arXiv subjects

Jiashi Yang

Publications and source records attributed to Jiashi Yang.

At least 19 recordsLinked to original sources

arXiv2026

On the flow of electrically charged particles in an elastic solid

This paper is a specialization of a broad and complicated continuum theory [arXiv:2403.07582] to a relatively simple and useful case so that it is more reader friendly. A continuum theory of the flow of charged particles in an elastic solid is presented. It can describe the behavior of soft solid electrolytes and elastic semiconductors. It is nonlinear and is valid for large deformation and strong fields. The theory is derived from a three-continuum mixture model including a charged lattice continuum, a bound charge continuum for electric polarization, and an ideal fluid for the flow of mobile charges. The basic electromechanical laws are applied systematically to the model. The electric fields are quasistatic and are in SI units.

cond-mat.soft↗

arXiv2024

On the Derivation of One and Two Dimensional Equations for Layered Elastic Beams and Plates with Interface Slips

Mindlins systematic procedure of power series expansion for deriving one and two dimensional equations of elastic beams and plates is extended to layered beams and plates with interface slips by adding a step function term to the power series expansion. A two layer beam is used as an example. In addition to the usual one dimensional equations for extension, bending and shear deformation, an equation associated with the interface slip also results from the procedure.

physics.class-ph↗

arXiv2024

Propagation of Shear Horizontal Acoustic Waves in a Quartz Plate with a Fluid Layer for Liquid Sensor Application

We study the propagation of shear horizontal (SH) acoustic waves in a quartz elastic plate in contact with a viscous fluid layer of a finite thickness as an acoustic wave sensor for measuring fluid viscosity or density. The first order elastic plate theory by Mindlin and the theory of Newtonian fluids are used. An equation for determining the dispersion relations of the SH waves is obtained. Approximate dispersion relations for long waves are given analytically. Numerical results showing the effects of the fluid on SH wave characteristics are presented.

physics.app-ph↗

arXiv2024

Partial Complementary Energy Densities, Their Variational Principles and Applications in Elasticity

Partial complementary energy densities are introduced through partial Legendre transforms from the strain energy density of linear elasticity. They have mixed components of the strain and stress tensors. Mixed variational principles based on these energy densities are presented. It is shown that these variational principles are useful in the derivation of two- and one-dimensional theories of elastic plates and rods.

physics.class-ph↗

arXiv2024

Effective Youngs Modulus of Two-Phase Elastic Composites by Repeated Isostrain and Isostress Constructions and Arithmetic-Geometric Mean

A relationship is established between the effective Youngs modulus of a two-phase elastic composite and a known mathematical mean value. Specifically, the effective Youngs modulus of a composite obtained from repeated parallel and serial constructions is equal to the arithmetic-geometric mean of the Youngs moduli of the component materials. This result also applies to electric circuits with resistors in repeated parallel and serial connections.

physics.class-ph↗

arXiv2024

On Generalizations of the Minimal Complementary Energy Variational Principle in Linear Elastostatics

It is shown that when the well-known minimal complementary energy variational principle in linear elastostatics is written in a different form with the strain tensor as an independent variable and the constitutive relation as one of the constraints, the removal of the constraints by Lagrange multipliers leads to a three-field variational principle with the displacement vector, stress field and strain field as independent variables. This three-field variational principle is without constrains and its variational functional is different from those of the existing three-field variational principles. The generalization is not unique. The procedure is mathematical and may be used in other branches of physics.

physics.class-ph↗

arXiv2024

A Note on the Objectivity (Rotational Invariance) of the Stored Energy Density in Continuum Physics

This short note is concerned with the rotational invariance of the stored energy density in continuum physics as a scalar function of a few vectors. A simple derivation is presented for the determination of the general form of the energy density in the case of a two-dimensional space. It is also shown that the general form of the energy density so determined may be further reduced. The three-dimensional case is also discussed.

physics.class-ph↗

arXiv2024

One-Dimensional Model for Coupled Flexural, Torsional and Extensional Motions of Elastic Beams with Embedded Point Magnets under Magnetic Fields

This paper establishes a one-dimensional theoretical model for an elastic beam with embedded point magnets in extensional, bending and torsional motions. The beam has a circular cross-section. The point magnets may be in the interior or at the ends of the beam. They are assumed to be small and rigid, and may be ferromagnetic with spontaneous magnetic moments that can change their directions with respect to the magnets. The model shows that the extensional, flexural and torsional motions of the beam may be coupled by the point magnets when an external magnetic field is applied. A few examples are given. Piezoelectric beams with point magnets are also discussed.

physics.app-ph↗

arXiv2024

A Continuum Theory of Elastic Semiconductors with Consideration of Mobile Charge Inertia

A set of nonlinear equations for the macroscopic theory of elastic semiconductors is derived which generalizes the seminal work of Tiersten by including the inertia of the mobile charge carriers. The equations obtained can describe carrier plasma waves and their interactions with elastic waves. Another generalization in this paper is that the internal energy densities of the mobile charges are allowed to depend on temperature in addition to charge densities. The equations are in SI units.

cond-mat.mtrl-sci↗

arXiv2024

Flow of Electrically Charged Fluids Through Elastic Porous Media

We study the flow of an electrically charged fluid through an elastic and porous medium. A three continuum model consisting of an elastic solid, a viscous fluid, and a mobile charge continuum is used. The relevant laws of physics are applied systematically to the constituents or the combined continuum, leading to their continuity equations for conservation of mass or charge, linear and angular momentum equations as well as constitutive relations. The analysis assumes quasistatic electric fields and is for nonmagnetizable materials. The resulting theory is nonlinear, valid for large deformations and strong fields and can be specialized or generalized in various ways.

cond-mat.soft↗

arXiv2024

On Purely Macroscopic Theory of Rigid Semiconductors Constructed from Multi-Continuum Model

A complete and systematic derivation of the purely macroscopic theory of rigid semiconductors is given. It is based on a five-continuum model of charged and interpenetrating continua, and the applications of the relevant laws of physics to the continua. The theory is within the quasistatic approximation of electrostatics and is limited to nonmagnetizable materials.

cond-mat.mtrl-sci↗

arXiv2023

Flow through an Electromechanical Tube Driven by a Voltage

We study the axial flow of a nonviscous and incompressible fluid in a circular tube made from an electromechanical material. The tube is driven into radial motion by an electric voltage across its thickness. A theoretical analysis is performed. An analytical solution is obtained from the relevant equations of fluid mechanics and piezoelectric shells. The solution shows that when the tube is contracting or expanding radially under a properly designed voltage, the fluid can flow along the tube axially. Hence the tube can function as a pump for driving the fluid. The effects of various physical parameters on the velocity profile of the flow are examined.

physics.app-ph↗

arXiv2023

A Continuum Theory of Elastic-Ferromagnetic Conductors

In this paper, a phenomenological theory of saturated ferromagnetoelastic conductors is established using a multi-continuum model and the classical laws of mechanics, thermodynamics and electromagnetics. The theory is nonlinear and is valid for large deformations and strong electromagnetic fields. The constitutive relations in the theory satisfy the saturation condition of the magnetization vector. The theory is with full electromagnetic couplings as governed by the equations of electrodynamics. It can describe the interactions of elastic, electromagnetic and spin waves. The theory can be reduced to various quasistatic theories with appropriate approximations of the electromagnetic fields. It is for anisotropic materials in general.

cond-mat.mtrl-sci↗

arXiv2023

Propagation of Coupled Acoustic, Electromagnetic and Spin Waves in Saturated Ferromagnetoelastic Solids

We study the propagation of plane waves in an unbounded body of a saturated ferromagnetoelastic solid. The equations by Tiersten for small fields superposed on finite initial fields in a saturated ferromagnetoelastic material are employed, with their quasistatic magnetic field extended to dynamic electric and magnetic fields for electromagnetic waves. Dispersion relations of the plane waves are obtained. The cutoff frequencies and long wave approximation of the dispersion curves are determined. Results show that acoustic, electromagnetic and magnetic spin waves are coupled in such a material. For YIG which is a cubic crystal without piezoelectric coupling, the acoustic and electromagnetic waves are not directly coupled but they can still interact indirectly through spin waves.

physics.app-ph↗

arXiv2023

A Macroscopic Theory of Saturated Ferromagnetic Conductors

A phenomenological theory of rigid and saturated ferromagnetic conductors is constructed from a four-continuum model consisting of a rigid lattice continuum, a bound charge continuum for polarization, a circulating current continuum for magnetization, and a free charge continuum for electrical conduction. The basic laws of physics are applied to the four continua. Thermal couplings and the related dissipative effects are also included. The theory includes the Landau-Lifshitz-Gilbert equation as one of a system of simultaneous equations.

cond-mat.mtrl-sci↗

arXiv2023

Theoretical Analysis of Quartz Plate Acoustic Wave Resonators and Sensors Using Three-Dimensional Equations of Anisotropic Elasticity or Piezoelectricity

This is a review of theoretical results from the three-dimensional equations of anisotropic elasticity or linear piezoelectricity on waves and vibrations in quartz crystal plates. It covers both the classical results on acoustic wave resonators and the relatively new applications in acoustic wave sensors. It discusses the basic thickness modes with various complications due to electrodes, mass loading, contact with fluids, and air gaps, etc. as well as the more complicated transversely varying modes. These results are fundamental for the understanding and design optimization of the widely used quartz crystal plate resonators and sensors.

physics.app-ph↗

arXiv2023

An Alternative Derivation of the Landau-Lifshitz-Gilbert Equation for Saturated Ferromagnets

The Landau-Lifshitz-Gilbert equation for rigid and saturated ferromagnets is derived using a two-continuum model constructed by H.F. Tiersten for elastic and saturated ferromagnets. The relevant basic laws of physics are applied systematically to the two continua or their combination. The exchange interaction is introduced into the model through surface distributed magnetic couples. This leads to a continuum theory with magnetization gradients in the stored energy density. The saturation condition of the magnetization functions as constraints on the energy density and has implications in the constitutive relations.

cond-mat.mtrl-sci↗

arXiv2023

Frequency perturbation integral for piezoelectric quartz crystal microbalances based on scalar differential equations

We study frequency shifts in a piezoelectric quartz resonator induced by a surface mass layer for sensor applications. The scalar differential equations for thickness-shear modes in a quartz plate are used. A first-order perturbation analysis is performed. The frequency shift is obtained and is expressed by a perturbation integral. It produces the well-known Sauerbrey equation for mass sensitivity in the special case of a uniform mass layer. As an application of the perturbation integral, frequency shifts due to a nonuniform mass layer are calculated.

physics.app-ph↗