A stress-strain integration algorithm for unsaturated soil elastoplasticity with automatic error control

Stress-strain integration algorithms are a very important component in the development of finite element codes. The use of accurate, robust and fast stress-strain integration algorithms accounts for a significant part of the performance of a finite element code, especially when complex elasto-plastic constitutive models are used. This paper presents the formulation of an algorithm for the stress-strain integration of the Barcelona Basic Model, an elasto-plastic volumetric hardening constitutive model for unsaturated soils. The proposed algorithm is based on some earlier ideas of substepping explicit integration with automatic error control. Stress-strain integration in the plastic domain is performed by using an explicit algorithm which accuracy is improved by dividing the initial strain increment in a number of substeps. The number of substeps depends on an estimation of the integration error that is obtained by using a modified Euler procedure. The performance of the stress-strain algorithm is presented for different types of stress paths to assess its dependency on factors such as, for example, the initial size of the strain increment, the error tolerance and the initial stress state. A drift correction algorithm is also proposed and its influence on the results is evaluated.