Abstract: To increase the computational precision of the finite element method (FEM) for multi-field coupling problems, we proposed a coupling magneto-electro-elastic (MEE) cell-based smoothed radial point interpolation method (CM-CS-RPIM) with the coupling MEE Wilson- \(\theta \) scheme for MEE structures. Generalized approximation field functions were established by using the linearly independent and consistent RPIM shape functions. The basic equations of CM-CS-RPIM were deduced by applying G space theory and the weakened weak formulation to the MEE multi-physics coupling field. Meanwhile, the coupling MEE Wilson- \(\theta \) scheme was proposed. Several numerical examples were modeled, and the behavior of MEE structures was studied under static and dynamic loads. The CM-CS-RPIM outperformed FEM with higher accuracy, convergence, and stability in static and dynamic analysis of MEE structures, even if the meshes were distorted extremely. And it worked well with simplex meshes (triangles or tetrahedrons) that can be automatically generated for complex structures. Therefore, the effectiveness and potential of CM-CS-RPIM were demonstrated for the design of smart devices, such as MEE sensors and energy harvesters. PubDate: 2019-05-01

Abstract: The dynamic collapse response of metal self-similar hierarchical corrugated sandwich plates is analyzed. The analytical model is derived for the reaction forces of the top and bottom face sheets. Finite element analysis is conducted to investigate the dynamic collapse of the self-similar hierarchical corrugated sandwich cores. Collapse modes of cores are found compressed at different impact velocities. The analytical model captures the average reaction forces reasonably. The collapse mechanism maps are constructed with axes representing the slenderness ratio of the big and small struts for hierarchical corrugated sandwich cores and are in good agreement with numerical results. The results reveal that the increase in the velocity changes the dominant deformation modes of the collapse mechanism maps. The region of Euler buckling of small struts increases with increasing velocity. PubDate: 2019-05-01

Abstract: We employ a micropolar surface model, capable of incorporating bending and twisting rigidities, to analyze the fundamental problem of the deformation of a micropolar half-plane containing a single-edge dislocation. The surface model is based on a Kirchhoff–Love micropolar thin shell of separate elasticity perfectly bonded to the surrounding micropolar bulk. Combining micropolar elasticity with a higher-order surface model allows for the incorporation of size effects well known to be essential in, for example, continuum-based modeling of nanostructured materials. The corresponding boundary value problems are solved analytically using Fourier integral transforms. We illustrate our results by constructing the resulting stress distributions for the most general case of a micropolar material with surface stretching, flexural, and micropolar twisting resistance. To verify our results, we show that under appropriate simplifying assumptions, our solutions reduce to the corresponding solutions in the literature from classical elasticity and also to those which employ micropolar elasticity in the absence of surface effects. Finally, we report on the significance of the contribution of the newly incorporated surface and bulk parameters on the overall solution of the micropolar edge dislocation problem. PubDate: 2019-05-01

Abstract: Enlightened by the Caputo fractional derivative, the present study treats with a novel mathematical model of generalized thermoelasticity to investigate the transient phenomena for a fiber-reinforced hollow cylinder due to the influence of thermal shock and magnetic field in the context of a three-phase-lag model of generalized thermoelasticity, which is defined in an integral form of a common derivative on a slipping interval by incorporating the memory-dependent heat transfer. Employing Laplace transform as a tool, the problem has been transformed to the space domain, where the Galerkin finite element technique is incorporated to solve the resulting equations in the transformed domain. The inversion of the Laplace transform is carried out numerically on applying a method of Bellman et al. According to the graphical representations corresponding to the numerical results, conclusions about the new theory are constructed. Excellent predictive capability is demonstrated due to the presence of reinforcement, memory-dependent derivative, and magnetic field also. PubDate: 2019-05-01

Abstract: This paper presents a 3D nanostructure modal vibration analysis by using finite element models. The modal frequencies and corresponding modal shapes of silicon nanowires of various thickness against length ratios are determined by solving a linear structural eigenvalue problem for the 3D solid finite element model, where surface stress effects are taken into account by using the stress stiffness matrix. The cases of fixed/fixed and fixed/free boundary conditions at the nanowire ends are investigated. The results obtained by 3D solid models and models based on the beam bending theory have been compared with each other, as well as with the results obtained elsewhere in the literature computationally and experimentally. It has been shown that the effects caused by surface stresses are insignificant for wires with length-to-width ratio less than 10. PubDate: 2019-05-01

Abstract: In this work, a stochastic time domain spectral element method (STSEM) is proposed for stochastic modeling and uncertainty quantification of engineering structures. To perform the analysis, both an isotropic Timoshenko beam (TB) and a sandwich beam are considered. The sandwich beam is modeled considering higher-order sandwich panel theory which is capable of addressing the core flexibility. The material properties are considered as 1D non-Gaussian random fields, and optimal linear estimation (OLE) is used for the discretization of the random fields. The OLE-based discretization of a random field allows simulating the random fields numerically, resulting in realizations of the stiffness, mass matrix, and dynamic stiffness matrix. In the current work, the computationally efficient time domain spectral element method (TSEM) is used to develop the STSEM formulation. The STSEM reduces the CPU time significantly as the number of degrees of freedom (dof) is much smaller than in FEM. TSEM also provides a consistent diagonal mass matrix which reduces the computation cost in case of dynamic problems. The deflection statistics of the beam for static, free vibration and dynamic cases are investigated for both TB and sandwich beam. The computational efficiency of the proposed method and the effect of material variability on the response statistics are also discussed. Moreover, the effect of different correlation lengths on the response statistics is studied. PubDate: 2019-05-01

Abstract: In Part I, we presented a general micropolar plasticity theory which rests on a class of micropolar curvature tensors related to each other by mixed transformations. In this paper, we derive, in the context of the theory of Part I, a micropolar counterpart of v.Mises conventional plasticity with kinematic and isotropic hardening. The predictive capabilities of the resulting model are illustrated for the case of tension loading of plates with a circular hole. PubDate: 2019-05-01

Abstract: A new nonlinear model of a micropolar continuum is suggested. The peculiarity of the model is that the constitutive equations depend only on the strain measures associated with rotational degrees of freedom, and at the same time, the stress tensor turns out to be different from zero. This mathematical model has been created with the view of its use for modeling various processes, including processes at the micro-scale level. Following the terminology of nineteenth-century scientists, we call our model the ether model, though in its mathematical content, it differs from the nineteenth-century ether models very significantly. There may be different points of view concerning the physical meaning of our model. On the one hand, one can suppose the same meaning that nineteenth-century scientists implied in their ether models. On the other hand, one can imagine a continuum consisting of quasi- or virtual particles. The choice of one of the aforementioned physical interpretations is not important for constructing the mathematical model. Our method of modeling thermo- and electrodynamic processes is as follows. In the framework of our model, we introduce mechanical analogies of physical quantities such as temperature, entropy, the electric field vector, the magnetic induction vector. We show that under certain simplifying assumptions the equations of our model coincide with well-known equations, in particular, with Maxwell’s equations. We explore the properties of our mathematical model in its most general form, investigate what processes can be described in the framework of our model, and suggest a possible interpretation of these processes. PubDate: 2019-05-01

Abstract: This paper studies the effects of thermal stress on failure modes of soft matter with a sharp–hard inclusion. Two failure modes, i.e., interface failure and penetration failure, are found, and the influences of mechanical loading on each mode are discussed, respectively. Based on theoretical analysis, we get significant insight into the failure behavior of this soft–hard system. Finite element analysis is employed with consideration of the large deformation of the soft matter, and the results demonstrate the effectiveness of theoretical predictions within a large range of loads. The penetration of the soft matter is determined by the thermal expansion coefficient and the change in temperature. In addition, their effects on the categories of the failure mode are shown in a phase diagram. Suitable remote uniform stress fields can counteract the effects of thermal stresses at the tips of the inclusion and, therefore, counteract penetration or interface separation as well. This paper provides a convenient approach to evaluating failure modes and avoiding failure. PubDate: 2019-05-01

Abstract: A frequently used technological solution for reducing oscillations of rotors excited by imbalance, time-varying forces or ground vibrations consists in inserting damping devices in the rotor supports. To achieve their optimum performance in a wide range of operating speeds their damping effect must be controllable to be possible to adapt it to the current working conditions. This is enabled by application of magnetorheological squeeze film dampers. In mathematical models the magnetorheological oils are represented mostly by Bingham or Herschel–Bulkley theoretical materials. Recent experimental measurements carried out at several working places show that with respect to the shape of the flow curves obtained for different magnitudes of magnetic induction the real magnetorheological fluids behave like a bilinear material. This enables a more accurate implementation of magnetorheological fluids in mathematical models of squeeze film dampers. In addition, unlike the Bingham fluid the flow curve of a bilinear material is continuous which reduces the nonlinear character of the procedures for calculation of the hydraulic forces by which the oil film acts on the shaft journal and the rotor casing. A new developed mathematical model of a short magnetorheological squeeze film damper based on representing the lubricating oil by bilinear material was implemented in the computational procedures for analysis of the steady state response of a Jeffcott rotor loaded by a stationary force and by the weight and imbalance of the disc. The performed computational simulations proved that these procedures were numerically stable and arrived at the solution also in cases when the methods based on representing the magnetorheological oil by Bingham material failed. PubDate: 2019-05-01

Abstract: In this study, thermodynamic incompatibility issues of the thermo-mechanical coupling of the Bammann-temperature-dependent plasticity-damage internal state variable (ISV) model are investigated. The exclusion of the thermal expansion phenomena from the Helmholtz free energy, as assumed in the model, is proven to contradict the First and Second Law of Thermodynamics, as well as the omnipresence principle. Four different approaches are discussed to address those issues, and the inclusion of the thermal expansion as a dependent variable in the Helmholtz free energy is considered the most appropriate and efficient. Based on these findings, a multiphysics ISV theory that couples the elasto-visco-plasticity-damage model of Bammann with thermal expansion is presented in which the kinematics, thermodynamics, and kinetics are internally consistent. Other material models may benefit from the findings of this study and apply similar modifications with their thermo-mechanical couplings. PubDate: 2019-05-01

Abstract: A folded chain, with one end fixed at the ceiling and the other end released from the same elevation, is commonly modeled as an energy-conserving system in one dimension. However, the analytical paradigm in the existing literature is unsatisfying: The theoretical prediction of the tension at the fixed end becomes infinitely large when the free end reaches the bottom, contradicting the experimental observations. Furthermore, the dependency of the total falling time on the link number demonstrated in numerical simulations is still unexplained. Here, considering the link transition between the two sub-chains and the geometry of each link, we introduce an additional term for the relation of balance of kinetic energy to account for the jump of link velocity at the fold. We derive analytical solutions of the maximal tension as well as the total falling time, in agreement with simulation results and experimental data reported in previous studies. This theoretical perspective extends the classical standard treatment, shows a simple representation of the complicated two-dimensional falling chain system and, in particular, specifies the signature of the chain properties. PubDate: 2019-05-01

Abstract: This paper explores the integration of an internal state variable (ISV) model for polymers (Bouvard et al. in Acta Mech 213(1):77–96, 2010; Int J Plast 42:168–193, 2013) with damage evolution (Horstemeyer and Gokhale in Int J Solids Struct 36:5029–5055, 1999; Horstemeyer et al. in Theor Appl Fract Mech 33(1):31–47, 2000; Francis et al. in Int J Solids Struct 51:2765–2776, 2014) into a multiphase ISV framework (Rajagopal and Tao in Advances in mathematics for the applied sciences, World Scientific, Singapore, 1995; Bammann in Proceedings of 2nd international conference on quenching and the control of distortion, vols 4–7, 1996) that features a finite strain theoretical framework for fiber-reinforced polymer (FRP) composites under various stress states, temperatures, strain rates, and history dependencies. In addition to the inelastic ISVs for the polymer matrix and interphase, new ISVs associated with the interaction between phases are introduced. A scalar damage variable is employed to capture the damage history of the FRP, which comprises three damage modes: matrix cracking, fiber breakage, and deterioration of the fiber–matrix interface. The constitutive model developed herein employs standard postulates of continuum mechanics with the kinematics, thermodynamics, and kinetics being internally consistent, whose ISVs can be either calculated from molecular dynamics simulations or calibrated through microstructural characterizations for specific FRPs. The developed elastothermoviscoplasticity and damage modeling framework is then employed to model the internal damage evolution of a glass fiber-reinforced polyamide 66 (Rolland et al. in Compos Part B Eng 90:65–377, 2016) in terms of above three damage mechanisms. A detailed description of the model parameter identification process is given by using the example of a unidirectional glass fiber-reinforced epoxy, and the mechanical behaviors and properties of the composites at varying temperature and fiber volume fraction are predicted by the model, which are in good agreement with the experimental result. PubDate: 2019-05-01

Abstract: To reveal the dynamic mechanical behavior of frozen soil under impact loading, nine groups of frozen-soil samples (the initial moisture content was 20%) under different experimental conditions are tested using the split Hopkinson pressure bar. In this study, a constitutive model for predicting the dynamic strength and compression deformation of frozen soil subjected to impact loading is developed. The model is derived from continuous fracture mechanics, and we assume that frozen soil is a continuous medium with preexisting microcracks. According to the modified Drucker–Prager criterion, a dynamic constitutive model coupled with the plastic and damage phase is established to describe the dynamic mechanical behavior of frozen soil before the peak stress. Considering the post-peak curve, the statistical significance of the uniform stress–strain relationship is not established; therefore, a cohesive crack model is used to model the frozen-soil softening process. Using a comparison, we find that the results of the experiment agree well with the calculated results; thus, the feasibility of the model is proven. PubDate: 2019-05-01

Abstract: Inspired by the seminal works of Eshelby (Philos Trans R Soc A 244A:87–112, 1951, J Elast 5:321–335, 1975) on configurational forces and of Noll (Arch Ration Mech Anal 27:1–32, 1967) on material uniformity, we study a thermoelastic continuum undergoing volumetric growth and in a dynamical setting, in which we call the divergence of the Eshelby stress the Eshelby force. In the classical statical case, the Eshelby force coincides with the negative of the configurational force. We obtain a differential identity for the modified Eshelby stress, involving the torsion of the connection induced by the material isomorphism of a uniform body, which includes, as a particular case, that found by Epstein and Maugin (Acta Mech 83:127–133, 1990). In this identity, the divergence of the modified Eshelby stress with respect to this connection of the material isomorphism takes the name of modified Eshelby force. Moreover, we show that Eshelby’s variational approach (1975) can be used to formulate not only the balance of material momentum, but also the balance of energy. In this case, we find that what we call Eshelby power is the temporal analogue of the Eshelby force, and we obtain a differential identity for the modified Eshelby power. This leads to concluding that the driving force for the process of growth–remodelling is the Mandel stress. Eventually, we find that the relation between the differential identities for the modified Eshelby force and modified Eshelby power represents the mechanical power expended in a uniform body to make the inhomogeneities evolve. PubDate: 2019-05-01

Abstract: When formulating finite deformation micropolar plasticity, the structure of the theory strongly depends on the choice of the variables describing the deformation kinematics. This holds true even for classical plasticity. However, in contrast to classical plasticity, the set of kinematical variables in micropolar plasticity includes, besides strain tensors, so-called micropolar curvature tensors. There are only a few investigations addressing such aspects, so the aim of the paper is to highlight the effect of a specific micropolar curvature kinematics on the structure of a micropolar plasticity. We do this by developing a general finite deformation micropolar plasticity, which relies upon a class of micropolar curvature tensors related to each other by mixed transformations. That means, the pull-back and push-forward transformations characterizing the class involve both deformation gradient and micropolar rotation tensors. The curvature kinematics is discussed by using geometrical methods developed previously. The plasticity theory is based on the assumption that the yield function and the flow rules are functions of specific micropolar Mandel’s stress tensors. The definition of the Mandel’s stress tensor is suggested by the adopted curvature kinematics and reveals a characteristic feature of the resulting plasticity. Moreover, the presence of curvature variables in plastic arc length gives reason to introduce a characteristic internal material length, which in turn seems to urge the form of the formulation of the theory. A specific version of von Mises micropolar plasticity with kinematic and isotropic hardening, derived in the theoretical context of the present paper, is elaborated in Part II. PubDate: 2019-05-01

Abstract: This paper presents a solution of the elastic fields of a half-plane composite structure containing distributed multiple circular inhomogeneities under boundary loading. The solution is obtained with a semi-analytical approach by combining the Green’s function and the equivalent inclusion method. This approach can achieve high accuracy and can be easily implemented with less computational effort compared with other numerical methods. Then, this solution is further used to explore the boundary effects on the elastic fields and effective elastic properties of the half-plane composite structure containing square periodically distributed circular inhomogeneities. Influences of the boundary and the inhomogeneity volume fraction on the elastic fields are examined in detail. Local effective elastic constants of the composite structure are predicted using the unit cells. The results show that the boundary has a significant effect on the elastic fields and elastic properties of the half-plane composite structure. The average displacement predicted with the conventional effective elastic constants of unit cells may deviate from the real value. Thus, we propose a design of a composite structure with a uniform elastic constant and develop an analytical model to calculate the average displacement. PubDate: 2019-05-01

Abstract: The fast and precise positioning of flexible mechanical structures is often corrupted by the unwanted dynamics in the form of a residual vibration. Therefore, we would like to find an appropriate control strategy that is capable to suppress this effect. The control strategies can be basically divided into two main groups: feedback control and feedforward control. The feedback control with the information from integrated sensors is capable to ensure the stability and robustness, but it may require large actuator effort, and it may be difficult to design satisfactory controllers for rapid movements. The feedforward methods including command/input shaping are based on the model of the system and usually require no additional sensors. They can significantly eliminate residual vibration, but feedforward methods cannot deal with disturbances, and the quality of their performance is strongly determined by the precision of the used model on which they are based. This paper proposes the novel solution to these problems, the so-called SHAVO (SHAper \(+\) serVO control) strategy that combines advantages of both approaches. Compared to other methods combining command shaping and feedback controller, the SHAVO approach differs in two key features. Firstly, it uses a different structure, the model of the system is used not only for shaper synthesis but also for predicting system outputs and states. Secondly, the shaper itself is highly optimized with arbitrary adjustable time length, not an impulse series, not limited by the system’s natural frequency. PubDate: 2019-05-01

Abstract: The telegraph equation \(\tau \partial ^2 u/\partial t^2 + \partial u/ \partial t = \tau c^2 \partial ^2 u / \partial x^2\) arises in studies of waves in dissipative media with a damping coefficient \(1/\tau \) , or from a Maxwell–Cattaneo type heat conduction with a relaxation time \(\tau \) . To elucidate basic properties of this equation, two harmonic wave solutions are compared: (1) temporally attenuated and spatially periodic (TASP) and (2) spatially attenuated and temporally periodic (SATP). The phase velocities of both waves are equal to the energy velocities and less than the group velocities. The phase velocities of the two waves are different, and less than c, but both naturally lead to a speed c for the propagation of discontinuities. The two harmonic wave solutions are suitable for different initial-boundary value problems: TASP for those with space periodicity and SATP for those with time periodicity. The asymptotic behaviors of the harmonic wave solutions when the telegraph equation transitions into a nondissipative wave equation or into a parabolic diffusion equation are presented. Only the SATP waves survive when the equation turns parabolic. The spectral finite element method is formulated for 1d Maxwell–Cattaneo heat conduction based on the SATP wave solutions. The element thermal conductivity matrix is reduced to that for a conventional (nonspectral) finite element when the frequency tends to zero. PubDate: 2019-05-01

Abstract: A PN junction between two types of piezoelectric semiconductors (PSCs) is analyzed based on the fully coupled nonlinear equations of PSCs without any assumptions. A perturbation theory is employed to obtain the analytical solution of the considered nonlinear problem. A general solution to one-dimensional problems for PSCs is represented by a sum of a series of perturbation solutions. Typical properties including the electromechanical fields, built-in potential and the current–voltage characteristics of the piezoelectric PN junction are investigated for conditions of mechanical loading combined with a bias. The results reveal that the simplified linear (i.e., first-order perturbation) solution reported in the literature fails to describe the nonlinear characteristics, such as current–voltage characteristics of the piezoelectric PN junction, although it can give the electromechanical fields as well as concentrations of the electrons and holes near the interface of the PN junction for small carrier concentration perturbations. The presented nonlinear solution is valid and corresponds closely with the numerical solutions based on the commercial software COMSOL. PubDate: 2019-05-01