On an implicit stress-calculation algorithm for a multidimensional constitutive law using a skeleton curve

In this paper, we present an implicit stress-calculation algorithm for a multidimensional constitutive law using a one-dimensional skeleton curve and a hysteresis curve. To consider the hysteretic behavior of soils, one-dimension skeleton curves (e.g., the Hardin-Drnevich model, Ramberg-Osgood (RO) model, and general hyperbolic equation (GHE) model) are widely used. In a multidimensional analysis, there are several methods for extending a constitutive law using a skeleton curve into multiple dimensions. However, because these methods are suitable for an explicit integration stress-calculation scheme, a calculated stress does not satisfy the function of skeleton curve when a large incremental strain is imposed in one step. In this paper, to resolve this problem, a nonlinear stress-strain relation using a skeleton curve and an implicit stress-calculation algorithm is presented. In addition, we show an example of an application of the GHE/RO model to the proposed algorithm.