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1. On the statics and dynamics of granular-microstructured rods with higher order effects

   https://doi.org/10.1177/10812865211009938  

   Nejadsadeghi, Nima; Misra, Anil (March 2021, Mathematics and Mechanics of Solids)

   null (Ed.)

   Granular-microstructured rods show strong dependence of grain-scale interactions in their mechanical behavior, and therefore, their proper description requires theories beyond the classical theory of continuum mechanics. Recently, the authors have derived a micromorphic continuum theory of degree n based upon the granular micromechanics approach (GMA). Here, the GMA is further specialized for a one-dimensional material with granular microstructure that can be described as a micromorphic medium of degree 1. To this end, the constitutive relationships, governing equations of motion and variationally consistent boundary conditions are derived. Furthermore, the static and dynamic length scales are linked to the second-gradient stiffness and micro-scale mass density distribution, respectively. The behavior of a one-dimensional granular structure for different boundary conditions is studied in both static and dynamic problems. The effects of material constants and the size effects on the response of the material are also investigated through parametric studies. In the static problem, the size-dependency of the system is observed in the width of the emergent boundary layers for certain imposed boundary conditions. In the dynamic problem, microstructural effects are always present and are manifested as deviations in the natural frequencies of the system from their classical counterparts. 

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2. Effect of Wrapping Force on the Effective Elastic Behavior of Packed Cylinders

   https://doi.org/10.1115/1.4056212  

   Yin, Huiming; Cui, Junhe; Teka, Linda G.; Zadshir, Mehdi (March 2023, Journal of Applied Mechanics)

   Abstract When cylinders are packed and wrapped by the bands around the surface, the effective elastic behavior in the cross section of the assembly, which is of significance to its stability and integrity, can be controlled by the wrapping force in the band. The wrapping force is transferred to the cylinders through the Hertz contact between each pair of neighboring cylinders, which is validated by the experiments. The Singum model is introduced to study the mechanical behaviors of the packed cylinders with two-dimensional (2D) packing lattices, in which an inner cylinder is simulated by a continuum particle of Singum and the inter-cylinder force is governed by the Hertz contact model so as to derive the effective stress-strain relationship. The wrapping force will produce configurational forces given a displacement variation, which significantly changes the effective stiffness of the packed cylinders. The hexagonal packing exhibits isotropic elasticity whereas the square packing is anisotropic. The efficacy of our model is demonstrated by comparing the closed form elasticity against the numerical simulation and the previous models. The explicit form of elasticity can be used for packing design and quality control of cable construction and installation. 

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3. Low-velocity impact response of wood-strand sandwich panels and their components

   https://doi.org/10.1515/hf-2017-0169  

   Mohammadabadi, Mostafa; Yadama, Vikram; Yao, LiHong; Bhattacharyya, Debes (July 2018, Holzforschung)

   Abstract Profiled hollow core sandwich panels (SPs) and their components (outer layers and core) were manufactured with ponderosa and lodgepole pine wood strands to determine the effects of low-velocity impact forces and to observe their energy absorption (EA) capacities and failure modes. An instrumented drop weight impact system was applied and the tests were performed by releasing the impact head from 500 mm for all the specimens while the impactors (IMPs) were equipped with hemispherical and flat head cylindrical heads. SPs with cavities filled with a rigid foam insulation material (SP foam ) were also tested to understand the change in EA behavior and failure mode. Failure modes induced by both IMPs to SPs were found to be splitting, perforating, penetrating, core crushing and debonding between the core and the outer layers. SP foam s absorbed 26% more energy than unfilled SPs. SP foam s with urethane foam suffer less severe failure modes than SPs. SPs in a ridge-loading configuration absorbed more impact energy than those in a valley-loading configuration, especially when impacted by a hemispherical IMP. Based on the results, it is evident that sandwich structure is more efficient than a solid panel concerning impact energy absorption, primarily due to a larger elastic section modulus of the core’s corrugated geometry. 

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4. A midsurface elasticity model for a thin, nonlinear, gradient elastic plate

   https://doi.org/10.1016/j.ijengsci.2024.104026  

   Rodriguez, C (April 2024, International Journal of Engineering Science)

   In this paper, we derive a dynamic surface elasticity model for the two-dimensional midsurface of a thin, three-dimensional, homogeneous, isotropic, nonlinear gradient elastic plate of thickness ℎ. The resulting model is parameterized by five, conceivably measurable, physical properties of the plate, and the stored surface energy reduces to Koiter’s plate energy in a singular limiting case. The model corrects a theoretical issue found in wave propagation in thin sheets and, when combined with the author’s theory of Green elastic bodies possessing gradient elastic material boundary surfaces, removes the singularities present in fracture within traditional/classical models. Our approach diverges from previous research on thin shells and plates, which primarily concentrated on deriving elasticity theories for material surfaces from classical three-dimensional Green elasticity. This work is the first in rigorously developing a surface elasticity model based on a parent nonlinear gradient elasticity theory. 

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5. Flexible Cube Tilt Lattice with Anisotropic Cosserat Effects and Negative Poisson’s Ratio

   https://doi.org/10.1002/pssb.201800512  

   Rueger, Z. (January 2019, Physica status solidi)

   A 3D lattice structure consisting of pivoting cubes with flexible links at the corners is presented. It exhibits anisotropic negative Poisson’s ratio -0.54 and -0.75. Size effects occur in torsion and bending; these effects are consistent with Cosserat elasticity but not with classical elasticity. Cosserat elastic solids exhibit sensitivity to strain gradients; size effects occur in torsion and bending; also reduction in stress concentrations. The observed Cosserat effects also reveal anisotropy. 

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