Computational Modeling and Design of Nonlinear Mechanical Systems and Materials

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Nonlinear mechanical systems and materials are broadly used in diverse fields. However, their modeling and design are nontrivial as they require a complete understanding of their internal nonlinearities and other phenomena. To enable their efficient design, we must first introduce computational models to accurately characterize their complex behavior. Furthermore, new inverse design techniques are also required to capture how the behavior changes when we change the design parameters of nonlinear mechanical systems and materials. Therefore, in this thesis, we introduce three novel methods for computational modeling and design of nonlinear mechanical systems and materials. In the first article, we address the design problem of nonlinear mechanical systems exhibiting stable periodic motions in response to a periodic force. We present a computational method that utilizes a frequency-domain approach for dynamical simulation and the powerful sensitivity analysis for design optimization to design compliant mechanical systems with large-amplitude oscillations. Our method is versatile and can be applied to various types of compliant mechanical systems. We validate its effectiveness by fabricating and evaluating several physical prototypes. Next, we focus on the computation modeling and mechanical characterization of contact-dominated nonlinear materials, particularly Discrete Interlocking Materials (DIM), which are generalized chainmail fabrics made of quasi-rigid interlocking elements. Unlike conventional elastic materials for which deformation and restoring forces are directly coupled, the mechanics of DIM are governed by contacts between individual elements that give rise to anisotropic kinematic deformation constraints. To replicate the biphasic behavior of DIM without simulating expensive microscale structures, we introduce an efficient anisotropic strain-limiting method based on second-order cone programming (SOCP). Additionally, to comprehensively characterize strong anisotropy, complex coupling, and other nonlinear phenomena of DIM, we introduce a novel homogenization approach for distilling macroscale deformation limits from microscale simulations and develop a data-driven macromechanical model for simulating DIM with homogenized deformation constraints.