ZHOU Yangjing, FENG Zhiqiang, PENG Lei. Application of the Bi-Potential Integration Algorithm to Non-Associated Materials[J]. Applied Mathematics and Mechanics, 2018, 39(1): 11-28. doi: 10.21656/1000-0887.380139
 Citation: ZHOU Yangjing, FENG Zhiqiang, PENG Lei. Application of the Bi-Potential Integration Algorithm to Non-Associated Materials[J]. Applied Mathematics and Mechanics, 2018, 39(1): 11-28.

# Application of the Bi-Potential Integration Algorithm to Non-Associated Materials

##### doi: 10.21656/1000-0887.380139
Funds:  The National Natural Science Foundation of China（11372260）
• Rev Recd Date: 2017-05-23
• Publish Date: 2018-01-15
• Given the formulation of material free energy, the bi-potential theory allows one to divide standard materials into 2 main categories: explicit or implicit. The Drucker-Prager (D-P) model was taken as an example, which typically describes non-associated materials through the constitutive cones. With a new description of the orthogonal law, the dual constitutive cones were proposed, which not only satisfy the constitutive law of the D-P model, but also meet the requirements of the implicit flow rules. On the basis of the D-P model, and according to the bi-potential theory, 5 forms of bi-potential functions were established: the elastic stage in rate form, the plastic stage in rate form, the elastic stage in incremental form, the plastic stage in incremental form and the elasto-plastic stage in incremental form. The bi-potential integration algorithm was then obtained. A numerical simulation example was given to verify the accuracy and stability of the bi-potential integration algorithm.
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