Zhihai Xiang

Identification of damage parameters for jointed rock

An algorithm for parameter identification based on the finite element method is proposed in this paper. It follows the main idea of the dual boundary control method, but introduces some modifications to improve its stability. This improvement is illustrated with a simple example. The algorithm is subsequently extended to identify the parameters in a three-dimensional anisotropic elastic damage model. This algorithms abilities to identify various parameters are evaluated by simulating a tunnel excavation process. The numerical results reveal that this is a stable and fast-converging algorithm when the physical character of the problem is intrinsically valid.

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.

Parameter identification and its application in tunneling

This paper focuses on discussing the parameter identification techniques in geotechnical engineering. Firstly, the general formulation of the parameter identification process is presented. Secondly, the problem of identifiability is discussed and illustrated by an example of identifying the initial damage parameters of a damage model for jointed rocks. Then the algorithms of designing the optimal layout of displacement measurements are proposed, based on the analyses of the well-posednesses of the parameter identification processes with the Gauss-Newton method and the Complex method, respectively. The validities of these algorithms are proved by some academic and applied engineering examples. Finally, the advantages and drawbacks of the gradient-type methods and the direct-search methods are carefully compared.

Parameter identification for coupled finite element–boundary element models

Abstract To solve problems involving semi-infinite domains, one efficient approach is to use finite elements (FE) to model the regions where detailed information about materials with complicated properties is needed and to use boundary elements (BE) to simulate the semi-infinite parts. In this paper, a parameter identification algorithm is developed for coupled FE–BE models in detail. The algorithm is designed to identify all the material parameters in the FE domain and the BE domain simultaneously. Its validity is illustrated using two examples. The distribution of the observational points is also briefly tested and discussed. The numerical results reveal that this is a stable and fast-converging algorithm.

Realizing the Willis equations with pre-stresses

Abstract 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.

An experimental verification of the one-dimensional static Willis-form equations

Abstract This paper investigates the behavior of a heavy soft spring in steady circular motion. Since the spring is inhomogeneous due to centrifugal force, one can rigorously prove that it follows the one-dimensional static Willis-form equations. The theoretical predictions agree very well with experimental results. It further demonstrates that these equations can give a clear understanding of the stress-stiffening and spin-softening effect. These findings reveal that the Willis-form equations can give very accurate linear approximations of finite deformation problems and are also helpful to clarify the classical concept of the principle of material frame indifference.

One dimensional Willis-form equations can retain time synchronization under spatial 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.

An inverse approach to identifying the in vivo material parameters of female pelvic floor muscles using MRI data

Key Laboratory of Applied Mechanics, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China; Plastic Surgery Hospital (Institute), Chinese Academy of Medical Sciences & Peking Union Medical College, Beijing 100144, China; Department of Obstetrics, Peking Union Medical College Hospital, Beijing 100730, China; Department of Radiology, Peking Union Medical College Hospital, Beijing 100730, China