A numerical procedure is presented for the inversion of leaky Lamb wave (LLW) data to determine certain material properties of a waveguide, using a modified version of the simplex algorithm. The technique is capable of computing the parameter values that best fit a particular set of data, given an analytical model of the associated phenomenon containing any number of variables and parameters. The basic theoretical concepts involved are reviewed, and the versatility and simplicity of the method are illustrated by examples. The inversion scheme is used to estimate the elastic properties and thickness of an adhesive layer between two aluminum plates and the elastic constants of a unidirectional graphite/epoxy composite laminate. The limitations of the LLW data in the determination of the elastic constants of a composite are discussed.

Two new renormalization schemes for conductivity upscaling in heterogeneous media are presented. The schemes follow previous ones by performing the renormalization over square cells of size 2 d with d being the dimensionality. Contrasting with previous schemes, the two-dimensional scheme makes use of the exact 2×2 block-conductivity. On the basis of the structure of the exact two-dimensional block-conductivity, an analogous threedimensional scheme is proposed. The new schemes are tested on a number of benchmark problems and are shown to be significantly more accurate than existing schemes.

A new methodology for computational plasticity of nonassociated frictional materials is presented. The new approach is inspired by the micromechanical origins of friction and results in a set of governing equations similar to those of standard associated plasticity. As such, procedures previously developed for associated plasticity are applicable with minor modification. This is illustrated by adaptation of the standard implicit scheme. Moreover, the governing equations can be cast in terms of a variational principle, which after discretization is solved by means of a newly developed second-order cone programming algorithm. The effects of nonassociativity are discussed with reference to localization of deformations and illustrated by means of a comprehensive set of examples.K. KRABBENHOFT ET AL. difficult to obtain than in the case where the flow rule is associated [7][8][9][10]. These complications have a tendency to be more pronounced for high (but realistic) values of the friction angle and the degree of nonassociativity. Similarly, for fixed material parameters, one usually observes a degradation of the performance as the number of finite elements in the model is increased.These facts motivate a closer look at the physical origins of nonassociated flow rules and the numerical methods used to solve problems of frictional plasticity. In the following, inspired by the micromechanical origins of friction and its modeling in terms of plasticity theory, a new approach to computational plasticity for frictional (and generally nonassociated) materials is presented. The resulting scheme essentially approximates the original nonassociated problem as one of associated plasticity. Consequently, all the well-established numerical procedures for standard associated plasticity are applicable with little modification.The paper is organized as follows. The governing equations are briefly summarized in Section 2 before the new approach of approximating general nonassociated plasticity models in terms of equivalent associated ones is presented in Section 3. In Section 4, two different solution algorithms are presented. The first one is a slight modification of the common fully implicit scheme by Simo and his coworkers [11,12]. Secondly, following recent work of the authors [13-16], we formulate the governing equations in terms of a mathematical program. For certain yield criteria, notably Drucker-Prager, the resulting discrete programs may be solved very efficiently using a second-order cone programming solver, SONIC, recently developed by the authors. Next, in Section 5, the consequences of nonassociativity in terms of the ultimate load bearing capacity are discussed before the new numerical schemes are tested on some common boundary value problems in Section 6. These problems also highlight the consequences of nonassociated flow rules in terms of localization of deformations. Finally, conclusions are drawn in Section 7.Matrix notation is used throughout with bold uppercase and lowercase letters representing matrices and ve...

The problem of extracting effective diffusivities of cement pastes on the basis of X-ray microtomography images is considered. A general computational homogenization framework is developed and applied to a variety of cement pastes whose microstructure has been digitized to a resolution of 1 µm. At this resolution, important submicron features are not resolved. Consequently, we propose a methodology whereby the pore space is ascribed a diffusivity less than the free diffusivity. For this purpose, a simple rule that incorporates microtomography data is proposed and shown to yield satisfactory results.

A two-dimensional numerical procedure is presented to analyse the transient response of saturated porous elastic soil layer under cyclic loading. The procedure is based on the element-free Galerkin method and incorporated into the periodic conditions (temporal and spatial periodicity). Its shape function is constructed by moving least-square approximants, essential boundary conditions are implemented through Lagrange multipliers and the periodic conditions are implemented through a revised variational formulation. Time domain is discretized through the Crank-Nicolson scheme. Analytical solutions are developed to assess the effectiveness and accuracy of the current procedure in one and two dimensions. For only temporal periodic problems, a one-dimensional transient problem of finite thickness soil layer is analysed for sinusoidal surface loading. For both temporal and spatial periodic problems, a typical two-dimensional wave-induced transient problem with the seabed of finite thickness is analysed. Finally, a moving boundary problem is analysed. It is found that the current procedure is simple, efficient and accurate in predicting the response of soil layer under cyclic loading.

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