Efficient Computational Models for Forward and Inverse Elasticity Problems
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2025
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Doctoral Thesis
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yes
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Abstract
Elasticity is at the core of many scientific and engineering applications, including the design of resilient structures and advanced materials, and the modeling of biological tissues. Simulating elastic systems poses significant computational challenges due to the inherent nonlinearity of the governing equations, which calls for efficient optimization methods to determine equilibrium states. Second-order methods are particularly attractive because of their superior convergence properties relative to first-order techniques. However, the effective use of second-order solvers requires that the underlying functions and their derivatives are sufficiently smooth and available in closed form. This smoothness can easily degrade when generalizing standard computational models to a broader set of design tasks. This thesis proposes efficient computational models that enable robust and effective simulations for physics-based modeling and the design of complex elastic systems. In chapter 2, we propose a novel fabric-like metamaterial that features persisting contacts between 3D-printed yarns. To avoid the complexities of explicit contact modeling, we adopt an Eulerian-on-Lagrangian simulation paradigm; however, current methods remain limited to straight rods. We leverage a C^2-continuous representation to allow for Newton-type minimization on naturally curved rods. Chapter 3 presents a computational paradigm for intrinsic minimization of distance-based objectives defined on triangle meshes. Although Euclidean distances meet the C^2-continuity requirement, geodesic distances on triangle meshes do not. To permit efficient second-order optimization of embedded elasticity problems, we provide analytical derivatives as well as suitable mollifiers to recover C^2-continuity. Finally, in chapter 4, we address non-smoothness issues that arise in nonlinear material design, where changes in geometry parameters can lead to discontinuous changes in simulation meshes. We employ neural networks with tailored nonlinearities as C^\infty-continuous and differentiable representations to characterize the elastic properties of families of mechanical metamaterials. The resulting smooth representation enables gradient-based inverse design for various high-level design goals.
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Examiner : Coros, Stelian
Examiner: Thomaszewski, Bernhard
Examiner : Jacobson, Alec
Examiner : Panetta, Julian
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ETH Zurich
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09620 - Coros, Stelian / Coros, Stelian
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866480 - Computational Models of Motion for Fabrication-aware design of Bioinspired Systems (EC)
200644 - Fabrication-oriented Design of Nonlinear Network Materials (SNF)
200644 - Fabrication-oriented Design of Nonlinear Network Materials (SNF)