Advanced Numerical Methods for Generalized Continuum Models

Extreme deformation events, where materials or structures undergo significant changes in shape or break down, are critical to many fields of engineering. Examples include landslides in geotechnical engineering, where large amounts of earth shift unexpectedly; cracks forming in buildings, bridges, or other structures in civil engineering; and the shaping or forming of metals during manufacturing. Understanding and predicting these extreme events is essential for ensuring safety, reliability, and efficiency in a wide range of applications. To simulate these events accurately, we need advanced tools that can model how materials behave not just on a large scale (the "macroscale") but also at a very small level (the "microscale"), where individual particles of material interact. When we consider how materials deform at the microscale, we can obtain superior predictions about how they will respond in real-world scenarios. However, doing so requires both sophisticated mathematical models and powerful computational methods capable of handling the complexity of these deformations. This project aims to develop and apply such advanced computational techniques. Specifically, we are focusing on the use of the Material Point Method, an advanced computational framework designed to handle extremely large deformations in materials and structures. In combination with micropolar continuum theorya mathematical approach that accounts for particle deformations at the microscopic levelthis method allows us to simulate extreme events with greater accuracy and detail. The outcome of this project will be a highly versatile and improved simulation framework that can be applied across various fields of engineering. It will enable engineers and scientists to better assess and understand how extreme deformations impact materials and structures. This improved understanding can lead to the development of stronger, more resilient materials, safer designs for infrastructure and manufacturing, and more sustainable practices. Whether it`s improving the safety of buildings, optimizing the design of industrial processes, or developing new composite materials, this project will provide valuable insights that contribute to solving some of the most pressing challenges in modern engineering.