Parameter Identification in Nonlinear Solid Mechanics

This course introduces numerical optimization-based approaches to parameter identification, where an objective function is minimized to compute optimal parameter sets by measuring deviations between simulation results and experimental data. The course covers theoretical and algorithmic concepts of (constrained) nonlinear optimization, accompanied by programming exercises for hands-on experience. Furthermore, students learn to apply tools for identification with nonlinear material models, conducting experiments in the materials characterization laboratory. Advanced concepts, such as parameter identification through inhomogeneous deformation processes using digital image correlation and finite element analysis, are also addressed. Additionally, the course helps in solving structural optimization problems in nonlinear solid mechanics.

The following course/module was developed at the TU Bergakademie Freiberg.

Learning outcomes / Competencies:

• Develop Numerical Skills: Acquire a objective-function based knowledge, enabling (process) mechanical / material engineers to focus on understanding fundamental theoretical and algorithmic concepts of (constrained) nonlinear optimization and engage in programming exercises for hands-on experience.
• Understanding Parameter Deviation: Integrate methods and approaches to study numerical optimization-based approaches to parameter identification, which involve minimizing an objective function that measures deviations between simulation results and experimental data 
• Establishing Theoretical & Algorithm Concepts: Gain knowledge, study courses or resources that cover topics such as constrained nonlinear optimization and engage in online exercises to apply these concepts.
• Using Digital Image & Finite Element Analysis: Comprehend processes, identification methods so as to combine these techniques to identify parameters through inhomogeneous deformation processes and obtain accurate models.
• Optimization in Nonlinear Solid Mechanics: Explore the involvement and application of numerical concepts to solve problems related to optimizing the design and performance of structures, considering nonlinear material behavior and mechanical responses