A simple and computationally efficient stress integration scheme based on numerical approximation of the yield function gradients: Application to advanced yield criteri

In this paper, we have modi?ed the stress integration scheme proposed by Choi and Yoon (2019), which is based on the numerical approximation of the yield function gradients, to implement in the ?nite element code ABAQUS three elastic isotropic, plastic anisotropic constitutive models with yielding described by Yld2004-18p (Barlat et al., 2005), CPB06ex2 (Plunkett et al., 2008) and Yld2011-27p (Aretz and Barlat, 2013) criteria, respectively. We have developed both VUMAT and UMAT subroutines for the three constitutive models, and have carried out cylindrical cup deep drawing test simulations and calculations of dynamic necking localization under plane strain tension, using explicit and implicit analyses. An original feature of this paper is that these finite element simulations are systematically compared with additional calculations performed using (i) the numerical approximation scheme developed by Choi and Yoon (2019), and (ii) the analytical computation of the first and second order yield functions gradients. This comparison has shown that the numerical approximation of the yield function gradients proposed in this paper facilitates the implementation of the constitutive models, and in the case of the implicit analyses, it leads to a significant decrease of the computational time without impairing the accuracy of the ?finite element results. In addition, we have demonstrated that there is a critical loading rate below which the dynamic implicit analyses are computationally more efficient than the explicit calculations.

Development of semi-implicit midpoint and Romberg stress integration algorithms for single hardening soil constitutive models

Purpose Semi-implicit type cutting plane method (CPM) and fully implicit type closest point projection method (CPPM) are the two most widely used frameworks for numerical stress integration. CPM is simple, easy to implement and accurate up to first order. CPPM is unconditionally stable and accurate up to second order though the formulation is complex. Therefore, this study aims to develop a less complex and accurate stress integration method for complex constitutive models. Design/methodology/approach Two integration techniques are formulated using the midpoint and Romberg method by modifying CPM. The algorithms are implemented for three different classes of soil constitutive model. The efficiency of the algorithms is judged via stress point analysis and solving a boundary value problem. Findings Stress point analysis indicates that the proposed algorithms are stable even with a large step size. In addition, numerical analysis for solving boundary value problem demonstrates a significant reduction in central processing unit (CPU) time with the use of the semi-implicit-type midpoint algorithm. Originality/value Traditionally, midpoint and Romberg algorithms are formulated from explicit integration techniques, whereas the present study uses a semi-implicit approach to enhance stability. In addition, the proposed stress integration algorithms provide an efficient means to solve boundary value problems pertaining to geotechnical engineering.

Estimating Pacejka (PAC2002) Tire Coefficients for Pneumatic Tires on Soft Soils With Application to BAJA SAE Vehicles

BAJA SAE is an engineering competition that challenges teams to design single-seat all-terrain vehicles that participate in a vast number of events, predominately on soft soils. Efficient performance in the events depends on the traction forces, which are dependent on the mechanical properties of the soil. To accurately model vehicle performance for each event, a model of the tire traction performance is required, and the tire model must be incorporated with a vehicle dynamics simulation. The traction forces at the soil-tire interface can be estimated using the Bekker-Wong stress integration method. However, commercially available vehicle dynamics simulation software, with a focus on on-road vehicles, does not utilize Bekker-Wong parameters. The Pacejka Magic Tire (MT) Formula is a common method for characterizing tire behavior for on-road vehicles. The parameters for the Pacejka MT Formula are usually produced by curve fitting measured tire data. The lack of available measured off-road tire data, as well as the additional variables for off-road tire performance (e.g. soil mechanics), make it difficult for BAJA SAE teams to simulate vehicle performance using commercial vehicle simulation tools. This paper discusses the process and results for estimating traction performance using the Bekker-Wong stress integration method for soft soils and then deriving the Pacejka coefficients based on the Bekker-Wong method. The process will enable teams to use the Pacejka Magic Tire Formula coefficients for simulating vehicle performance for BAJA SAE events, such as the hill climb, (off-road) land maneuverability, tractor pull, etc.

Estimating Traction Forces for Pneumatic Tires on Soft Soils With Application to BAJA SAE Vehicles

BAJA SAE is an engineering competition that tasks team with designing single-seat all-terrain vehicles that partake in a variety of events, predominantly on soft soils. Events range from (off-road) land maneuverability, hill climb, tractor pull, and timed acceleration. Tire-terrain interaction strongly influences the performance of off-road vehicles. Tire terrain traction is limited by the mechanical properties for soft soils; therefore, understanding tire-terrain traction forces is important for assessing vehicle performance. Using the stress integration method (SIM) initiated by Bekker and developed by Wong, this paper analyzes the performance of BAJA SAE tires using Bekker’s defined terrain measurements for soft soils. The relative rigidity of the tire versus the soil, in terms of pressure, was compared for operating conditions and used to determine the tire state (rigid wheel or pneumatic tire). Tire state determines shape of the tire-terrain interface, and integration limits. Based on the operating conditions, the tire sinkage into the soil was calculated and used to determine compaction resistance, tire hysteresis, and normal pressures along the tire-terrain interface. Using the SIM, the longitudinal and lateral tractive forces vs the slip ratio and slip angle, respectively, were calculated for a range of operation conditions. The tire-terrain traction forces were evaluated for different tire diameters and tire pressure for a range of soil types. The described process can be used to predict performance for BAJA SAE teams participating in specific events and the results can be used as a basis for selecting tires and tire pressure for dynamic events.