Wrinkled membrane element based on the wrinkling potential

For a membrane structure, wrinkles have an important effect on its mechanical behaviors. Wrinkling level characterizes the development of wrinkles and reflects the performance of a membrane in its service, and it plays a very significant role in the wrinkling analysis. The shell elements combined with the stability theory would be an ideal solution to the wrinkling problem. However, this approach requires a dense mesh and the computation is very time consuming. Also the wrinkling parameters are very sensitive to the size of shell elements. Existing wrinkling models based on membrane elements are derived from the Tension Field Theory which are incapable of describing fully the wrinkling behaviors. A new wrinkling model adopting the wrinkling strain as a measure of the wrinkling level is proposed in this paper to address these issues. According to the analogy between the wrinkling strain and the elasto-plastic strain, a wrinkling potential surface is assumed to exist and its normal direction defines the direction of the wrinkling strain tensor by virtue of the flow rule. Based on the consistent condition of the wrinkling potential surface, a modified constitutive tensor is obtained. To avoid the switching of the wrinkling state in the numerical solution, a new wrinkling criterion is proposed, in which the predominant influence of the previous state is included. Besides, a new approach to determine the wrinkling orientation is given to improve the efficiency of convergence in the slack region. The objectivity of the wrinkling coordinate frame is also demonstrated as an accompanying set of results. Finally, two benchmark problems are analyzed with the proposed wrinkling model, and their results are compared with those in the literatures. Results indicate that the proposed wrinkling model is valid and accurate to characterize the wrinkling level of a membrane and it exhibits efficient convergence even in the slack region.