| Popis: |
It is well recognized that for proper functioning of a constitutive model selection of a computationally efficient and stable stress integration, algorithm is a key. Implementation of an advanced elastoplastic constitutive model into a finite element program requires the development of a robust and efficient numerical procedure in order to perform the local stress integration of the constitutive equations along a given loading path. Besides, as the physical domain of the problem increases, the simulation becomes time and resource consuming. Complex algorithms make the simulation even more time-consuming as accuracy and numerical complexity are strongly proportional to each other. Semi-implicit type Cutting Plane Method (CPM) and fully implicit type Closest Point Projection Method (CPPM), are the two most widely used methods for numerical integration. CPM is simple and easy to implement but less accurate and CPPM is stable and precise method, but the formulation is complex, especially for the constitutive models that contain multiple and coupled state variables, stiffness nonlinearity, multiple yielding and hardening conditions, and non-associativity. In this study, we have tried to bridge the gap by developing efficient integration schemes that provide close result to that of fully implicit method. We formulate an integration technique, namely Midpoint integration by enhancing the semi-implicit CPM framework. The algorithm is implemented for extended Mohr-Coulomb type soil constitutive model. The analysis show that the proposed integration methods gives result close to CPPM although their complexity is similar to CPM, which normally drifts away from accuracy in high plastic region. |
