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To describe the elastic behavior of rubber-like materials, numerous specific forms of strain energy functions have been proposed in the literature. This bibliography provides a list of references on the strain energy functions for rubber-like materials on isothermal condition using the phenomenological approach. The published works, either containing the strain energy function proposals or the discussions on such proposals, based upon the phenomenological approach, are classified.

The paper describes an extension of classical shakedown theory for structural problems involving constant mechanical loads and cyclic variations in temperature. The objective of the theory is to provide a simple means of distinguishing between circumstances where thermal cycling can cause structural ratchetting for small or zero mechanical loads from those where very substantial thermal stresses can occur with no danger of ratchetting. This distinction is of particular importance in the design of Liquid Metal Fast Breeder Reactors and current design codes do not address this problem directly. An extended definition of material shakedown is described that provides a conservative theory, taking into account cyclic strain hardening. Some simple experiments on a two-bar structure demonstrates the relevance of the theory to observed structural behavior.

This paper describes an upper bound technique for the evaluation of the shakedown limit of thin cyclindrical shells subject to thermal loading. The method is based upon the upper bound kinematic shakedown theorem of Koiter. By suitable choice of displacement field, in a finite element form, and yield surface, the problem is reduced to a linear programming problem. A number of solutions are presented involving a tube subjected to a moving temperature front which indicates that the technique provides, in an eficient way, a complete description of the load levels at which ratchetting would occur and the corresponding modes of deformation. The technique seems therefore, to provide a useful intermediary between the use of the simple rules incorporated in design codes and full inelastic analysis.

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