Principle Of Dissipation Research Articles

Nonlinear electromechanical coupling in ferroelectric materials: large deformation and hysteresis

Smart materials respond to external stimuli, e.g., electric fields, which enables their use as sensors and actuators. The electromechanical coupling of the direct and converse piezoelectric effects, for instance, is used for both actuation and sensing in diverse engineering applications. The response of ferroelectric materials depends on their state of remanent polarization and the presence of an external electric field. To extend the operational range of sensors and actuators, an accurate understanding of the evolution of the material’s state of polarization is imperative, which requires both physical and geometric nonlinearities to be taken into account. Moreover, polymeric smart materials like PVDF allow significantly larger deformation as compared to conventional piezoelectric ceramics. The electromechanical coupling in piezoelectric materials manifests in ferroelectric and ferroelastic hystereses, which are related to both reversible and irreversible processes. Focusing on the latter, we transfer phenomenological models for domain switching in ferroelectric materials to the geometrically nonlinear regime. For this purpose, we follow related concepts of geometrically nonlinear elastoplasticity, where the concept of a multiplicative decomposition of the deformation gradient plays a key role. Accordingly, an additional deformation path that describes the evolution of the poled state from the unpoled referential configuration is introduced. The constitutive response of the material to mechanical and electrical loads is discussed, and dissipative internal forces that drive the evolution of the remanent polarization are derived within a thermodynamical framework and the principle of maximum dissipation.

A tribological model for geometrically structured anisotropic surfaces in a covariant form

AbstractThis contribution proposes a tribological model within a three‐dimensional contact formulation considering structural anisotropy of the contact interface. A simple elastoplastic constitutive law is adopted for the description of the behavior on the anisotropic contact interface. Starting with the establishment of the thermodynamic framework of the contact problem, the dissipative, irreversible process is described. By applying the principle of maximum dissipation, the evolution equations and the expressions of the tangential contact forces for the cases of sticking and sliding are obtained and, subsequently, formulated in algorithmic form, in order to enable their implementation into finite element codes. The anisotropic behavior is incorporated through the definition of a tensor of anisotropy. The form of this tensor is defined in a general curvilinear coordinate system. The cases of both constant and nonconstant anisotropic tensor are studied. The analytical solution of a numerically computed problem, serves the validation of the proposed model.

From thermomass energy to dark energy: Re-exploration to the origin of dark energy

Dark energy constitutes 68% of the matter of our universe, which has been successfully used in the standard cosmological model to explain the phenomenon of cosmic acceleration. However, the scholars still have different opinions in the origin of dark energy, making it one of the most important unsolved problems in the modern cosmology. There are several candidates to explain the origin of dark energy, such as vacuum energy, scalar field theory, light pressure, etc. However, all these models are still in debate and we are far from a commonly agreed theory to understand the true nature of dark energy. In this report, we intend to re-explore some fundamental properties and the origin of dark energy from the perspective of thermomass theory in the framework of energy conservation principle. Thermomass theory is a newly developed theory in the field of heat transfer, including some new physical quantities, such as thermomass, thermomass velocity, thermomass energy, etc. Thermomass is the relativistic mass of heat and thermomass energy is the relativistic energy. Based on the thermomass theory, the heat transfer can be understood as the direct flow of thermomass under a certain temperature gradient. Then the principle of fluid mechanics can be used to solve the heat transfer problems and a general heat conduction law has been established. Some non-Fourier heat transfer phenomena under the extreme conditions, such as ultrafast laser heating, ultrahigh heat flux at nanoscales, can be well explained by using the general heat conduction law. Meanwhile, a simplified expression of thermomass energy was defined as entransy. Guided by a minimum entransy dissipation principle, the structure of a complicated heat exchanger network can be optimized to increase the energy efficiency. Both the general heat conduction law and entransy model have been experimentally validated. The thermomass theory have been widely accepted and applied in the field of thermal science. But a question still remains: The thermomass energy dissipates during the heat transfer process, where does it go? Actually, we find an answer that the dissipated thermomass energy is closely related with the dark energy. Under the normal temperature and pressure conditions, the order of magnitude of thermomass and its energy is much smaller than that of the static mass and its energy. In the beginning of the Big Bang, the temperature exceeds 1015°C and the thermomass energy equals to or even is larger than the energy of static mass. According to the energy conservation principle, the energy at high level, i.e., electrical energy, optical energy, mechanical energy, etc., will dissipate into the energy at low level, i.e., heat. But in the heat transfer process, heat (thermomass) is conserved, while the thermomass energy will dissipate into a lower level, “invisible” energy. This kind of energy has four features: Filling the whole space, ultra-low energy density, negative pressure and gradually accumulated with time. All these features are in consistence with the performance of dark energy. Hence, we hypothesize that the dark energy comes from the dissipated thermomass energy, which is the motivating force of the cosmic acceleration and forms the main body of our universe.

Anisotropic and curved lattice members enhance the structural integrity and mechanical performance of architected metamaterials

Architected metamaterials exhibit unique properties bestowed by their engineered structure rather than their chemical composition. Extrinsic material properties have been achieved as a result of advances in additive manufacturing. Contemporary fabrication techniques, such as multiphoton lithography and digital light processing, have enabled the fabrication of complex structures with inherent hierarchies at length scales ranging from nanometers to micrometers. However, despite significant insight into the role of buckling in the mechanical behavior of materials reported in earlier studies, particularly strength and energy dissipation, the structural and design principles responsible for the improved mechanical performance were not fully elucidated, thus limiting the design space of these structures. The principal objective of this study was to investigate how controlled three-dimensional assembly and orientation of intertwined lattice members influence localized buckling and the overall mechanical response of such metamaterial structures. The novelty of the present design approach stems from a mechanical metamaterial inspired by the three-compound octahedron and the symmetry variance observed during phase change of crystalline solids. For a specific orientation and tactical joining of the unit cells, this geometry demonstrates unprecedented resilience to large deformations and high energy dissipation capacity. The selective shape modification of specific lattice members is shown to greatly improve the structural integrity of ultralight structures undergoing large deformation. Results from finite element simulations and in situ scanning electron microscopy-microindentation experiments reveal the actual deformation of metamaterial structures with straight and curved lattice members and elucidate the effects of anisotropy and orientation characteristics on the dominant mechanisms affecting the mechanical performance of intertwined lattice structures.

Development of Programmable Logic Array for Multiple-Valued Logic Functions

The binary information technology reaches its limits set by the atomic size miniaturization, by calculation speed and by the fundamental principle of energy dissipation per bit processing. Employing multiple-valued logic (MVL) cells as computing and memory units reduces energy losses and enables to pack of unprecedented high-density information, but the current silicon-based material technologies have been studied marginally for the material realization of MVL devices. Here, we propose to use the ferroelectrics for the implementation of MVL units using their ability to pin the polarization as a sequence of multistable states. More specifically, the realization of a programmable logic array (PLA) based on MVL units is considered with the application of the ferroelectrics technology in implementation of memory units. The specific of the PLA construction is the use of generalized Reed-Muller expression for the representation of an MVL function. In this article, several possible implementations of such PLAs are considered, and their properties are analyzed from the logic design point of view.

Grain Boundary Triple Junction Dynamics: A Continuum Disconnection Model

The microstructure of polycrystalline materials consists of networks of grain boundaries (GBs) and triple junctions (TJs), along which three GBs meet. The evolution of such microstructures may be driven by surface tension (capillarity), applied stresses, or other means that lead to a jump in chemical potential across the GBs. Here, we develop a model for the concurrent evolution of the GB/TJ network based upon the microscopic mechanism of motion; the motion of line defects (disconnections) in the GB that have both dislocation and step character. The evolution involves thermally-activated disconnection formation/annihilation and migration of multiple disconnections modes/types. We propose this crystallography-respecting continuum model for the disconnection mechanism of GB/TJ dynamics derived with a variational approach based on the principle of maximum energy dissipation. The resultant TJ dynamics is reduced to an optimization problem with constraints that account for local microstructure geometry, conservation of Burgers vectors, and thermal-kinetic limitations on disconnection fluxes. We present analysis of and numerical simulations based upon our model to demonstrate the dependence of the GB and TJ mobilities and the TJ drag effect on the disconnection properties, and compare the predictions with molecular dynamics and experimental observations.

Minimum Required Distance of Strain Gauge from Specimen for Measuring Transmitted Signal in Split Hopkinson Pressure Bar Test

The minimum required distance of the strain gauge on the transmitted bar of the split Hopkinson bar has been determined from the position of a metallic specimen via an explicit finite element analysis. The minimum required distance was determined when the strain-time profiles at r = 0, 0.5Ro and 1.0Ro, were coincident (r is the radial position and Ro is the radius of the bar.). The determined minimum required distance, f(x), is presented as a function of the relative specimen diameter to that of the bar (x = D/D0): j(x) = - 0.9385.x3 + 0.6624.x2 - 0.7459.x + 1.4478 (0.1 ≤ x ≤ 0.9). This result demonstrates the Saint-Venant's principle of rapid dissipation of localized stress in transient loading. The result will be useful for the design/modification of the pseudo-one-dimensional impact instruments that utilise a stress pulse transmitted through the specimen. The result will also allow one to avoid unnecessarily remote strain gage position from the specimen.

Application of Generalized Reed–Muller Expression for Development of Non-Binary Circuits

Semiconductor devices and binary information technology reach their limits set by the atomic size of miniaturization, calculation speed, and the fundamental principle of energy dissipation per bit processing. Therefore, new technologies in logic design and mathematical approaches must be investigated. Application of multiple-valued logic (MVL) in logic design allows developing gates and circuits with more than two stable states. This enables packing an unprecedented high-density of information. Based on this idea, a new technique of the programmable logic arrays (PLA) construction based on MVL units is considered. The unique aspect of this technique is the application of recurrent generalized Reed–Muller expression (GRME) for MVL function representation. The recurrent procedure for this expression’s construction is considered and applied in the PLA development. The proposed structure of PLA consists of two blocks that are memory and logic block. In this paper, we also consider the possibility to use the ferroelectrics for the implementation of cells of the memory block of PLA. The development of gates with multi-stable states is possible by the ferroelectrics ability to pin the polarization as a sequence of stable states.

Study on a New Combined Anti-Galloping Device for UHV Overhead Transmission Lines

These years, galloping of bundle conductors has severely threatened the safety of overhead transmission lines and caused enormous losses of economy. So, it is noted that the studies on the development of effective anti-galloping devices, have a great significance for resisting the galloping disaster of a power system and for improving the safe and stable operation of the grids. In this paper, a new combined anti-galloping device, based on the principles of energy dissipation, restraining the torsion, and detuning, was developed for ultra-high voltage overhead transmission lines. To perform such analysis, the combined anti-galloping design method was presented and the new applicable device was developed on the rotation-free spacer damper. Then, the arrangement of this new anti-galloping device was detailed and the efficiency assessment was carried out for verifying its galloping deterrence effect. Finally, the elastic and damping tests, the high voltage tests as well as the fatigue tests were realized to prove that the device designed satisfies the necessary requirements of overhead transmission lines.

An energy approach to Modified Cam-Clay plasticity and damage modeling of cohesive soils

An alternative approach to Modified Cam-Clay (MCC) critical state plasticity coupled with damage is proposed. The provided hyper-elastoplastic/damage framework is motivated by a desire to ensure thermodynamic consistency of model predictions, and is shown to satisfy the principle of maximum plastic dissipation, enabling enforcement of the plastic dissipation (and Clausius–Planck) inequality. A small strain Eshelby-like stress is derived as being energy-conjugate to the plastic strain rate, and relation to the damage-energy release rate is exploited to pose a coupled damage/yield MCC criteria (MCC-D). Relations between volumetric damage and porosity changes are examined, along with a method for estimating the damage state from bulk moduli measurements. The model is shown to simulate well existing high pressure compression measurements of Boulder clay, and connections between damage-related model parameters and behavior exemplifying different microstructural states is examined through numerical experiments.

Thermodynamic Optimization of Water-Cooled Infrastructure for Vehicle Lithium–Ion Battery Based on Exergy

Electric vehicle technology is developing rapidly with the attention of energy and environmental issues, lithium–ion batteries as the important component are widely used for their superior performance. However, batteries generate a lot of heat during operation. If not cooled in time, heat will accumulate in the battery package, causing a rapid temperature rise and an increasing temperature nonuniformity. Thermodynamic analysis based on the least exergy dissipation principle is to optimize both the configuration and operating strategy of a water-cooled system for the vehicle lithium–ion battery packages. Four typical structures and 24 packages of 96 lithium–ion single batteries from an e-powered SUV were designed and tested to verify the exergy-based optimization. The test results showed a good agreement with the theoretical analysis and prediction. Under various battery discharging conditions, the best thermal performance was observed when the cooling water was inlet to the middle-positioned battery packages, at which the measured maximum temperature gradient among the 24 battery packages can be controlled within 3.1 K, much lower than the other three configurations, and the measured peak temperature was 1.1–5.9 K lower than the other three configurations.

Small strain crystal plasticity based on the primal‐dual interior point method

AbstractThe paper presents a novel approach for rate‐independent single crystal plasticity based on the Infeasible Primal‐Dual Interior Point Method in a small strain framework. Therein, the principle of maximum dissipation together with the yield functions on the slip systems in the crystal are considered as the constrained optimization problem. The constraint conditions adapted using slack variables and a Lagrangian is formulated using barrier functions. The equations are linearized and solved using Newton's method. Numerical examples are presented for slip on the individual slip systems in a single crystal under global rotation.

Mechanical Properties of a Novel Plastic Hinge Seismic Fuse Based on Frictional Energy Dissipation to Avoid Brittle Failures in Beam-to-Column Moment-Resistant Joints

Traditional steel structure joints are prone to brittle failure under seismic excitation, and it is difficult to precisely control the location of the resulting plastic hinge or repair these joints after an earthquake. Therefore, based on the energy dissipation principle of the friction pendulum isolation bearing and automobile braking device, a low-cost friction-based plastic hinge (PH) joint is proposed to provide predictable energy dissipation and realize quickly repairable structures. The proposed PH was analysed theoretically, and five half-scale specimens using different bolt and friction materials were tested using cyclic reversing load. The test results showed that models PH-1 and PH-2 with Grade 4.8 and 8.8 limiting bolts, respectively, both provided a plastic rotation angle greater than 0.03 rad, exhibited experimental moment capacities of 0.91 and 0.93 times their theoretical capacities, and exhibited ductility coefficients of 2.75 and 3.14, respectively. It was found that high-strength limiting bolts were unsuitable as they damaged difficult-to-replace PH components. The selected PH configuration experienced damage to only the limiting bolts and friction plates and exhibited good plastic deformation capacity and hysteretic energy dissipation performance that met the plastic rotation, ductility, and friction energy dissipation requirements. Thus, the proposed PH can be used to improve the seismic performance of beam-to-column joints and the frames they form.

The Generalized Stochastic Smoluchowski Equation

We study the dynamics of a system of overdamped Brownian particles governed by the generalized stochastic Smoluchowski equation associated with a generalized form of entropy and involving a long-range potential of interaction [P.H. Chavanis, Entropy 17, 3205 (2015)]. We first neglect fluctuations and provide a macroscopic description of the system based on the deterministic mean field Smoluchowski equation. We then take fluctuations into account and provide a mesoscopic description of the system based on the stochastic mean field Smoluchowski equation. We establish the main properties of this equation and derive the Kramers escape rate formula, giving the lifetime of a metastable state, from the theory of instantons. We relate the properties of the generalized stochastic Smoluchowski equation to a principle of maximum dissipation of free energy. We also discuss the connection with the dynamical density functional theory of simple liquids.

Plane-stress constrained multiplicative hyperelasto-plasticity with nonlinear kinematic hardening. Consistent theory based on elastic corrector rates and algorithmic implementation

Small-strain plane-stress projected formulations are typically employed in 2D, plate and thin membrane problems because of their efficiency. However, at large strains, equivalent algorithms have been precluded by the difficulties of kinematics, specially using the multiplicative decomposition and nonlinear kinematic hardening. In this paper, we present a plane-stress constrained formulation for large strain multiplicative hyperelasto-plasticity based on the novel framework which uses elastic strain corrector rates. The proposed plane-stress projected model is consistent with the principle of maximum dissipation as in the 3D/plane-strain case, and it is valid for any stored energy function (e.g. for soft materials). Hyperelasticity-based nonlinear kinematic hardening at large strains, which preserves Masing's rules if desired, is also included in the formulation. The consistent tangent moduli tensor for the plane stress subspace is also derived to provide the asymptotic second order convergence of Newton algorithms during global equilibrium iterations. Some numerical examples are presented in order to evaluate both the congruency with the equivalent 3D formulation and the numerical performance of the proposed plane-stress projected algorithm.

Entransy functions for steady heat transfer

In this paper, the entransy functions for steady heat transfer are summarized and discussed based on the variational theory and the entransy theory. The entransy functions for steady convective heat transfer are derived for the first time. In steady heat transfer processes, it is shown that the steady distributions of heat flux and temperature (radiative thermal potential) should make the corresponding entransy functions reach their minimum values when the temperature (radiative thermal potential) or the heat flux of the boundary is given. The extremum entransy dissipation principles and the minimum entransy-dissipation-based thermal resistance principles are compared with the entransy functions It is shown that the entransy functions can describe a steady state, but cannot directly give a way to optimize heat transfer processes, while the extremum entransy dissipation principles and the minimum entransy-dissipation-based thermal resistance principles act in an opposite way.

Research on Fractal Characteristics and Energy Dissipation of Concrete Suffered Freeze-Thaw Cycle Action and Impact Loading.

In order to study the fractal characteristics and energy dissipation of concrete suffered freeze-thaw cycle actions and impact loading, C35 concrete was taken as the research object in this paper, and freeze-thaw cycle tests were carried out with a freeze-thaw range of −20 °C~20 °C and a freeze-thaw frequency of 0~50 times. The degradation characteristics of concrete material and the variation rules of basic physical parameters under various freeze-thaw cycle conditions were obtained consequently. By using the SHPB (separated Hopkinson pressure bar) test device, impact compression tests of concrete specimens under different freeze-thaw cycle actions were developed, then the process of impact crushing and the mechanism of damage evolution were analyzed. Based on the screening statistical method and the fractal theory, the scale-mass distribution rules and fractal dimension characteristics of crushing blocks are investigated. Furthermore, the absorption energy, fracture energy and block kinetic energy of concrete under different conditions were calculated according to the energy dissipation principle of SHPB test. The relationship between the energy consumption density and the fractal dimension of fragments was established, and the coupling effect mechanism of freeze-thaw cycle action and strain rate effect on the fractal characteristics and energy consumption was revealed additionally. The research results show that the concrete under different freeze-thaw cycle conditions and impact loading speeds has fractal properties from the microscopic damage to the macroscopic fracture. The energy dissipation is intrinsically related to the fractal characteristics, and the energy consumption density increases with the increase of the fractal dimension under a certain freeze-thaw cycle condition. When at a certain loading speed, with the growth of freeze-thaw cycles, the energy consumption density reduces under the same fractal dimension, while the fractal dimension improves under the same energy consumption density.

A constitutive model for rock based on energy dissipation and transformation principles

The study on constitutive relations is of great significance to the understanding of the complex mechanical properties and failure criteria of rock. The establishment of a scientific rock constitutive model can provide theoretical support for engineering safety and geological disaster prevention. From the view point of energy, a new rock constitutive model under triaxial compression was developed by connecting the law of energy transformation with the mechanical properties of rock in the paper. First, the concepts of elastic energy conversion rate and elastic energy conversion function were proposed to describe principles of energy dissipation and energy transformation in the whole stress-strain process of rock. And, a mathematical description was made of the work of external force transforming into elastic energy. Second, assumptions were proposed to describe the evolution laws of some important mechanical parameters. Finally, the quasi-static constitutive model for rock under triaxial compression based on conservation of energy was established, combining theories of damage mechanics and thermodynamic, and the fitted results of this constitutive model were compared to experimental data of sandstone under triaxial cyclic loading tests. The rationality of the constitutive model for rock was proved by describing the whole stress-strain process of triaxial compression under different confining pressures. And, the model can describe the initial compaction stage and residual stress of stress-strain curve, which can reflect the nonlinear characteristics of rock.

Unified variational theory of reversible and irreversible dynamics - Discovery of dissipative Lagrangians weighted in time.

Reversible dynamics is well-known to obey variational principles based on the action being the time integral of a Lagrangian with time-reversal symmetry. The purpose of the present paper is to find dissipative Lagrangians giving variational principles in dissipative dynamics with broken time-reversal symmetry. Conceptually the present theory insists on new Least Dissipation & Work Principles (LDWP) based on variational integrals weighted in time, in order to unify variational principles of physics including irreversible processes on many-body systems. This is also closely related to the present author’s theory of entropy production in Kubo’s scheme of transport phenomena and all nonlinear responses beyond. Through these investigations, we can understand the meaning (as a variational integral) of the action of reversible dynamics.

Non-local Thermoelasticity Based on Equilibrium Statistical Thermodynamics

The purpose of this work is the formulation of energetic constitutive relations for thermoelasticity of non-simple materials based on atomistic considerations and equilibrium statistical thermodynamics (EST). In particular, both (unrestricted) canonical, and (restricted) quasi-harmonic, formulations are considered. In the canonical case, (spatial) non-locality results from relaxation of the assumption that atoms subject to continuum deformation change position uniformly and affinely. In the quasi-harmonic case, the analogous assumption on mean atomic position (i.e., Cauchy-Born) is relaxed. Two types of spatial non-locality, i.e., strong and weak, are considered. In the former case, atomic position (or mean position) is a functional of the deformation gradient boldsymbol{F}, while in the latter, this functional is approximated by a function of boldsymbol{F} and its higher-order gradients nabla^{1}!boldsymbol{F},ldots ,nabla^{n}!boldsymbol{F}. On this basis, canonical and quasi-harmonic non-local model relations are obtained for the thermoelastic free energy, entropy, internal energy, and stress. In addition, such relations are formulated for thermoelastic material properties (e.g., stiffness).In the second part of the work, basic relations from the continuum thermodynamics of (non-polar) simple materials are generalized to higher-order deformation gradient (i.e., weakly non-local) continua and applied to energetic thermoelasticity. The corresponding formulation is based in particular on (i) Euclidean frame-indifference of the energy balance and (ii) the dissipation principle. As in the standard case, necessary for (i) is linear momentum balance and the symmetry of the (generalized) Kirchhoff stress (i.e., angular momentum balance). In the context of (ii), the free energy density determines in particular the first Piola-Kirchhoff stress boldsymbol{P}, the higher-order stress measures conjugate to nabla^{1}!boldsymbol{F},ldots ,nabla^{n}!boldsymbol{F}, as well as the generalized Kirchhoff stress. Modeling the phenomenological free energy on the corresponding (weakly non-local) canonical free energy yields EST-based constitutive forms for the entropy, all stress measures, and thermoelastic material properties. Alternatively, one can model the former energy as an approximation to the latter. An example of this for the second-order (n=2) case is discussed both theoretically and computationally in the last part of the work.