Inverse Problems for Identification of Memory Kernels in Viscoelasticity

Inverse problems for identification of the memory kernel in the linear constitutive stress–strain relation of Boltzmann type are reduced to a non-linear Volterra integral equation using Fourier's method for solving the direct problem. To this equation the contraction principle in weighted norms is applied. In this way global existence of a solution to the inverse problem is proved and stability estimates for it are derived. © 1997 by B. G. Teubner Stuttgart-John Wiley & Sons Ltd.     

Radon Transform for Solving an Inverse Scattering Problem in a Planar Layered Acoustic Medium

A two-dimensional inverse scattering problem in a layered acoustic medium occupying a half-plane is considered. Data is the scattered wavefield from a surface point source measured on the boundary of the half-plane. On the basis of the Radon transform, an algorithm is constructed that recovers the velocity and the acoustic impedance of the medium from the scattering data. An analytical solution is presented for an inverse scattering problem, and several inverse scattering problems are solved numerically.     

Inverse Parameter Identification for Orthotropic Elasto-Plastic Sheet-Steel

In this contribution the Finite Element Model Updating (FEMU) approach is utilized to determine the material parameters of sheet-steel. From experimental testing it is observed that the considered cold-rolled steel exhibits orthotropic behaviour. To regard this in the simulation, a user-implemented material model based on a quadratic yield function is used. Via the method of digital image correlation (DIC), the displacement field of a biaxially loaded specimen is measured from images taken at different stages of loading. Comparing the experimentally determined displacements to those obtained by simulation an error measure is defined which can be minimized by optimization algorithms. Starting with initial values for the orthotropic elasto-plastic material parameters, the FEM model is thus updated consecutively until a specified error margin is reached. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Delamination of Grain-Interfaces in Silicon Nitride

Intergranular cracking due to delamination of grain interfaces along with the development of bridging grains is the most important mechanism for the high fracture toughness of silicon nitride. In this line, an interface behavior, which is extending the Coulomb friction concept into the tensile domain has been implemented into a thermodynamical consistent frame work of Helmholtz free energy and dissipation. The model is used to describe the fracture process in a simple model geometry with a β-Si₃N₄ grain embedded into a precracked matrix of oxynitride glass. The material model considers the thermoelastic anisotropy of the grain and the thermal residual stresses, which evolve during the cooling of the model from the glass transition temperature to room temperature. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Gauss-Newton and Inverse Gauss-Newton Methods for Coefficient Identification in Linear Elastic Systems

The “inverse problem” of determining parameter distributions in linear elastic structures has been explored widely in the literature. In the present article we discuss this problem in the context of a particular formulation of linear elastic systems, dividing the associated inverse problems into two classes which we call Case 1 and Case 2. In the first case the elastic parameters can be obtained by solving a certain set of linear algebraic equations, typically poorly conditioned. In the second case the corresponding problem involves nonlinear equations which usually must be solved by approximation methods, including the Gauss-Newton method for overdetermined systems. Here we discuss the application of this method and a related, empirically more stable, method which we call the inverse Gauss-Newton method. Convergence theorems are established and computational results for sample problems are presented.     

An Iterative Way of Solving the Inverse Scattering Problem for an Acoustic System of Equations in an Absorptive Layered Nonhomogeneous Medium

An algorithm is considered for solving the inverse scattering problem of seismic waves in a layered medium. The algorithm is based on solving a nonclassical ordinary differential equation with respect to an acoustic impedance, which also contains an unknown function characterizing the dissipative properties of the medium. The uniqueness of determining of these functions and the functional dependence associating them is established by solving the inverse problem of ground seismics. Results are presented from a computing experiment on applying the proposed algorithm.     

Delamination in visco-elastic materials with thermal effects

This contribution reports on a model describing the evolution of brittle delamination between two visco-elastic bodies Ω₊ and Ω₋, bonded along a prescribed contact surface Γ_C, over a fixed time interval (0, T); a detailed discussion and a rigorous mathematical analysis can be found in [1]. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Delamination of Unidirectional Viscoelastic Composite Materials

The delamination of unidirectional composite materials takes place under compression along the reinforcing elements and often occurs near the free surfaces or planes of these materials. The first investigation in this field was made in 1976 and since then numerous studies have been carried out. However, the approaches developed in these investigations are applicable only to time-independent composite materials. In the present paper, an approach for investigating unidirectional viscoelastic composite materials is proposed, with a particular problem as an example. The investigations are performed within the framework of exact three-dimensional geometrically nonlinear equations of viscoelasticity theory.     

一些反演关系的反演链

本文主要提出和讨论了一般反演关系的反演链和反演对的理论.在此基础上,具体给出Gould-Hsu反演的两类反演链和Gould-Hsu反演的q-模拟的相关问题.最后,本文结合一些常用的反演对,建立了众多的组合恒等式.