Multi-Surface and Bounding Surface Plasticity

Abstract

The mathematical theory of plasticity described so far in this book is based on the concept of a single yield surface. This single yield surface is used to separate the domains of elastic and plastic states. As demonstrated in Chapter 6, single yield sur-face plasticity offers a reasonable explanation of the overall stress-strain behaviour of soils for the case of proportional loading where the load increases monotonically and no unloading occurs. However further application of the single yield surface plasticity theory indicates that it suffers from the following main shortcomings: (1) The elastic domain assumed is often too large when compared with experimen-tal data. In addition, the sudden change from elastic to plastic domains pre-dicted by the single yield surface theory is also in contrast to the gradual change in stiffness from elastic to plastic states observed in experiments. (2) The isotropic hardening and Prager's or Ziegler's kinematic hardening (Prager, 1955; Ziegler, 1959) cannot generally model the complex behaviour of soils observed in experiments under cyclic or repeated loading conditions where stress reversals occur frequently. These limitations of the classical theory of plasticity provided a strong incentive for extensive research from the 1960s to search for better hardening rules for model-ling both smooth elastic-plastic transition and cyclic behaviour. Although several approaches have been proposed, the two most successful and widely used theories for this purpose are: (a) The theory of multi-surface plasticity due to Mroz (1967) and Iwan (1967); and (b) The theory of bounding surface (or two surface) plasticity due to Dafalias and Popov (1975) and Krieg (1975). Both of these concepts were initially developed for metals, but quickly found applications in modelling geomat-erials (e.g. Prevost, 1977, 1978; Mroz etal., 1978, 1979, 1981; DafaUas and Herr-mann, 1982). This chapter aims to present the concepts of the multi-surface and bounding sur-face plasticity and demonstrate how these concepts can be used to develop more accurate constitutive models for describing soil behaviour under both monotonic and cyclic loading conditions. Our presentation is limited to formulations in stress space, although multi-surface plasticity models can also be formulated in strain space (e.g. Yoder and Iwan, 1981; Zheng et al, 1986; Simpson, 1992).