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: 2016-05-06

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: 2016-05-05

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: 2016-05-02

Abstract: The present paper is devoted to a model for elastic layered prismatic shells which is constructed by means of a suggested in the paper approach which essentially differs from the known approaches for constructing models of laminated structures. Using Vekua’s dimension reduction method after appropriate modifications, hierarchical models for elastic layered prismatic shells are constructed. We get coupled governing systems for the whole structure in the projection of the structure. The advantage of this model consists in the fact that we solve boundary value problems separately for each ply. In addition, beginning with the second ply, we use a solution of a boundary value problem of the preceding ply. We indicate ways of investigating boundary value problems for the governing systems. For the sake of simplicity, we consider the case of two plies, in the zeroth approximation. However, we also make remarks concerning the cases when either the number of plies is more than two or higher-order approximations (hierarchical models) should be applied. As an example, we consider a special case of deformation and solve the corresponding boundary value problem in the explicit form. PubDate: 2016-05-01

Abstract: The time development of an interface separating two immiscible fluids of different densities in heterogeneous two-dimensional porous media is studied. The governing equations are simplified with the help of approximate Green’s functions which allow computation of the shape of the interface directly without resolving the fluid flow in the entire domain. The new formulation is amenable to numerical approximation, and the reduction in dimension leads to a significant gain in efficiency in the numerical simulation of the interfacial dynamics. Several test cases are investigated, and the numerical solutions are compared to known exact solutions and experimental data. PubDate: 2016-05-01

Abstract: In this article, an alternative to the classical dynamic equation formulation is presented. To achieve this goal, we need to derive the reciprocal theorem in rates and the principle of virtual work in rates, in a small deformation regime, with which we will be able to obtain an expression for damping force. In this new formulation, some terms that are not commonly considered in the classical formulation appear, e.g., the term that is function of jerk (the rate of change of acceleration). Moreover, in this formulation the term that characterizes material nonlinearity, in dynamic analysis, appears naturally. PubDate: 2016-05-01

Abstract: This is the concluding part III of a series of papers. The aim of the current paper is to simulate and analyze the procedure of variant reorientation in a magnetic shape-memory alloy (MSMA) sample and to predict the response of the sample subject to various loading conditions. The sample to be considered in this paper has a 3D cuboid shape and is subject to typical magneto-mechanical loading conditions. Variant reorientation in the sample is realized through twin interface movements. To investigate the key features of twin interface movements, the properties of configurational forces on the twin interfaces are analyzed. For both the stress-assisted MFIS tests and the field-assisted quasi-elasticity tests, the magneto-mechanical behavior of the MSMA sample during the whole loading procedure is simulated by using the finite element method. The influence of the initial variant distribution in the sample on its global response is discussed. The obtained numerical results are compared with the experimental results. It can be seen that the model predictions can fit the experimental results both at a qualitative as well as at a quantitative level. PubDate: 2016-05-01

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: 2016-05-01

Abstract: In Bertram (Continuum Mech Thermodyn. doi:10.1007/s00161-014-0387-0, 2015), a mechanical framework for finite gradient elasticity and plasticity has been given. In the present paper, this is extended to thermodynamics. The mechanical theory is only briefly repeated here. A format for a rather general constitutive theory including all thermodynamic fields is given in a Euclidian invariant setting. The plasticity theory is rate-independent and unconstrained. The Clausius–Duhem inequality is exploited to find necessary and sufficient conditions for thermodynamic consistency. The residual dissipation inequality restricts the flow and hardening rules in combination with the yield criterion. PubDate: 2016-05-01

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: 2016-05-01

Abstract: It is well known that the crystallisation and melting behaviour of semicrystalline polymers depends in a pronounced manner on the temperature history. If the polymer is in the liquid state above the melting point, and the temperature is reduced to a level below the glass transition, the final degree of crystallinity, the amount of the rigid amorphous phase and the configurational state of the mobile amorphous phase strongly depend on the cooling rate. If the temperature is increased afterwards, the extents of cold crystallisation and melting are functions of the heating rate. Since crystalline and amorphous phases exhibit different densities, the specific volume depends also on the temperature history. In this article, a thermodynamically based phenomenological approach is developed which allows for the constitutive representation of these phenomena in the time domain. The degree of crystallinity and the configuration of the amorphous phase are represented by two internal state variables whose evolution equations are formulated under consideration of the second law of thermodynamics. The model for the specific Gibbs free energy takes the chemical potentials of the different phases and the mixture entropy into account. For simplification, it is assumed that the amount of the rigid amorphous phase is proportional to the degree of crystallinity. An essential outcome of the model is an equation in closed form for the equilibrium degree of crystallinity in dependence on pressure and temperature. Numerical simulations demonstrate that the process dependences of crystallisation and melting under consideration of the glass transition are represented. PubDate: 2016-05-01

Abstract: We propose a Bhatnagar–Gross–Krook (BGK) kinetic model in which the collision frequency is a linear combination of polynomials in the velocity variable. The coefficients of the linear combination are determined so as to enforce proper relaxation rates for a selected group of moments. The relaxation rates are obtained by a direct numerical evaluation of the full Boltzmann collision operator. The model is conservative by construction. Simulations of the problem of spatially homogeneous relaxation of hard spheres gas show improvement in accuracy of controlled moments as compared to solutions obtained by the classical BGK, ellipsoidal-statistical BGK and the Shakhov models in cases of strong deviations from continuum. PubDate: 2016-05-01

Abstract: Multi-mechanism models (MM models) have become an important tool for modeling complex material behavior. In particular, two-mechanism models are used. They are applied to model ratcheting in metal plasticity as well as steel behavior during phase transformations. We consider a small-deformation setting. The characteristic trait of multi-mechanism models is the additive decomposition of the inelastic (e.g., plastic or viscoplastic) strain into several parts. These parts are sometimes called mechanisms. In comparison with rheological models, the mechanisms can interact with each other. This leads to new properties and allows to describe important observable effects. Up to now, each mechanism has one kinematic internal variable. As a new feature, we develop multi-mechanism models (in series) with several kinematic variables for each mechanism as well as with several isotropic variables for each flow criterion. We describe this complex situation by three structural matrices which express the mutual relations between mechanisms, flow criteria, kinematic, and isotropic variables. The well-known Chaboche model with a unique inelastic strain and several kinematic variables represents a special case of these general multi-mechanism models. In this work, we also present a matrix-based approach for these new complex MM models. The presented models can form the basis for developing numerical algorithms for simulation and parameter identification. PubDate: 2016-05-01

Abstract: Gurson-type material models are based on concepts of porous materials and have been largely used to describe mechanical degradation under inelastic deformation. In addition to mechanical damage, temperature evolution is also relevant to this class of problems owing to thermal softening effects. This work addresses a finite strain thermo-elastic-plastic formulation fully coupled to the energy conservation equation and investigates the sensitivity of the mechanical response with respect to the temperature evolution based on tensile tests for small to moderate temperatures. The results indicate that the initial temperature, sensitivity of the yield stress to temperature and the heat transfer coefficient at the specimen surface play an important role on the evolution of the void fraction, stress distribution and, ultimately, the load-bearing capacity. PubDate: 2016-05-01

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: 2016-05-01

Abstract: The intersection between the two concepts of structural control and defectiveness is discussed. Two simple oscillators differently connected by serial spring-dashpot arrangement are used to simply simulate technically relevant cases: dissipatively coupled adjacent free-standing structures, structures equipped by TMD and base-isolated structures. Eigensolution loci of the two classes of systems are tracked against one or more significant parameters to determine the potential benefits realized by different combinations of stiffness and viscosity. In both studied cases, codimension-two manifolds in the four-parameter space corresponding to coalescing eigenvalues are determined by analytical expressions. Conditions to discern semi-simple eigenvalues from defective ones confirm that the latter is the generic case laying in a two-parameter space while the former span a one-parameter subspace. The knowledge of the location of the defective systems in the parameter space permits to determine regions with specific dynamical properties useful for control design purpose. PubDate: 2016-05-01

Abstract: This paper reports the results of a study into global and local conditions of uniqueness and the criteria excluding the possibility of bifurcation of the equilibrium state for small strains. The conditions and criteria are derived on the basis of an analysis of the problem of uniqueness of a solution involving the basic incremental boundary problem of coupled generalized thermo-elasto-plasticity. This work forms a follow-up of previous research (Śloderbach in Bifurcations criteria for equilibrium states in generalized thermoplasticity, IFTR Reports, 1980, Arch Mech 3(35):337–349, 351–367, 1983), but contains a new derivation of global and local criteria excluding a possibility of bifurcation of an equilibrium state regarding a comparison body dependent on the admissible fields of stress rate. The thermal elasto-plastic coupling effects, non-associated laws of plastic flow and influence of plastic strains on thermoplastic properties of a body were taken into account in this work. Thus, the mathematical problem considered here is not a self-conjugated problem. PubDate: 2016-04-05