... Sneddon remembers Tony's arrival in Keele, with his own problem, which he considered too tough to solve analytically and advised him to tackle it numerically; his abiding memory of Tony at Keele is of the long hours he spent working away with an electric desk calculator.

With Ronald Rivlin and Albert Green, Tony Spencer embarked on his remarkable studies into the application of the theory of invariants and its role in the development of constitutive laws in continuum mechanics. These studies have now become a milestone in the history of the development of continuum mechanics. References to the collaborative work of Tony Spencer, Ronald Rivlin and Albert Green are standard citations in treatises in modern continuum mechanics. As Tony himself once remarked: 'My debt to Rivlin in particular is huge, and I also owe a great deal to Albert Green, from whom I learned much'.

The authors determine a basis for the invariants, under the orthogonal group, of a set of symmetric 3 × 3 matrices. The ideas which underlie the necessarily elaborate computations are the following. By means of the Cayley-Hamilton theorem it is shown that any product of symmetric 3 × 3 matrices can be expressed as a linear combination of matrix products of limited total degree, and of certain explicitly determined types, with coefficients expressible in terms of the traces of matrix products. From this result it is shown that a basis for the orthogonal invariants of five or fewer symmetric 3 × 3 matrices is given by the traces of an explicitly stated set of matrix products. The basis for the orthogonal invariants of a larger number of matrices is then deduced by using Peano's theorem.

The non-linear elasticity problem of the finite extension and torsion of a solid circular cylinder of incompressible isotropic material has been solved by Rivilin; the present paper applies the perturbation method of Green, Rivlin, and Shield to consider the effects of a small deformation superposed on the finite deformation. Specifically, instability is analyzed by finding the loading conditions for which an adjacent equilibrium position exists. A particular strain energy function (Neo-Hookean) is chosen, and the condition for existence of an adjacent equilibrium position is obtained in the form of a transcendental equation, which is solved numerically for two loading conditions. The reduction to the linear elasticity case is also checked. The labour is considerable, and the results form a useful addition to the literature on non-linear elastic stability theory. The authors use general tensors associated with a curvilinear coordinate system moving with the body.

... where he was chiefly engaged in the effects and detection of underground explosions.

Continuum mechanics comprises the mechanics of fluids and the mechanics of solids: two major branches of physics and applied mathematics which also provide the basis of civil and mechanical engineering. The modern trend, followed in this book, is to adopt a unified approach to the teaching of these two branches---emphasizing the general mechanical principles which apply to all materials. Once familiar with the underlying principles, the student can specialise in any of the different branches of continuum mechanics. After introductory chapters on matrix algebra, vectors and Cartesian tensors, and an analysis of deformation and stress, the author examines the mathematical statements of the laws of conservation of mass, momentum and energy and the formulation of the mechanical constitutive equations for various classes of fluids and solids. The book includes a number of worked examples and a graded selection of problems (with answers where appropriate). It is written as a textbook for second- and third-year undergraduate students of applied mathematics but will also be valuable to physicists and engineers.

He travelled extensively throughout the world to collaborate with numerous colleagues, attending conferences to give keynote presentations and generally supporting the research enterprise in continuum mechanics. His research productivity showed no signs of diminishing. In fact, to the contrary, since relinquishing his departmental responsibilities, he was possibly even more productive than ever. At a stage in life when many of his contemporaries, and even some of his much younger colleagues, were fading under the frustrations of 'modernity', Tony 'pressed on regardless'. In this way he was an inspiration to all, just as he inspired those around him when he headed the talented group of academics associated with the Department at Nottingham.

A procedure has been developed in previous papers for constructing exact solutions of the equations of linear elasticity in a plate (not necessarily thin) of inhomogeneous isotropic linearly elastic material in which the elastic moduli depend in any specified manner on a coordinate normal to the plane of the plate. The essential idea is that any solution of the classical equations for a hypothetical thin plate or laminate (which are two-dimensional theories) generates, by straightforward substitutions, a solution of the three-dimensional elasticity equations for the inhomogeneous material. In this paper we consider a thick plate of isotropic elastic material with a thin surface layer of different isotropic elastic material. It is shown that the interface tractions and in-plane stress discontinuities are determined only by the initial two-dimensional solution, without recourse to the three-dimensional elasticity theory. Two illustrative examples are described.

Tony Spencer was keenly interested in football, a member of the Nottinghamshire County Cricket Club, and followed the fortunes of the Boston Red Sox baseball team. He enjoyed walking and in his younger days was a keen cyclist.