to be done in this area. Face recognition is a problem that scarcely clamoured for attention before the computer age but, having surfaced, has involved a wide range of techniques and has attracted the attention of some fine minds (David Mumford was a Fields Medallist in 1974). This singular application of mathematical modelling to a messy applied problem of obvious utility and importance but with no unique solution is a pretty one to share with students: perhaps, returning to the source of our opening quotation, we may invert Duncan's earlier observation, 'There is an art to find the mind's construction in the face!'.

Linear and nonlinear waves, by G. B. Whitham. Pp.636. £50. 1999. ISBN 0 471 35942 4 (Wiley).

https://www.math.ubc.ca/~peirce/Computer%20simulation%20of%20HF_Adachi_Siebrits_Peirce_Desroaches_IJRM_MS_V44_p739_2007.pdf

Computer simulation of hydraulic fractures

With reference to practical engineering problems it is shown that considerable differences may be encountered between the results from associated and those from nonassociated plasticity theories. Next, the need for a non-associated plasticity theory is demonstrated by considering test results for sand, concrete and rock. Elementary material parameters are discussed such as Young's modulus and Poisson's ratio for the description of the elastic properties; and a cohesion and a friction angle for the determination of the strength. The salient difference from associated plasticity theory concerns the introduction of a dilatancy angle which controls the inelastic (plastic) volume changes. This dilatancy angle is not only a suitable parameter for the description of soils, but also appears to be useful for concrete and rock. Basically, the paper consists of three parts as we consider three types of models of increasing complexity. The first model is a perfectly-plastic model, which employs the five aforementioned parameters. It is based on test data rather than on Drucker's hypothesis of material stability. The consequences thereof are examined. The second model is a straightforward extension of the first model by augmenting it with friction hardening and cohesion softening. This novel idea is introduced to account for the degradation of the cohesion of cemented granular materials with increasing inelastic deformation. The model is employed in an analysis which shows that plastic deformations tend to localize in thin shear bands, which may occur even before peak strength is reached. Finally, a review is given of concepts for modelling hysteresis and strain accumulation in cyclic loading. The concept of a bounding surface in addition to a yield surface is discussed and is adapted for use in a sophisticated model for loose and cemented granular materials under cyclic loading.

/pdf/non-associated-plasticity-for-soils-concrete-and-rock-1k1jstx009.pdf

Non-Associated Plasticity for Soils, Concrete and Rock

Introduction: Realistic Image Synthesis, Goals and Limitations A Short Historical Perspective of Image Synthesis Radiosity and Finite Element Methods The Radiosity Algorithm and This Book Rendering Concepts: Motivation Basic Optics Radiometry and Photometry The Light Field Reflection Functions The Rendering Equation Discretizing the Radiosity Equation: the Radiosity Function Making Image Synthesis Tractable The Radiosity Approach Approximating the Radiosity Across a Surface Error Metrics Constant Element Radiosities Higher Order Basic Functions Parametric Mapping to a Master Element Summary The Form Factor, The Form Factor Integral: the Coefficients of K The Differential Form Factor Three Formulations of the Form Factor Computing the Form Factor Closed Form Solutions for the Form Factor: Formulae for Simple Shapes Differential Area to Convex Polygon General Polygon to Polygon Numerical Solutions for the Form Factor: Numerical Integration in General Evaluating the Inner Integral Full Area to Area Quadrature Contour Integral Formulation A Simple Test Environment Non-Constant Basis Functions Acceleration Techniques Radiosity Matrix Solutions: Qualities of the Matrix Linear System Solution Methods Relaxation Methods Dynamic Environments Parallel Implementations Domain Subdivision: Error Metrics Mesh Characteristics and Accuracy Automatic Meshing Algorithms Hierarchical and Importance Based Algorithms: Observations About K Two Level Hierarchy Multi-Level Hierarchy Importance Meshing Hierarchical Basis Functions Summary of Hierarchical Radiosity Methods Meshing: Basic Subdivision Techniques Mesh Template Methods Decomposition Methods Mesh Smoothing Discontinuity Meshing Topological Data Structures and Operators Alternatives to Meshing Rendering: Reconstructing the Radiosity Functions Interpolation Methods for Rendering Two-Pass Methods Incorporating Surface Detail Mapping Radiosities to Pixel Colours Colour Summary Extensions: Non-Diffuse Light Sources Directional Reflection Participating Media Conclusion and Future Directions

Radiosity and Realistic Image Synthesis

SUMMARY The present paper is concerned with the effective numerical implementation of the two-dimensional dual boundary element method, for linear elastic crack problems. The dual equations of the method are the displacement and the traction boundary integral equations. When the displacement equation is applied on one of the crack surfaces and the traction equation on the other, general mixed-mode crack problems can be solved with a single-region formulation. Both crack surfaces are discretized with discontinuous quadratic boundary elements; this strategy not only automatically satisfies the necessary conditions for the existence of the finite-part integrals, which occur naturally, but also circumvents the problem of collocation at crack tips, crack kinks and crack-edge corners. Examples of geometries with edge, and embedded crack are analysed with the present method. Highly accurate results are obtained, when the stress intensity factor is evaluated with the J-integral technique. The accuracy and efficiency of the implementation described herein make this formulation ideal for the study of crack growth problems under mixed-mode conditions.

https://msvlab.hre.ntou.edu.tw/cite/DualBEM_Crack_Aliabadi_IJNME_1992.pdf

The dual boundary element method: Effective implementation for crack problems

Boundary concepts are introduced and immediately applied in simple - but useful - computer codes. These codes facilitate the comprehension of boundary elements. This text also discusses basic concepts, potential problems, elastostatics and other topics of interest to engineers.

Boundary Elements: An Introductory Course

Elements for the numerical analysis of wave motion in layered strata

Non‐Linear Finite Element Analysis of Solids and Structures, Volume 1

Absorbing boundary conditions are generally required for numerical modeling of wave phenomena in unbounded domains. Local absorbing boundary conditions are generally preferred for transient analysis because of their computational efficiency. However, their accuracy is severely limited because the more accurate high-order boundary conditions cannot be implemented easily. In this paper, a new arbitrarily high-order absorbing boundary condition based on continued fraction approximation is presented. Unlike the existing boundary conditions, this one does not contain high-order derivatives, thus making it amenable to implementation in conventional C0 finite element and finite difference methods. The superior numerical properties and implementation aspects of this boundary condition are discussed. Numerical examples are presented to illustrate the performance of these new high-order boundary condition.

Continued-fraction absorbing boundary conditions for the wave equation

The feasibility of conducting a detailed analysis of pile driving using a finite element technique is examined in this paper, taking into account the non-linear behaviour of undrained clayey soil and tracing the penetration of the pile into the soil. A three-dimensional model is used for this purpose, which is handled by two-dimensional analysis due to the axisymmetric nature of the problem. A non-linear time-domain dynamic analysis is performed in which the hammer blows on the pile are represented by a periodic forcing function, and the pile penetration is treated using a frictional contact slideline algorithm. The model is applied 10 the driving of a concrete pile in a clayey soil.

John L. Tassoulas

Papers

Boundary Elements: An Introductory Course

Elements for the numerical analysis of wave motion in layered strata

Non‐Linear Finite Element Analysis of Solids and Structures, Volume 1

Continued-fraction absorbing boundary conditions for the wave equation

A finite element model for the simulation of pile driving