arXiv subjects

Zhihai Xiang

Publications and source records attributed to Zhihai Xiang.

6 recordsLinked to original sources

arXiv2025

Deeper understandings of the gauge theory for the first order inhomogeneous linear elasticity

Our previous study [1] has demonstrated that the gauge theory is a proper framework for characterizing the local temporal and spatial interactions in inhomogeneous elastic media. However, in that study temporal interactions were interpreted as the compensation for the loss of kinetic energy resulting from homogenization process, distinct from damping effects. In addition, that study did not account for the integration of temporal and spatial transformations, leading to the omission of some crucial information such as thermal stresses. In this paper, we address this oversight to establish generalized equations by employing a unified methodology that encompasses the integrated temporal-spatial transformations and the principle of minimum dissipation. Among many interesting new findings, we highlight that the newly derived equations are inherently consistent with the first and the second laws of thermodynamics, because this gauge theory naturally incorporates the fundamental mechanism that governs the partitioning between the dissipative and the non-dissipative energy.

physics.class-ph↗

arXiv2022

Understanding the First Order Inhomogeneous Linear Elasticity through Local Gauge Transformations

It is well-known that classical linear elasticity equations are not form-invariant under local transformations. This is intrinsically related to the inhomogeneity of elastic media. However, the reported new linear elasticity equations for inhomogeneous media may appear in different forms. This paper tries to clarify this issue by investigating the form-invariance of the Lagrangian under local temporal or spatial gauge transformations. In this way, these new equations in different forms can be easily understood as the results from different choices of gauge fixing schemes. It recommends to choose appropriate gauges with clear physical meanings to simplify calculations.

math.AP↗

arXiv2019

Manipulate elastic waves with conventional isotropic materials

Transformation methods have stimulated many interesting applications of manipulating electromagnetic and acoustic waves by using metamaterials, such as super-lens imaging and cloaking. These successes are mainly due to the form-invariant property of the Maxwell equations and acoustic equations. However, the similar progress in manipulating elastic waves is very slow, because the elastodynamic equations are not form-invariant. Here we show that the expression of the elastodynamic potential energy can almost retain its form after conformal mapping, if the longitudinal wave velocity is much larger than the transverse wave velocity, or if the wavelength can be shortened by converting the waves into surface modes. Based on these findings, it is possible to design and fabricate novel devices with ease to manipulate elastic waves at will. One example presented in this paper is an efficient vibration isolator, which contain a 180-degree wave bender made of conventional rubbers. Compared with a conventional isolator of the same shape, similar static support stiffness and smaller damping ratio, this isolator can further reduce wave transmissions by up to 39.9dB in the range of 483 to 1800 Hz in the experiment.

physics.app-ph↗

arXiv2017

Modified 1D elastic wave equations that retain time synchronization under spatial coordinate transformations

In contrast to the traditional elastodynamic equations, a more comprehensive formulation of one dimensional (1D) elastodynamic equations is given for inhomogeneous media by using the coordinate transformation method. These modified equations consider the gradient of pre-stresses so that they are form-invariant and can retain time synchronization under spatial coordinate transformation, which comply with the principle of general invariance. A numerical example is conducted to compare the distributions of wave speeds calculated by the modified equations and the traditional equations. It demonstrates that the traditional equations are good approximations of the modified equations only when the wave frequency is sufficiently high.

physics.class-ph↗

arXiv2015

Realizing the Willis equations with pre-stresses

This paper proves that the linear elastic behavior of the material with inhomogeneous pre-stresses can be described by the Willis equations. In this case, the additional terms in the Willis equations, compared with the classical linear elastic equations for homogeneous media, are related to the gradient of pre-stresses. In this way, the material length scale is naturally incorporated in the framework of continuum mechanics. All these findings also coincide with the results of transformation elastodynamics, so that they can meet the requirement of the principle of material objectivity and the principle of general invariance.

physics.class-ph↗

arXiv2014

The form-invariance of wave equations without requiring a priori relations between field variables

According to the principle of relativity, the equations describing the laws of physics should have the same forms in all admissible frames of reference, i.e., form-invariance is an intrinsic property of correct wave equations. However, so far in the design of metamaterials by transformation methods, the form-invariance is always proved by using certain relations between field variables before and after coordinate transformation. The main contribution of this paper is to give general proofs of form-invariance of electromagnetic, sound and elastic wave equations in the global Cartesian coordinate system without using any assumption of the relation between field variables. The results show that electromagnetic wave equations and sound wave equations are intrinsically form-invariant, but traditional elastodynamic equations are not. As a by-product, one can naturally obtain new elastodynamic equations in the time domain that are locally accurate to describe the elastic wave propagation in inhomogeneous media. The validity of these new equations is demonstrated by some numerical simulations of a perfect elastic wave rotator and an approximate elastic wave cloak. These findings are important for solving inverse scattering problems in many fields such as seismology, nondestructive evaluation and metamaterials.

physics.class-ph↗