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1. Dynamics and topology of non-Hermitian elastic lattices with non-local feedback control interactions

   https://doi.org/10.1088/1367-2630/ab81b6  

   Rosa, Matheus I. N.; Ruzzene, Massimo (May 2020, New Journal of Physics)

   Abstract We investigate non-Hermitian elastic lattices characterized by non-local feedback interactions. In one-dimensional lattices, proportional feedback produces non-reciprocity associated with complex dispersion relations characterized by gain and loss in opposite propagation directions. For non-local controls, such non-reciprocity occurs over multiple frequency bands characterized by opposite non-reciprocal behavior. The dispersion topology is investigated with focus on winding numbers and non-Hermitian skin effect, which manifests itself through bulk modes localized at the boundaries of finite lattices. In two-dimensional lattices, non-reciprocity is associated with directional wave amplification. Moreover, the combination of skin effect in two directions produces modes that are localized at the corners of finite two-dimensional lattices. Our results describe fundamental properties of non-Hermitian elastic lattices, and suggest new possibilities for the design of meta materials with novel functionalities related to selective wave filtering, amplification and localization. The considered non-local lattices also provide a platform for the investigation of topological phases of non-Hermitian systems. 

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2. Capturing Animation-Ready Isotropic Materials Using Systematic Poking

   https://doi.org/10.1145/3618406  

   Chen, Huanyu; Zhao, Danyong; Barbič, Jernej (December 2023, ACM Transactions on Graphics)

   Capturing material properties of real-world elastic solids is both challenging and highly relevant to many applications in computer graphics, robotics and related fields. We give a non-intrusive, in-situ and inexpensive approach to measure the nonlinear elastic energy density function of man-made materials and biological tissues. We poke the elastic object with 3d-printed rigid cylinders of known radii, and use a precision force meter to record the contact force as a function of the indentation depth, which we measure using a force meter stand, or a novel unconstrained laser setup. We model the 3D elastic solid using the Finite Element Method (FEM), and elastic energy using a compressible Valanis-Landel material that generalizes Neo-Hookean materials by permitting arbitrary tensile behavior under large deformations. We then use optimization to fit the nonlinear isotropic elastic energy so that the FEM contact forces and indentations match their measured real-world counterparts. Because we use carefully designed cubic splines, our materials are accurate in a large range of stretches and robust to inversions, and are therefore animation-ready for computer graphics applications. We demonstrate how to exploit radial symmetry to convert the 3D elastostatic contact problem to the mathematically equivalent 2D problem, which vastly accelerates optimization. We also greatly improve the theory and robustness of stretch-based elastic materials, by giving a simple and elegant formula to compute the tangent stiffness matrix, with rigorous proofs and singularity handling. We also contribute the observation that volume compressibility can be estimated by poking with rigid cylinders of different radii, which avoids optical cameras and greatly simplifies experiments. We validate our method by performing full 3D simulations using the optimized materials and confirming that they match real-world forces, indentations and real deformed 3D shapes. We also validate it using a Shore 00 durometer, a standard device for measuring material hardness. 

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3. Evaluation of the parallel coupling constitutive model for biomaterials using a fully coupled network-matrix model

   https://doi.org/10.1016/j.jmbbm.2024.106583  

   Dey, MK; Merson, J; Picu, RC (July 2024, Journal of the Mechanical Behavior of Biomedical Materials)

   In this article we discuss the effective properties of composites containing a crosslinked athermal fiber network embedded in a continuum elastic matrix, which are representative for a broad range of biological materials. The goal is to evaluate the accuracy of the widely used biomechanics parallel coupling model in which the tissue response is defined as the additive superposition of the network and matrix contributions, and the interaction of the two components is neglected. To this end, explicit, fully coupled models are used to evaluate the linear and non-linear response of the composite. It is observed that in the small strain, linear regime the parallel model leads to errors when the ratio of the individual stiffnesses of the two components is in the range 0.1–10, and the error increases as the matrix approaches the incompressible limit. The data presented can be used to correct the parallel model to improve the accuracy of the overall stiffness prediction. In the non-linear large deformation regime linear superposition does not apply. The data shows that the matrix reduces the stiffening rate of the network, and the response is softer than that predicted by the parallel model. The correction proposed for the linear regime mitigates to a large extent the error in the non-linear regime as well, provided the matrix Poisson ratio is not close to 0.5. The special case in which the matrix is rendered auxetic is also evaluated and it is seen that the auxeticity of the matrix may compensate the stiffening introduced by the network, leading to a composite with linear elastic response over a broad range of strains. 

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4. A Relaxation Approach to Feature Selection for Linear Mixed Effects Models

   https://doi.org/10.1080/10618600.2023.2231496  

   Sholokhov, Aleksei; Burke, James V.; Santomauro, Damian F.; Zheng, Peng; Aravkin, Aleksandr (September 2023, Journal of Computational and Graphical Statistics)

   Jones, G.; Faming, L. (Ed.)

   Linear Mixed-Effects (LME) models are a fundamental tool for modeling correlated data, including cohort studies, longitudinal data analysis, and meta-analysis. Design and analysis of variable selection methods for LMEs is more difficult than for linear regression because LME models are nonlinear. In this article we propose a novel optimization strategy that enables a wide range of variable selection methods for LMEs using both convex and nonconvex regularizers, including 𝓁1, Adaptive-𝓁1, SCAD, and 𝓁0. The computational framework only requires the proximal operator for each regularizer to be readily computable, and the implementation is available in an open source python package pysr3, consistent with the sklearn standard. The numerical results on simulated data sets indicate that the proposed strategy improves on the state of the art for both accuracy and compute time. The variable selection techniques are also validated on a real example using a data set on bullying victimization. Supplementary materials for this article are available online. 

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5. Chirality in topologically interlocked material systems

   https://doi.org/10.1016/j.mechmat.2024.104956  

   Kim, Dong Young; Siegmund, Thomas (April 2024, Mechanics of Materials)

   The present study focuses on the mechanical chirality in plate-type topologically interlocked material systems. Topologically interlocked material (TIM) systems are a class of dense architectured materials for which the mechanical response emerges from the elastic behavior of the building blocks and the contact-frictions interactions between the blocks. The resulting mechanical behavior is strongly non-linear due to the stability-instability characteristics of the internal load transfer pattern. Two tessellations are considered (square and hexagonal) and patches from each are used as templates. While individual building blocks are achiral, chirality emerges from the assembly pattern. The measure of \textit{microstructure circulation} is introduced to identify the geometric chirality of TIM systems. TIM systems identified as geometrically chiral are demonstrated to possess mechanical chiral response with a force-torque coupling under transverse mechanical loading of the TIM plate. The chiral length is found to be constant during the elastic response, yet size-dependent. During nonlinear deformation, the chiral length scale increases significantly and again exhibits a strong size dependence. The principle of dissection is introduced to transform non-chiral TIM systems into chiral ones. In the linear deformation regime, the framework of chiral elasticity is shown to be applicable. In the non-linear deformation regime, chirality is found to strongly affect the mechanical behavior more significantly than in the linear regime. Experiments on selected TIM systems validate key findings of the main computational study with the finite element method. 

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