Efficient numerical frameworks for stochastic contact analysis

• Applicant: Zhibao Zheng, Ph.D.
• Subject Area: Mechanics ; Applied Mechanics, Statics and Dynamics
• Term: since 2026
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 575372789

Contact problems play an important role in various fields and have been well established. However, there is only limited experience in the treatment of stochastic contact problems (SCP). The challenges of SCP are from the effective treatment of the coupling of stochastic contact and other nonlinearities, stochastic contact on random geometric boundaries (RGB), and their uncertainty quantification (UQ). Based on the applicants’ preliminary work, the overall goal of this project is to overcome these challenges and develop efficient numerical methods for nonlinear SCP, linear and nonlinear SCP on RGB, and the corresponding reliability analysis. Specifically, this project includes four parts: 1) Develop efficient numerical algorithms for nonlinear SCP: The coupling of stochastic contact and other nonlinearities results in high complexity and computational effort compared to deterministic contact analysis and linear elastic SCP. In this proposal, combining the applicants’ preliminary work on linear elastic SCP with effective treatments of other nonlinearities, efficient numerical algorithms will be developed to solve nonlinear SCP, with special emphasis on elastoplastic and/or finite strain SCP with high-dimensional random inputs. 2) Develop efficient frameworks for SCP on RGB: The determination of contact state is the most critical in contact analysis and is costly even for deterministic contact problems. In SCP, in addition to contact states, one has to determine the stochastic contact states, which makes SCP more costly. It is more challenging if the contact occurs on RGB, To this end, combining effective treatments of random geometries with the applicants’ preliminary work on linear elastic SCP and the above nonlinear SCP algorithms, efficient numerical frameworks will be proposed to solve both linear and nonlinear SCP on RGB. 3) Develop unified UQ paradigms for SCP: Based on the above stochastic solutions, the failure probabilities in reliability analysis will be estimated by unified computational paradigms. Two types of methods will be developed, including the stochastic solution sample-based direct estimation and the explicit representation-based estimation, in which one of the focuses will be the explicit representations of (discontinuous) stochastic solutions. 4) Benchmark models and validation: To validate the above methods, benchmark models will be investigated, including elastoplastic and finite strain SCP for the Goal 1, the linear and nonlinear SCP on RGB for the Goal 2, and the corresponding reliability analysis of these models for the Goal 3. The computational accuracy and efficiency of these methods will be emphasized and compared with the reference solutions obtained by standard MCS with a large number of random samples. Furthermore, the proposed overall framework will also be applied to practical applications such as tire rolling contact on random surfaces and femoral bone density evolution with implanted prostheses.

• DFG Programme: Research Grants
• Co-Investigator: Professor Dr.-Ing. Udo Nackenhorst