Nonlinear analysis on electrical properties in a bended composite piezoelectric semiconductor beam

In this paper,the interactions between the transverse loads and the electrical field quantities are investigated based on the nonlinear constitutive relation.By considering a composite beam consisting of a piezoelectric semiconductor and elastic layers,the nonlinear model is established based on the phenomenological theory and Euler’s beam theory.Furthermore,an iteration procedure based on the differential quadrature method(DQM)is developed to solve the nonlinear governing equations.Before analysis,the convergence and correctness are surveyed.It is found that the convergence of the proposed iteration is fast.Then,the transverse pressure induced electrical field quantities are investigated in detail.From the calculated results,it can be found that the consideration of nonlinear constitutive relation is necessary for a beam undergoing a large load.Compared with the linear results,the consideration of the nonlinear constitutive relation breaks the symmetry for the electric potential,the electric field,and the perturbation carrier density,and has little influence on the electric displacement.Furthermore,the non-uniform pressures are considered.The results show that the distributions of the electric field quantities are sensitively altered.It indicates that the electrical properties can be manipulated with the design of different transverse loads.The conclusions in this paper could be the guidance on designing and manufacturing electronic devices accurately.

Constitutive equations of 1060 pure aluminum based on modified double multiple nonlinear regression model

In order to study the work-ability and establish the optimum hot formation processing parameters for industrial 1060 pure aluminum, the compressive deformation behavior of pure aluminum was investigated at temperatures of 523?823 K and strain rates of 0.005?10 s?1 on a Gleeble?1500 thermo-simulation machine. The influence rule of processing parameters (strain, strain rate and temperature) on flow stress of pure aluminum was investigated. Nine analysis factors consisting of material parameters and according weights were optimized. Then, the constitutive equations of multilevel series rules, multilevel parallel rules and multilevel series &parallel rules were established. The correlation coefficients (R) are 0.992, 0.988 and 0.990, respectively, and the average absolute relative errors (AAREs) are 6.77%, 8.70% and 7.63%, respectively, which proves that the constitutive equations of multilevel series rules can predict the flow stress of pure aluminum with good correlation and precision.

Large deflections of non-prismatic nonlinearly elastic cantilever beams subjected to non-uniform continuous load and a concentrated load at the free end

This work studies large deflections of slen- der, non-prismatic cantilever beams subjected to a combined loading which consists of a non-uniformly distributed con- tinuous load and a concentrated load at the free end of the beam. The material of the cantilever is assumed to be non- linearly elastic. Different nonlinear relations between stress and strain in tensile and compressive domain are considered. The accuracy of numerical solutions is evaluated by com- paring them with results from previous studies and with a laboratory experiment.

Dynamic mechanical behavior and nonlinear hyper-viscoelastic constitutive model of SiO_(2) particle-reinforced silicone rubber composite:experimental and numerical investigation

SiO_(2)-particle reinforced silicon rubber composite(SP-RSRC)is a widely utilized material that offers shock absorption protection to various engineering structures in impact environments.This paper presents a comprehensive investigation of the mechanical behavior of SP-RSRC under various strain rates,employing a combination of experimental,theoretical,and numerical analyses.Firstly,quasi-static and dynamic compression tests were performed on SP-RSRC utilizing a universal testing machine and split Hopkinson pressure bar(SHPB)apparatus.Nonlinear stress-strain relationships of SP-RSRC were obtained for strain rates ranging from 1×10^(−3) to 3065 s^(−1).The results indicated that the composite showed evident strain rate sensitivity,along with nonlinearity.Then,a nonlinear visco-hyperelastic constitutive model was developed,consisting of a hyperelastic component utilizing the 3rd-order Ogden energy function and a viscous component employing a rate-dependent relaxation time scheme.The model accurately characterized the dynamic mechanical response of SP-RSRC,effectively mitigating the challenge of calibrating an excessive number of material parameters inherent in conventional viscoelastic models.Furthermore,the simplified rubber material(SRM)model,integrated within the LS-DYNA software,was chosen to depict the mechanical properties of SP-RSRC in numerical simulations.The parameters of the SRM model were further calibrated based on the strain-stress relationships of SP-RSRC,as predicted by the developed nonlinear visco-hyperelastic constitutive model.Finally,an inverse ballistic experiment using a single-stage air gun was conducted for SP-RSRC.Numerical simulations of SHPB experiments and the inverse ballistic experiment were then performed,and the reliability of the calibrated SRM model was verified by comparing the results of experiments and numerical simulations.This study offers a valuable reference for the utilization of SP-RSRC in the realm of impact protection.

EVOLUTION OF THE MICROCRACKS IN WHISKER TOUGHENING CERAMIC MATRIX COMPOSITES

The modified equivalent inclusion theory by the authors and the internal variable theory are employed to investigate the evolution of the microcracks in whisker toughening ceramics and the influence of the microcracks on the mechanical properties of the material. The effect of residual thermostrain, whisker content and aspect ratio is considered. The modulus, initial nonlinear load, strength and nonlinear constitutive relation are calculated and some important conclusions are given.

Micro-vibration response analysis and its application of electronic workshop raw land based on whale optimization algorithm

Environmental micro-vibration is one of the key factors impacting the running of electronic workshop.Low frequency micro-vibration has a significant influence on the normal operation of high precision machining and testing equipment,and even causes irreversible damage to the equipment.Micro-vibration testing and response analysis are important to guide the vibration isolation design and ensure the stable operation of various precision equipment in the workshop.Parameters of Davidenkov model are fitted based on whale swarm optimization algorithm,and its applicability is verified.At the same time,taking the testing project of an electronic workshop raw land as an example,the micro-vibration response is analyzed.The results show that the nonlinear constitutive model constructed by whale optimization algorithm can simulate the dynamic nonlinear behavior of soil under the action of micro-vibration better.Compared with the traditional equivalent linearization method,the nonlinear constitutive model based on the whale optimization algorithm has a smaller acceleration response value.It can effectively suppress the“virtual resonance effect”produced by the equivalent linearization method.

Numerical simulation of hypersonic thermochemical nonequilibrium flows using nonlinear coupled constitutive relations

To predict aeroheating performance of hypersonic vehicles accurately in thermochemical nonequilibrium flows accompanied by rarefaction effect,a Nonlinear Coupled Constitutive Relations(NCCR)model coupled with Gupta’s chemical models and Park’s two-temperature model is firstly proposed in this paper.Three typical cases are intensively investigated for further validation,including hypersonic flows over a two-dimensional cylinder,a RAM-C II flight vehicle and a type HTV-2 flight vehicle.The results predicted by NCCR solution,such as heat flux coefficient and electron number densities,are in better agreement with those of direct simulation Monte Carlo or flight data than Navier-Stokes equations,especially in the extremely nonequilibrium regions,which indicates the potential of the newly-developed solution to capture both thermochemical and rarefied nonequilibrium effects.The comparisons between the present solver and NCCR model without a two-temperature model are also conducted to demonstrate the significance of vibrational energy source term in the accurate simulation of high-Mach flows.

MODAL DISCONTINUOUS GALERKIN METHOD FOR SHOCK WAVE STRUCTURES

The discontinuous Galerkin(DG)finite element method has been popular as a numerical technique for solving the conservation laws.In the present study,in order to investigate the shock wave structures in highly thermal nonequilibrium,an explicit modal cell-based DG scheme is developed for solving the conservation laws in conjunction with nonlinear coupled constitutive relations(NCCR).Convergent iterative methods for solving algebraic constitutive relations are also implemented in the DG scheme.It is shown that the new scheme works well for all Mach numbers,for example,Ma=15.

Enhanced Constitutive Theories for Classical Thermoviscoelastic Polymeric Fluids

This paper presents ordered rate nonlinear constitutive theories for thermoviscoelastic fluids based on Classical Continuum Mechanics (CCM). We refer to these fluids as classical thermoviscoelastic polymeric fluids. The conservation and balance laws of CCM constitute the core of the mathematical model. Constitutive theories for the Cauchy stress tensor are derived using the conjugate pair in the entropy inequality, additional desired physics, and the representation theorem. The constitutive theories for the Cauchy stress tensor consider convected time derivatives of Green’s strain tensor or the Almansi strain tensor up to order n and the convected time derivatives of the Cauchy stress tensor up to order m. The resulting constitutive theories of order (m, n) are based on integrity and are valid for dilute as well as dense polymeric, compressible, and incompressible fluids with variable material coefficients. It is shown that Maxwell, Oldroyd-B, and Giesekus constitutive models can be described by a single constitutive theory. It is well established that the currently used Maxwell and Oldroyd-B models predict zero normal stress perpendicular to the flow direction. It is shown that this deficiency is a consequence of not retaining certain generators and invariants from the integrity (complete basis) in the constitutive theory and can be corrected by including additional generators and invariants in the constitutive theory. Similar improvements are also suggested for the Giesekus constitutive model. Model problem studies are presented for BVPs consisting of fully developed flow between parallel plates and lid-driven cavities utilizing the new constitutive theories for Maxwell, Oldroyd-B, and Giesekus fluids. Results are compared with those obtained from using currently used constitutive theories for the three polymeric fluids.

THE EXISTENCE OF SOLUTION TO THE FINITE ELASTODYNAMICS WITH MIXEDBOUNDARY CONDITIONS

In this paper the existence of solution to finite elastodynamics constrainted by mixed boundary conditions is derived when the hyperpotential and its gradient (for Green's strain) satisfy adequate conditions.

TEST AND STUDY ON THE CONSTITUTIV ERELATIONSHIP OF DESERT SAND UNDER MOVING VEHICLE

The mechanical properties of the sand of Takelamagan desert in Xinjiang under moving vehicle are studied by soil dynamic triaxial test apparatus. The nonlinear elastic constitutive model of the sand under moving vehicle is established first. These results lay the foundations for studying the interaction between vehicle running gear and the sand of Takelamagan desert in Xinjiang. and developing sand vehicle.

Analytical method of nonlinear coupled constitutive relations for rarefied non-equilibrium flows

It is well known that Navier-Stokes equations are not valid for those high-Knudsen and high-Mach flows, in which the local thermodynamically non-equilibrium effects are dominant. To extend the non-equilibrium describing the ability of macroscopic equations, Nonlinear Coupled Constitutive Relation(NCCR) model was developed from Eu’s generalized hydrodynamic equations to substitute linear Newton’s law of viscosity and Fourier’s law of heat conduction in conservation laws. In the NCCR model, how to solve the decomposed constitutive equations with reasonable computational cost is a key ingredient of this scheme. In this paper, an analytic method is proposed firstly. Compared to the iterative procedure in the conventional NCCR model, the analytic method not only obtains exact roots of the decomposed constitutive polynomials, but also preserves the nonlinear constitutive relations in the original framework of NCCR methods. Numerical tests to assess the efficiency and accuracy of the proposed method are conducted for argon shock structures, Couette flows, two-dimensional hypersonic flows over a cylinder and threedimensional supersonic flows over a three-dimensional sphere. These superior advantages of the current method are expected to render itself a powerful tool for simulating the hypersonic rarefied flows and microscale flows of high Knudsen number for engineering applications.

VIBRATION SUPPRESSION OF CANTILEVER LAMINATED COMPOSITE PLATE WITH NONLINEAR GIANT MAGNETOSTRICTIVE MATERIAL LAYERS

In this paper, a nonlinear and coupled constitutive model for giant magnetostrictive materials （GMM） is employed to predict the active vibration suppression process of cantilever laminated composite plate with GMM layers. The nonlinear and coupled constitutive model has great advantages in demonstrating the inherent and complicated nonlinearities of GMM in re- sponse to applied magnetic field under variable bias conditions （pre-stress and bias magnetic field）. The Hamilton principle is used to derive the nonlinear and coupled governing differential equation for a cantilever laminated composite plate with GMM layers. The derived equation is handled by the finite element method （FEM） in space domain, and solved with Newmark method and an iteration process in time domain. The numerical simulation results indicate that the proposed active control system by embedding GMM layers in cantilever laminated composite plate can efficiently suppress vibrations under variable bias conditions. The effects of embedded placement of GMM layers and control gain on vibration suppression are discussed respectively in detail.

Dynamic modelling and analysis of space webs

Future space missions demand operations on large flexible structures,for example,space webs,the lightweight cable nets deployable in space,which can serve as platforms for very large structures or be used to capture orbital objects.The interest in research on space webs is likely to increase in the future with the development of promising applications such as Furoshiki sat-ellite of JAXA,Robotic Geostationary Orbit Restorer (ROGER) of ESA and Grapple,Retrieve And Secure Payload (GRASP) of NASA.Unlike high-tensioned nets in civil engineering,space webs may be low-tensioned or tensionless,and extremely flexible,owing to the microgravity in the orbit and the lack of support components,which may cause computational difficulties.Mathematical models are necessary in the analysis of space webs,especially in the conceptual design and evaluation for prototypes.A full three-dimensional finite element (FE) model was developed in this work.Trivial truss elements were adopted to reduce the computational complexity.Considering cable is a compression-free material and its tensile stiffness is also variable,we introduced the cable material constitutive relationship to work out an accurate and feasible model for prototype analysis and design.In the static analysis,the stress distribution and global deformation of the webs were discussed to get access to the knowledge of strength of webs with different types of meshes.In the dynamic analysis,special attention was paid to the impact problem.The max stress and global deformation were investigated.The simulation results indicate the interesting phenomenon which may be worth further research.