29 November, 2023
Congratulations to Bram van der Heijden for successfully defending his thesis and receiving his PhD degree.
Thesis: Towards Data-Driven and Model-Free Predictions for Forward and Inverse Problems in Solid mechanics
Committee:
Abstract
In the realm of solid mechanics, precise predictions are crucial for engineering and science. We often rely on complex mathematical models to design structures. However, these models can be challenging to use effectively, as they require information about material behaviour. Unlike other aspects of modelling of structures, material models lack strong foundational support in physics. This thesis introduces two data-driven approaches to address these challenges.
First, "Frankenstein's method" is a model-free approach that directly translates real-world observations of tested systems into predictions for structural problems, circumventing constitutive models altogether. It uses displacement fields from actual structures to predict both local and non-local phenomena without presuming local continuum mechanics.
While "Frankenstein's method" offers advantages, it may not integrate well with traditional numerical methods. To bridge this gap, our second strategy focuses on an inverse problem: extracting the parameters of a material model, from measurements. We've improved the efficiency of this process using fast gradient descent optimization with automated derivatives, enabled by differentiable programming and physics-informed neural networks.
Our research contributes to solid mechanics by providing two data-centric methods for more accurate predictions of structural performance. These approaches address the challenges of complex constitutive equations, potentially eliminating their necessity or enhancing material property extraction precision.
Bio
Bram van der Heijden is a PhD candidate that works on novel numerical tools to predict deformations of solid mechanics. These tools to predict structural behavior and complicated fracture processes that the traditional tools, such as FEM, fail to accurately capture. For his MSc in Aerospace Engineering at the TU Delft, he has worked on structural optimization algorithms for fatigue resistant and reliable structures by fatigue crack growth life maximization.