-0586-6
Issue No: Vol. 30, No. 1 (2018)

• Modeling interface shear behavior of granular materials using micro-polar
continuum approach
• Authors: Babak Ebrahimian; Ali Noorzad; Mustafa I. Alsaleh
Pages: 95 - 126
Abstract: Abstract Recently, the authors have focused on the shear behavior of interface between granular soil body and very rough surface of moving bounding structure. For this purpose, they have used finite element method and a micro-polar elasto-plastic continuum model. They have shown that the boundary conditions assumed along the interface have strong influences on the soil behavior. While in the previous studies, only very rough bounding interfaces have been taken into account, the present investigation focuses on the rough, medium rough and relatively smooth interfaces. In this regard, plane monotonic shearing of an infinite extended narrow granular soil layer is simulated under constant vertical pressure and free dilatancy. The soil layer is located between two parallel rigid boundaries of different surface roughness values. Particular attention is paid to the effect of surface roughness of top and bottom boundaries on the shear behavior of granular soil layer. It is shown that the interaction between roughness of bounding structure surface and the rotation resistance of bounding grains can be modeled in a reasonable manner through considered Cosserat boundary conditions. The influence of surface roughness is investigated on the soil shear strength mobilized along the interface as well as on the location and evolution of shear localization formed within the layer. The obtained numerical results have been qualitatively compared with experimental observations as well as DEM simulations, and acceptable agreement is shown.
PubDate: 2018-01-01
DOI: 10.1007/s00161-017-0588-4
Issue No: Vol. 30, No. 1 (2018)

• Modeling and analysis of time-dependent processes in a chemically reactive
mixture
• Authors: M. P. Ramos; C. Ribeiro; A. J. Soares
Pages: 127 - 144
Abstract: Abstract In this paper, we study the propagation of sound waves and the dynamics of local wave disturbances induced by spontaneous internal fluctuations in a reactive mixture. We consider a non-diffusive, non-heat conducting and non-viscous mixture described by an Eulerian set of evolution equations. The model is derived from the kinetic theory in a hydrodynamic regime of a fast chemical reaction. The reactive source terms are explicitly computed from the kinetic theory and are built in the model in a proper way. For both time-dependent problems, we first derive the appropriate dispersion relation, which retains the main effects of the chemical process, and then investigate the influence of the chemical reaction on the properties of interest in the problems studied here. We complete our study by developing a rather detailed analysis using the Hydrogen–Chlorine system as reference. Several numerical computations are included illustrating the behavior of the phase velocity and attenuation coefficient in a low-frequency regime and describing the spectrum of the eigenmodes in the small wavenumber limit.
PubDate: 2018-01-01
DOI: 10.1007/s00161-017-0591-9
Issue No: Vol. 30, No. 1 (2018)

• Effective balance equations for elastic composites subject to
inhomogeneous potentials
• Authors: Raimondo Penta; Ariel Ramírez-Torres; José Merodio; Reinaldo Rodríguez-Ramos
Pages: 145 - 163
Abstract: Abstract We derive the new effective governing equations for linear elastic composites subject to a body force that admits a Helmholtz decomposition into inhomogeneous scalar and vector potentials. We assume that the microscale, representing the distance between the inclusions (or fibers) in the composite, and its size (the macroscale) are well separated. We decouple spatial variations and assume microscale periodicity of every field. Microscale variations of the potentials induce a locally unbounded body force. The problem is homogenizable, as the results, obtained via the asymptotic homogenization technique, read as a well-defined linear elastic model for composites subject to a regular effective body force. The latter comprises both macroscale variations of the potentials, and nonstandard contributions which are to be computed solving a well-posed elastic cell problem which is solely driven by microscale variations of the potentials. We compare our approach with an existing model for locally unbounded forces and provide a simplified formulation of the model which serves as a starting point for its numerical implementation. Our formulation is relevant to the study of active composites, such as electrosensitive and magnetosensitive elastomers.
PubDate: 2018-01-01
DOI: 10.1007/s00161-017-0590-x
Issue No: Vol. 30, No. 1 (2018)

• Double-diffusive convection in an inclined porous layer with a
concentration-based internal heat source
• Authors: Anjanna Matta; Antony A. Hill
Pages: 165 - 173
Abstract: Abstract The thermosolutal instability of double-diffusive convection in an inclined fluid-saturated porous layer with a concentration-based internal heat source is investigated. The linear instability of small-amplitude perturbations to the system is analyzed with respect to transverse and longitudinal rolls. The resultant eigenvalue problem is solved numerically utilizing the Chebyshev tau method. It is shown that an increasing inclination angle causes a strong stabilization in the transverse rolls irrespective of the internal heat source or vertical solutal Rayleigh number. Furthermore, substantial qualitative changes are demonstrated in the linear instability thresholds with variations in the inclination angle and concentration-based heat source.
PubDate: 2018-01-01
DOI: 10.1007/s00161-017-0592-8
Issue No: Vol. 30, No. 1 (2018)

• A geometric rationale for invariance, covariance and constitutive
relations
• Authors: Giovanni Romano; Raffaele Barretta; Marina Diaco
Pages: 175 - 194
Abstract: Abstract There are, in each branch of science, statements which, expressed in ambiguous or even incorrect but seemingly friendly manner, were repeated for a long time and eventually became diffusely accepted. Objectivity of physical fields and of their time rates and frame indifference of constitutive relations are among such notions. A geometric reflection on the description of frame changes as spacetime automorphisms, on induced push–pull transformations and on proper physico–mathematical definitions of material, spatial and spacetime tensor fields and of their time-derivatives along the motion, is here carried out with the aim of pointing out essential notions and of unveiling false claims. Theoretical and computational aspects of nonlinear continuum mechanics, and especially those pertaining to constitutive relations, involving material fields and their time rates, gain decisive conceptual and operative improvement from a proper geometric treatment. Outcomes of the geometric analysis are frame covariance of spacetime velocity, material stretching and material spin. A univocal and frame-covariant tool for evaluation of time rates of material fields is provided by the Lie derivative along the motion. The postulate of frame covariance of material fields is assessed to be a natural physical requirement which cannot interfere with the formulation of constitutive laws, with claims of the contrary stemming from an improper imposition of equality in place of equivalence.
PubDate: 2018-01-01
DOI: 10.1007/s00161-017-0595-5
Issue No: Vol. 30, No. 1 (2018)

• Propagation of a Dugdale crack at the edge of a half plane
• Authors: Hicheme Ferdjani; Radhi Abdelmoula
Pages: 195 - 205
Abstract: Abstract This work deals with the propagation of a Dugdale crack at the edge of a half plane. The corresponding singular integral equation is solved semi-analytically. The expressions of the stress intensity factor and of the crack gap are deduced. A propagation criterion deduced from the revisited Griffith theory (Ferdjani and Marigo in Eur J Mech A Solids 53:1–9, 2015) is applied. The length of the process zone is calculated and compared with the literature results. The presented results show the evolution of the applied load with the crack length for different values of the ratio of the critical length of the Dugdale model to the initial crack length. The shape of the crack gap is also presented. Finally, a comparison between the Griffith and Dugdale models is performed.
PubDate: 2018-01-01
DOI: 10.1007/s00161-017-0594-6
Issue No: Vol. 30, No. 1 (2018)

• Micropolar nematic model for polarized liquid crystals
• Authors: Maurizio Romeo
Pages: 207 - 219
Abstract: Abstract A micromorphic electroelastic model for polarized liquid crystals is proposed on the basis of a representation of electric multipoles in terms of microdeformation. Nematic liquid crystals are modeled as micropolar continua endowed with intrinsic electric dipole and quadrupole. A nonlinear dimensionless problem for a homogeneous nematic layer is formulated and solved numerically. The existence of a threshold electric potential is discussed, and the corresponding linearized system is also obtained to compare results on small values of deformation and electric field. Differently from common results of the classical continuum approach, asymmetric deformations and electric potentials within the layer are obtained due to the occurrence of non-null intrinsic quadrupole.
PubDate: 2018-01-01
DOI: 10.1007/s00161-017-0598-2
Issue No: Vol. 30, No. 1 (2018)

• Thermodynamic potential of free energy for thermo-elastic-plastic body
• Authors: Z. Śloderbach; J. Pająk
Pages: 221 - 232
Abstract: Abstract The procedure of derivation of thermodynamic potential of free energy (Helmholtz free energy) for a thermo-elastic-plastic body is presented. This procedure concerns a special thermodynamic model of a thermo-elastic-plastic body with isotropic hardening characteristics. The classical thermodynamics of irreversible processes for material characterized by macroscopic internal parameters is used in the derivation. Thermodynamic potential of free energy may be used for practical determination of the level of stored energy accumulated in material during plastic processing applied, e.g., for industry components and other machinery parts received by plastic deformation processing. In this paper the stored energy for the simple stretching of austenitic steel will be presented.
PubDate: 2018-01-01
DOI: 10.1007/s00161-017-0597-3
Issue No: Vol. 30, No. 1 (2018)

• An affine microsphere approach to modeling strain-induced crystallization
in rubbery polymers
• Authors: A. Nateghi; H. Dal; M.-A. Keip; C. Miehe
Abstract: Abstract Upon stretching a natural rubber sample, polymer chains orient themselves in the direction of the applied load and form crystalline regions. When the sample is retracted, the original amorphous state of the network is restored. Due to crystallization, properties of rubber change considerably. The reinforcing effect of the crystallites stiffens the rubber and increases the crack growth resistance. It is of great importance to understand the mechanism leading to strain-induced crystallization. However, limited theoretical work has been done on the investigation of the associated kinetics. A key characteristic observed in the stress–strain diagram of crystallizing rubber is the hysteresis, which is entirely attributed to strain-induced crystallization. In this work, we propose a micromechanically motivated material model for strain-induced crystallization in rubbers. Our point of departure is constructing a micromechanical model for a single crystallizing polymer chain. Subsequently, a thermodynamically consistent evolution law describing the kinetics of crystallization on the chain level is proposed. This chain model is then incorporated into the affine microsphere model. Finally, the model is numerically implemented and its performance is compared to experimental data.
PubDate: 2018-01-13
DOI: 10.1007/s00161-017-0612-8

• Constitutive equations for the cyclic behaviour of short carbon

• Authors: Louis Leveuf; Libor Navrátil; Vincent Le Saux; Yann Marco; Jérôme Olhagaray; Sylvain Leclercq
Abstract: Abstract A constitutive model for the cyclic behaviour of short carbon fibre-reinforced thermoplastics for aeronautical applications is proposed. First, an extended experimental database is generated in order to highlight the specificities of the studied material. This database is composed of complex tests and is used to design a relevant constitutive model able to capture the cyclic behaviour of the material. A general 3D formulation of the model is then proposed, and an identification strategy is defined to identify its parameters. Finally, a validation of the identification is performed by challenging the prediction of the model to the tests that were not used for the identification. An excellent agreement between the numerical results and the experimental data is observed revealing the capabilities of the model.
PubDate: 2018-01-06
DOI: 10.1007/s00161-017-0616-4

• Modelling of elastic heat conductors via objective rate equations
• Authors: Angelo Morro
Abstract: Abstract A thermoelastic solid is modelled by letting the heat flux be given by a rate equation. As any constitutive property, the rate equation has to be objective and consistent with thermodynamics. Accordingly, firstly a theorem is given that characterizes objective time derivatives. This allows the known objective time derivatives to be viewed as particular elements of the set so specified. Next the thermodynamic consistency is established for the constitutive models involving objective time derivatives within appropriate sets. It emerges that the thermodynamic consistency holds provided the stress contains additively terms quadratic in the heat flux vector in a form that is related to the derivative adopted for the rate of the heat flux.
PubDate: 2018-01-02
DOI: 10.1007/s00161-017-0617-3

• Multi-scale kinetic description of granular clusters: invariance, balance,
and temperature
• Authors: Gianfranco Capriz; Paolo Maria Mariano
Abstract: Abstract We discuss a multi-scale continuum representation of bodies made of several mass particles flowing independently each other. From an invariance procedure and a nonstandard balance of inertial actions, we derive the balance equations introduced in earlier work directly in pointwise form, essentially on the basis of physical plausibility. In this way, we analyze their foundations. Then, we propose a Boltzmann-type equation for the distribution of kinetic energies within control volumes in space and indicate how such a distribution allows us to propose a definition of (granular) temperature along processes far from equilibrium.
PubDate: 2017-12-19
DOI: 10.1007/s00161-017-0613-7

• Correction to: Thermodynamic potential of free energy for
thermo-elastic-plastic body
• Authors: Z. Śloderbach; J. Pająk
Abstract: Abstract Unfortunately, the original article was online published with error in equations, and the same is corrected here.
PubDate: 2017-12-18
DOI: 10.1007/s00161-017-0614-6

• Helmholtz and Gibbs ensembles, thermodynamic limit and bistability in
polymer lattice models
• Authors: Stefano Giordano
Abstract: Abstract Representing polymers by random walks on a lattice is a fruitful approach largely exploited to study configurational statistics of polymer chains and to develop efficient Monte Carlo algorithms. Nevertheless, the stretching and the folding/unfolding of polymer chains within the Gibbs (isotensional) and the Helmholtz (isometric) ensembles of the statistical mechanics have not been yet thoroughly analysed by means of the lattice methodology. This topic, motivated by the recent introduction of several single-molecule force spectroscopy techniques, is investigated in the present paper. In particular, we analyse the force–extension curves under the Gibbs and Helmholtz conditions and we give a proof of the ensembles equivalence in the thermodynamic limit for polymers represented by a standard random walk on a lattice. Then, we generalize these concepts for lattice polymers that can undergo conformational transitions or, equivalently, for chains composed of bistable or two-state elements (that can be either folded or unfolded). In this case, the isotensional condition leads to a plateau-like force–extension response, whereas the isometric condition causes a sawtooth-like force–extension curve, as predicted by numerous experiments. The equivalence of the ensembles is finally proved also for lattice polymer systems exhibiting conformational transitions.
PubDate: 2017-12-18
DOI: 10.1007/s00161-017-0615-5

• Continuum modeling of twinning, amorphization, and fracture: theory and
numerical simulations
• Authors: J. D. Clayton; J. Knap
Abstract: Abstract A continuum mechanical theory is used to model physical mechanisms of twinning, solid-solid phase transformations, and failure by cavitation and shear fracture. Such a sequence of mechanisms has been observed in atomic simulations and/or experiments on the ceramic boron carbide. In the present modeling approach, geometric quantities such as the metric tensor and connection coefficients can depend on one or more director vectors, also called internal state vectors. After development of the general nonlinear theory, a first problem class considers simple shear deformation of a single crystal of this material. For homogeneous fields or stress-free states, algebraic systems or ordinary differential equations are obtained that can be solved by numerical iteration. Results are in general agreement with atomic simulation, without introduction of fitted parameters. The second class of problems addresses the more complex mechanics of heterogeneous deformation and stress states involved in deformation and failure of polycrystals. Finite element calculations, in which individual grains in a three-dimensional polycrystal are fully resolved, invoke a partially linearized version of the theory. Results provide new insight into effects of crystal morphology, activity or inactivity of different inelasticity mechanisms, and imposed deformation histories on strength and failure of the aggregate under compression and shear. The importance of incorporation of inelastic shear deformation in realistic models of amorphization of boron carbide is noted, as is a greater reduction in overall strength of polycrystals containing one or a few dominant flaws rather than many diffusely distributed microcracks.
PubDate: 2017-12-14
DOI: 10.1007/s00161-017-0604-8

• Extended thermodynamics, effective elastic coefficients and
electromagnetoelastic waves in superconducting layer
• Authors: Bogdan T. Maruszewski; Malgorzata A. Jankowska; Roman Starosta
Abstract: Abstract The paper deals with the analysis of an influence of the thermal field and its relaxation properties on the compressional and flexural magnetoelastic waves propagation in a vibrating superconducting layer. The investigations have been confined only to the vortex elastic field in the type-II superconductor. The description is based on the extended thermodynamical model of interactions. Contrary to the existing dynamical descriptions of electromagnetothermoelastic interactions in solids and/or in the magnetic vortex field of elastic character in the type-II superconductor, the influence of the thermal field on the electromagnetoelastic field (or electromagnetoelastic waves in such a medium) has been considered by the use of the effective elastic coefficients dependent on temperature and the relaxation time of the thermal field in low temperatures.
PubDate: 2017-12-07
DOI: 10.1007/s00161-017-0609-3

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