Authors:Alireza Gharahi; Peter Schiavone Pages: 675 - 688 Abstract: We propose a linear surface/interface model for plane deformations of a micropolar elastic solid based on a higher-order surface elasticity theory capable of incorporating bending and twisting effects. The surface/interface is modeled as a bending-resistant Kirchhoff micropolar thin shell perfectly bonded to the boundary of the solid. It is anticipated that by combining micropolar bulk and surface effects in this way, the enhanced model will most accurately capture the essential characteristics (in particular, size dependency) required in the modeling of materials with significant microstructure as well as in the modeling of classes of nanomaterials. The corresponding boundary value problems are particularly interesting in that they involve boundary conditions of order higher than that of the governing field equations. We illustrate our theory by analyzing the simple problem of a circular hole in a micropolar sheet noting, in particular, the extent to which surface effects and micropolar properties each contribute to the deformation of the sheet. PubDate: 2018-05-01 DOI: 10.1007/s00161-018-0637-7 Issue No:Vol. 30, No. 3 (2018)

Authors:Diego Said Schicchi; Antonio Caggiano; Martin Hunkel; Eduardus A. B. Koenders Abstract: A multiscale framework for thermo-mechanical analysis with phase transformations is proposed in this work. The formulation covers those cases including coupled constitutive equations for simulating thermo-mechanical processes considering phase transformation phenomena. The general case of temperature- and phase-dependent procedures, involving nonlinear plasticity concepts, is considered as main framework in order to formulate the material dissipation at both micro- and macroscopic level of observation. Thermodynamic consistency conditions for computational up/downscaling between micro- and macroscales are presented, with special focus on phase transformation phenomena, for both the mechanical and thermal homogenization. Classical Coleman–Gurtin thermodynamics is employed at the microscale, whereas an extended framework is considered at the macroscale due to the temperature gradient dependency of the macro stress. The multiscale procedure is based on a variational approach largely discussed in the literature. The overall coupled process at both micro- and macroscopic scales, averaging criteria, thermal, mechanical and phase change constitutive expressions, as well as the corresponding homogenization rules, are discussed and derived in detail. PubDate: 2018-06-04 DOI: 10.1007/s00161-018-0682-2

Authors:Arkadi Berezovski; M. Erden Yildizdag; Daria Scerrato Abstract: In this paper, elastic wave propagation in a one-dimensional micromorphic medium characterized by two internal variables is investigated. The evolution equations are deduced following two different approaches, namely using: (i) the balance of linear momentum and the Clausius–Duhem inequality, and (ii) an assumed Lagrangian functional (including a gyroscopic coupling) together with a variational principle. The dispersion relation is obtained and the possibility of the emerging band gaps is shown in such microstructured materials. Some numerical simulations are also performed in order to highlight the dispersive nature of the material under study. PubDate: 2018-05-29 DOI: 10.1007/s00161-018-0683-1

Authors:S. N. Gavrilov; A. M. Krivtsov; D. V. Tsvetkov Abstract: We consider unsteady heat transfer in a one-dimensional harmonic crystal surrounded by a viscous environment and subjected to an external heat supply. The basic equations for the crystal particles are stated in the form of a system of stochastic differential equations. We perform a continualization procedure and derive an infinite set of linear partial differential equations for covariance variables. An exact analytic solution describing unsteady ballistic heat transfer in the crystal is obtained. It is shown that the stationary spatial profile of the kinetic temperature caused by a point source of heat supply of constant intensity is described by the Macdonald function of zero order. A comparison with the results obtained in the framework of the classical heat equation is presented. We expect that the results obtained in the paper can be verified by experiments with laser excitation of low-dimensional nanostructures. PubDate: 2018-05-21 DOI: 10.1007/s00161-018-0681-3

Authors:Hien Nho Gia Nguyen; Olivier Millet; Gérard Gagneux Abstract: This manuscript focuses on the meridional profile of the axisymmetric capillary bridges built between two unequal-sized solid spheres. We propose an original method of resolution of Young Laplace equation based on inverse problem. The shapes of capillary bridges are classified into different categories depending on the geometrical properties, including neck radius, half-filling angle, wetting angle, and distance between two spheres. Practically, all the physical characteristics of capillary bridges, such as the free surface area of the liquid bridge and the inter-particle force, can be calculated easily. In addition, the experimental data provided in this manuscript are compared with analytical results, by matching the theoretical estimation with the data obtained from real experiments using image processing algorithm. PubDate: 2018-05-17 DOI: 10.1007/s00161-018-0658-2

Authors:Emilio Turco; Anil Misra; Rizacan Sarikaya; Tomasz Lekszycki Abstract: In order to get detailed information about the mechanical behavior of pantographic elementary substructure and elements, small-scale specimens were sintered using polyamide powder, constituted by three orthogonal pairs of beams interconnected through pivots forming pantographic cells. The mechanical properties of interconnecting pivots and constituting beams are investigated by comparing experimental evidence with an enhanced Piola–Hencky model. The careful agreement between experimental and predicted results allows us to estimate: (i) the macro-shear stiffness of interconnecting pivots (corresponding to micro-torsional stiffness), (ii) extensional stiffness and (iii) bending stiffness of constituting beams. PubDate: 2018-05-17 DOI: 10.1007/s00161-018-0678-y

Authors:Stéphane Lejeunes; Dominique Eyheramendy Abstract: We explore the formulation of nearly incompressible behaviors at finite strain in the context of a hybrid or a mixed energy. Such an energy is a function of both an isochoric deformation and a pressure-like quantity that can be considered as an internal variable. From thermodynamical and physical considerations, new energy functions are developed to correctly describe both nearly incompressible elasticity and thermoelastic behaviors. We discuss the advantages of such a formulation; in particular, we show that this approach makes it possible to unify the variational and the thermodynamical formulations in the nearly incompressible context without using Lagrange multipliers or other specific variational principles. PubDate: 2018-05-17 DOI: 10.1007/s00161-018-0680-4

Authors:David González; Francisco Chinesta; Elías Cueto Abstract: In the paradigm of data-intensive science, automated, unsupervised discovering of governing equations for a given physical phenomenon has attracted a lot of attention in several branches of applied sciences. In this work, we propose a method able to avoid the identification of the constitutive equations of complex systems and rather work in a purely numerical manner by employing experimental data. In sharp contrast to most existing techniques, this method does not rely on the assumption on any particular form for the model (other than some fundamental restrictions placed by classical physics such as the second law of thermodynamics, for instance) nor forces the algorithm to find among a predefined set of operators those whose predictions fit best to the available data. Instead, the method is able to identify both the Hamiltonian (conservative) and dissipative parts of the dynamics while satisfying fundamental laws such as energy conservation or positive production of entropy, for instance. The proposed method is tested against some examples of discrete as well as continuum mechanics, whose accurate results demonstrate the validity of the proposed approach. PubDate: 2018-05-17 DOI: 10.1007/s00161-018-0677-z

Authors:Milad Shirani; Cheng Luo; David J. Steigmann Abstract: A model of nonlinearly elastic surfaces composed of continuously distributed embedded fibers is formulated. This takes account of the elastic resistance of the fibers to extension, bending and twist. Twist is regarded as being kinematically independent of surface deformation, just as the twist in a spatial Kirchhoff rod is independent of the deformation of the curve of the rod. PubDate: 2018-05-12 DOI: 10.1007/s00161-018-0679-x

Authors:Ioannis Tsagrakis; Elias C. Aifantis Abstract: A thermodynamically consistent model of strain gradient elastodiffusion is developed. Its formulation is based on the enhancement of a robust theory of gradient elasticity, known as GRADELA, to account for a Cahn–Hilliard type of diffusion. Linear stability analysis is employed to determine the influence of concentration and strain gradients on the spinodal decomposition. For finite domains, spherically symmetric conditions are considered, and size effects on spinodal and miscibility gaps are discussed. The theoretical predictions are in agreement with the experimental trends, i.e., both gaps shrink as the grain diameter decreases and they are completely eliminated for crystals smaller than a critical size. PubDate: 2018-05-10 DOI: 10.1007/s00161-018-0673-3

Authors:Marta Perez; Adrien Scheuer; Emmanuelle Abisset-Chavanne; Amine Ammar; Francisco Chinesta; Roland Keunings Abstract: When addressing the flow of concentrated suspensions composed of rods, dense clusters are observed. Thus, the adequate modelling and simulation of such a flow requires addressing the kinematics of these dense clusters and their impact on the flow in which they are immersed. In a former work, we addressed a first modelling framework of these clusters, assumed so dense that they were considered rigid and their kinematics (flow-induced rotation) were totally defined by a symmetric tensor \({\mathbf {c}}\) with unit trace representing the cluster conformation. Then, the rigid nature of the clusters was relaxed, assuming them deformable, and a model giving the evolution of both the cluster shape and its microstructural orientation descriptor (the so-called shape and orientation tensors) was proposed. This paper compares the predictions coming from those models with finer-scale discrete simulations inspired from molecular dynamics modelling. PubDate: 2018-05-09 DOI: 10.1007/s00161-018-0659-1

Authors:Antonio Battista; Aziz Hamdouni; Olivier Millet Abstract: In this work, a formal deduction of a two-dimensional membrane theory, similar to Landau–Lifshitz model, is performed via an asymptotic development of the weak formulation of the three-dimensional equations of elasticity. Some interesting aspects of the deduced model are investigated, in particular the property of obtaining a hyperbolic equation for the out-of-plane displacement under a certain class of boundary conditions and loads. Some simple cases are analyzed to show the relevant aspects of the model and the phenomenology that can be addressed. In particular, it is shown how this mathematical formulation is capable to describe instabilities well known as wrinkling, often observed for the buckling of very thin membranes. PubDate: 2018-05-09 DOI: 10.1007/s00161-018-0676-0

Authors:Ramiro dell’Erba Abstract: In swarm robotics, just as for an animal swarm in nature, one of the aims is to reach and maintain a desired configuration. One of the possibilities for the team, to reach this aim, is to see what its neighbours are doing. This approach generates a rules system governing the movement of the single robot just by reference to neighbour’s motion. The same approach is used in position-based dynamics to simulate behaviour of complex continuum materials under deformation. Therefore, in some previous works, we have considered a two-dimensional lattice of particles and calculated its time evolution by using a rules system derived from our experience in swarm robotics. The new position of a particle, like the element of a swarm, is determined by the spatial position of the other particles. No dynamic is considered, but it can be thought as being hidden in the behaviour rules. This method has given good results in some simple situations reproducing the behaviour of deformable bodies under imposed strain. In this paper we try to stress our model to highlight its limits and how they can be improved. Some other, more complex, examples are computed and discussed. Shear test, different lattices, different fracture mechanisms and ASTM shape sample behaviour have been investigated by the software tool we have developed. PubDate: 2018-05-09 DOI: 10.1007/s00161-018-0675-1

Authors:Czesław Szymczak; Marcin Kujawa Abstract: The investigation concerns local buckling of compressed flanges of axially compressed composite channel columns. Cooperation of the member flange and web is taken into account here. The buckling mode of the member flange is defined by rotation angle a flange about the line of its connection with the web. The channel column under investigation is made of unidirectional fibre-reinforced laminate. Two approaches to member orthotropic material modelling are performed: the homogenization with the aid of theory of mixture and periodicity cell or homogenization upon the Voigt–Reuss hypothesis. The fundamental differential equation of local buckling is derived with the aid of the stationary total potential energy principle. The critical buckling stress corresponding to a number of buckling half-waves is assumed to be a minimum eigenvalue of the equation. Some numerical examples dealing with columns are given here. The analytical results are compared with the finite element stability analysis carried out by means of ABAQUS software. The paper is focused on a close analytical solution of the critical buckling stress and the associated buckling mode while the web–flange cooperation is assumed. PubDate: 2018-05-08 DOI: 10.1007/s00161-018-0674-2

Authors:Tamás Fekete Abstract: Structural integrity calculations play a crucial role in designing large-scale pressure vessels. Used in the electric power generation industry, these kinds of vessels undergo extensive safety analyses and certification procedures before deemed feasible for future long-term operation. The calculations are nowadays directed and supported by international standards and guides based on state-of-the-art results of applied research and technical development. However, their ability to predict a vessel’s behavior under accidental circumstances after long-term operation is largely limited by the strong dependence of the analysis methodology on empirical models that are correlated to the behavior of structural materials and their changes during material aging. Recently a new scientific engineering paradigm, structural integrity has been developing that is essentially a synergistic collaboration between a number of scientific and engineering disciplines, modeling, experiments and numerics. Although the application of the structural integrity paradigm highly contributed to improving the accuracy of safety evaluations of large-scale pressure vessels, the predictive power of the analysis methodology has not yet improved significantly. This is due to the fact that already existing structural integrity calculation methodologies are based on the widespread and commonly accepted ’traditional’ engineering thermal stress approach, which is essentially based on the weakly coupled model of thermomechanics and fracture mechanics. Recently, a research has been initiated in MTA EK with the aim to review and evaluate current methodologies and models applied in structural integrity calculations, including their scope of validity. The research intends to come to a better understanding of the physical problems that are inherently present in the pool of structural integrity problems of reactor pressure vessels, and to ultimately find a theoretical framework that could serve as a well-grounded theoretical foundation for a new modeling framework of structural integrity. This paper presents the first findings of the research project. PubDate: 2018-05-08 DOI: 10.1007/s00161-018-0657-3

Authors:Jacek Chróścielewski; Rüdiger Schmidt; Victor A. Eremeyev Abstract: This paper addresses modeling and finite element analysis of the transient large-amplitude vibration response of thin rod-type structures (e.g., plane curved beams, arches, ring shells) and its control by integrated piezoelectric layers. A geometrically nonlinear finite beam element for the analysis of piezolaminated structures is developed that is based on the Bernoulli hypothesis and the assumptions of small strains and finite rotations of the normal. The finite element model can be applied to static, stability, and transient analysis of smart structures consisting of a master structure and integrated piezoelectric actuator layers or patches attached to the upper and lower surfaces. Two problems are studied extensively: (i) FE analyses of a clamped semicircular ring shell that has been used as a benchmark problem for linear vibration control in several recent papers are critically reviewed and extended to account for the effects of structural nonlinearity and (ii) a smart circular arch subjected to a hydrostatic pressure load is investigated statically and dynamically in order to study the shift of bifurcation and limit points, eigenfrequencies, and eigenvectors, as well as vibration control for loading conditions which may lead to dynamic loss of stability. PubDate: 2018-05-07 DOI: 10.1007/s00161-018-0672-4

Authors:K. Langenfeld; P. Junker; J. Mosler Abstract: This paper deals with a constitutive model suitable for the analysis of quasi-brittle damage in structures. The model is based on incremental energy relaxation combined with a viscous-type regularization. A similar approach—which also represents the inspiration for the improved model presented in this paper—was recently proposed in Junker et al. (Contin Mech Thermodyn 29(1):291–310, 2017). Within this work, the model introduced in Junker et al. (2017) is critically analyzed first. This analysis leads to an improved model which shows the same features as that in Junker et al. (2017), but which (i) eliminates unnecessary model parameters, (ii) can be better interpreted from a physics point of view, (iii) can capture a fully softened state (zero stresses), and (iv) is characterized by a very simple evolution equation. In contrast to the cited work, this evolution equation is (v) integrated fully implicitly and (vi) the resulting time-discrete evolution equation can be solved analytically providing a numerically efficient closed-form solution. It is shown that the final model is indeed well-posed (i.e., its tangent is positive definite). Explicit conditions guaranteeing this well-posedness are derived. Furthermore, by additively decomposing the stress rate into deformation- and purely time-dependent terms, the functionality of the model is explained. Illustrative numerical examples confirm the theoretical findings. PubDate: 2018-05-03 DOI: 10.1007/s00161-018-0669-z

Authors:A. K. Lazopoulos Abstract: Fractional differential equations are solved with L-fractional derivatives, using numerical procedures. Two characteristic fractional differential equations are numerically solved. The first equation describes the motion of a thin rigid plate immersed in a Newtonian fluid connected by a massless spring to a fixed point, and the other one the diffusion of gas in a fluid. PubDate: 2018-02-23 DOI: 10.1007/s00161-018-0632-z

Authors:Elena Ionela Chereches; K. Viswanatha Sharma; Alina Adriana Minea Abstract: Ionic liquids are a new class of fluids to be considered for heat transfer due to their remarkable thermophysical properties. Experimental researches on ionic liquids have increased over the last few years and, as an extension, a new class of heat transfer fluids, the ionanofluids were considered in some recent experimental studies. Ionanofluids consists in suspending little amounts of high conductive nanoparticles in ionic liquids. In spite of a lot of inconsistent reports—mainly due to the deficient understanding of the involved mechanisms—ionanofluids have been demonstrated as a new favorable heat transfer fluid. The enhanced thermal conductivity of ionanofluids over the basic ionic liquids is considered one of the driving factors for enhancing convection. Nonetheless, the thermal conductivity is the most studied parameter in spite of the important influence of viscosity variation on the convective flow. This numerical study employed Ansys Fluent commercial code and showed that a correct description of thermophysical properties may make ionanofluids a very promising new heat transfer fluid since the preliminary results are encouraging. PubDate: 2018-02-20 DOI: 10.1007/s00161-018-0634-x

Authors:Yahui Zheng; Jiulin Du; Faku Liang Abstract: We have constructed a nonextensive thermodynamic formalism consisting of two sets of parallel Legendre transformation structures in previous papers. One is the physical set and the other is the Lagrange set. In this paper, we study the thermodynamic stability criterion with a dual interpretation of the thermodynamic relations and quantities. By recourse to the assumption that volume in nonextenstive system is nonadditive, we conclude that it is the physical pressure that is responsible for the mechanical balance between any two parts in a given nonextensive system. It is verified that in the physical set of transformation structures, the stability criterion can be expressed in terms of heat capacity and isothermal compressibility. We also discuss the fluctuation theory in nonextensive thermodynamics. PubDate: 2018-02-09 DOI: 10.1007/s00161-018-0628-8