Elastic moduli of simple mass spring models

Kot, Maciej; Nagahashi, Hiroshi; Szymczak, Piotr

doi:10.1007/s00371-014-1015-5

Cited by 61 publications

(101 citation statements)

References 15 publications

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“…The present work is a continuation of [3], where basic properties of mass spring models have been discussed. Below we summarize the most important results; however, the reader is encouraged to refer to [3] for a more detailed introduction.…”

Section: Mass Spring Modelsmentioning

confidence: 99%

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Mass spring models with adjustable Poisson’s ratio

Kot

Nagahashi

2015

Vis Comput

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In this paper we show how to construct mass spring models for the representation of homogeneous isotropic elastic materials with adjustable Poisson's ratio. Classical formulation of elasticity on mass spring models leads to the result, that while materials with any value of Young's modulus can be modeled reliably, only fixed value of Poisson's ratio is possible. We show how to extend the conventional model to overcome this limitation. The technique is demonstrated on cubic lattice as well as disordered networks.

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Section: Mass Spring Modelsmentioning

confidence: 99%

“…The standard lattice-based models used in physics, mechanical engineering and other related fields offer a description of elastic solids which is as accurate as the limitations of linear elasticity theory allow it to be [3,4,9]. There is, however, a limitation to what can be modeled with MSMs.…”

Section: Introductionmentioning

confidence: 98%

Mass spring models with adjustable Poisson’s ratio

Kot

Nagahashi

2015

Vis Comput

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“…Springs between mass nodes are damped and so approximate the behavior of a Kelvin-Voigt viscoelastic solid with Poisson ratio of 1/4 (Kot et al 2015). As done previously (Frouard et al 2016), we consider a binary in a circular orbit, with a spinning body resolved with masses and springs.…”

Section: Description Of Mass-spring Model Simulationsmentioning

confidence: 99%

“…The parameter ds is the maximum rest length of any spring. For the cubic lattice we chose ds so that cubic cell face diagonals and cubic cell cross diagonals are connected (see Figure 1 by Kot et al 2015 for an illustration).…”

Section: Description Of Mass-spring Model Simulationsmentioning

confidence: 99%

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Tidal spin-down rates of homogeneous triaxial viscoelastic bodies

Quillen

Kueter-Young

Frouard

et al. 2016

Mon. Not. R. Astron. Soc.

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We use numerical simulations to measure the sensitivity of the tidal spin down rate of a homogeneous triaxial ellipsoid to its axis ratios by comparing the drift rate in orbital semi-major axis to that of a spherical body with the same mass, volume and simulated rheology. We use a mass-spring model approximating a viscoelastic body spinning around its shortest body axis, with spin aligned with orbital spin axis, and in circular orbit about a point mass. The torque or drift rate can be estimated from that predicted for a sphere with equivalent volume if multiplied by 0.5where b/a and c/a are the body axis ratios and index α c ≈ 1.05 is consistent with the random lattice mass spring model simulations but α c = 4/3 suggested by scaling estimates. A homogeneous body with axis ratios 0.5 and and 0.8, like Haumea, has orbital semi-major axis drift rate about twice as fast as a spherical body with the same mass, volume and material properties. A simulation approximating a mostly rocky body but with 20% of its mass as ice concentrated at its ends has a drift rate 10 times faster than the equivalent homogeneous rocky sphere. However, this increase in drift rate is not enough to allow Haumea's satellite, Hi'iaka, to have tidally drifted away from Haumea to its current orbital semi-major axis.

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Deciphering, Designing, and Realizing Self‐Folding Biomimetic Microstructures Using a Mass‐Spring Model and Inkjet‐Printed, Self‐Folding Hydrogels

Cui

Yin

Han

2020

Adv Funct Materials

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Flat, organic microstructures that can self-fold into 3D microstructures are promising for tissue regeneration, for being capable of distributing living cells in 3D while forming highly complex, biomimetic architectures to assist cells in performing regeneration. However, the design of self-folding microstructures is difficult due to a lack of understanding of the underlying formation mechanisms. This study helps bridge this gap by deciphering the dynamics of the self-folding using a mass-spring model. This numerical study reveals that self-folding procedure is multi-modal, which can become random and unpredictable by involving the interplays between internal stresses, external stimulation, imperfection, and self-hindrance of the folding body. To verify the numerical results, bilayered, hydrogel-based micropatterns capable of self-folding are fabricated using inkjet-printing and tested. The experimental and numerical results are consistent with each other. The above knowledge is applied to designing and fabricating self-folding microstructures for tissue-engineering, which successfully creates 3D, cell-scaled, and biomimetic microstructures, such as microtubes, branched microtubes, and hollow spheres. Embedded in self-folded microtubes, human mesenchymal stem cells proliferate and form linear cell-organization mimicking the cell morphology in muscles and tendons. The above knowledge and study platforms can greatly contribute to the research on self-folding microstructures and applications to tissue regeneration.

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Elastic moduli of simple mass spring models

Cited by 61 publications

References 15 publications

Mass spring models with adjustable Poisson’s ratio

Mass spring models with adjustable Poisson’s ratio

Tidal spin-down rates of homogeneous triaxial viscoelastic bodies

Deciphering, Designing, and Realizing Self‐Folding Biomimetic Microstructures Using a Mass‐Spring Model and Inkjet‐Printed, Self‐Folding Hydrogels

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