Size effects in lattice-structured cellular materials: edge softening effects

Yoder, Marcus; Thompson, Lonny L.; Summers, Joshua D.

doi:10.1007/s10853-018-3103-9

Cited by 11 publications

(9 citation statements)

References 23 publications

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“…As mentioned earlier, the observation of size effects in a heterogeneous medium is not new, although previous reports of such effects have usually indicated that reducing overall size to that of the length scale of the underlying material heterogeneity will be accompanied by an increase in material stiffness or rigidity, behaviour described here as a conventional or positive effect which concurs with that forecast by more generalised deformation theories such as Cosserat (micropolar) elasticity. While more recent research [22,23,24] has indicated that 2D materials may exhibit both conventional positive and contradictory negative size effects when loaded in bending, the results presented here indicate that the nature of these effects may be even more involved than existing theoretical forecasts would imply or any previous work has identified. The complete inversion of the size effect from positive to negative in braced open cell cubic lattices subject to twisting while the corresponding effect in bending remains positive is an entirely new result that cannot be adequately predicted by such theories.…”

Section: Discussioncontrasting

confidence: 56%

“…This inversion occurs even when the redistribution of matrix material from edges to diagonals results in almost no change in volume fraction (figure 16). The causes of such size effect inversion have recently been explained for 2D layered [22] and latticed based materials [23,24] loaded in flexure. In the first case a layered material comprised of alternating stiff and compliant layers was shown to exhibit a conventional, positive size effect when the stiffer layers were located furthest from the neutral axis of bending and an opposite, negative effect when the more compliant layers were located thus.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Very recently, both conventionally anticipated [19] and more involved [20] size effects have been reported in additively manufactured mechanical metamaterials. Some of these contrasting and more involved effects have been analytically explained for various materials notably those comprised of more rigid periodic inclusions within a compliant matrix [21], layered composite laminates [22] and those formed of periodic 2D lattices [23,24].…”

Section: Introductionmentioning

confidence: 99%

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Size effect anomalies in the behaviour of loaded 3D mechanical metamaterials

Dunn

Wheel

2019

Philosophical Magazine

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Size effects exhibited by mechanical metamaterials when loaded may be positive such that reducing overall size towards that of the length scale of the underlying structure intrinsic to the material is accompanied by increasing stiffness or rigidity, a phenomenon that has been repeatedly observed and is also forecast by various more generalized continuum theories of deformation in loaded heterogeneous continua. However, such effects may in certain circumstances be contradictory in that decreasing size is accompanied by increasing compliance, the transition from the conventional, positive to this theoretically unanticipated negative behaviour having been explained recently in terms of the distribution of material within 2D continua subject to bending. Here we report on a novel phenomenon newly observed in periodic 3D lattice materials comprised of repeated cubic unit cells formed of exterior edge and interior diagonal connectors. Subtle redistribution of matrix material from edges to diagonals causes the size effect to change dramatically, inverting from positive to negative when loaded in the torsional mode while the corresponding effect for the flexural mode remains entirely positive under the same circumstances. This observation may lead to the prospect of optimising the design of 3D periodic metamaterials to provide a stiffer response in one loading mode and a more compliant response in another, a feature that could potentially be exploited in various innovative applications.

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Section: Discussioncontrasting

confidence: 56%

Section: Numerical Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Size effect anomalies in the behaviour of loaded 3D mechanical metamaterials

Dunn

Wheel

2019

Philosophical Magazine

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“…Note that the investigated size effects result from the bending deformation of the cantilever beam. Nevertheless, it should be mentioned that the mechanism of size effects could also be the result of the so-called edge effects [58,87], which lead to a softer response of structures. Therefore, in order to understand size effects, softening effects must be studied, and this will be left for the future.…”

Section: Discussionmentioning

confidence: 99%

Effective strain gradient continuum model of metamaterials and size effects analysis

Yang

Timofeev

Giorgio

et al. 2020

Continuum Mech. Thermodyn.

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In this paper, a strain gradient continuum model for a metamaterial with a periodic lattice substructure is considered. A second gradient constitutive law is postulated at the macroscopic level. The effective classical and strain gradient stiffness tensors are obtained based on asymptotic homogenization techniques using the equivalence of energy at the macro-and microscales within a so-called representative volume element. Numerical studies by means of finite element analysis were performed to investigate the effects of changing volume ratio and characteristic length for a single unit cell of the metamaterial as well as changing properties of the underlying material. It is also shown that the size effects occurring in a cantilever beam made of a periodic metamaterial can be captured with appropriate accuracy by using the identified effective stiffness tensors. Keywords Effective continuum • Strain gradient elasticity • Asymptotic homogenization method • Finite element method Communicated by Luca Placidi.

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“…From the perspective of pile impedance and foundation settlement, Liu et al studied the size effect of the rigid pile composite foundation [20]. Yoder et al found that the dimensional effect of porous material was related to the bending strain energy [21]. Lee & Han studied the size effect of the foundation, and they found that the bearing capacity coefficient decreased with increase of the foundation width [22].…”

Section: State Of the Artmentioning

confidence: 99%

Size Effect Analysis of Scale Test Model for High-speed Railway Foundation under Dynamic Loading Condition

Wang¹,

Kunpeng

Zou

et al. 2021

Teh. vjesn.

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To determine the energy attenuation and energy reflection coefficients in layered foundation is the key factor to reveal the dynamic response characteristics of the high-speed railway foundation. Based on the foundation test model under the dynamic loading of the high-speed railway, the energy attenuation and energy reflection coefficients were introduced and the attenuation formulas of the vibration acceleration in the layered foundation were deduced. Five scale models of 1:1, 1:2, 1:5, 1:10 and 1:20 are established respectively by using Abaqus technique. The energy attenuation mechanism and interfacial energy reflection characteristics in the layered foundation were analyzed. Results show that it is appropriate to use vibration acceleration to characterize the propagation rule of the energy attenuation in the layered foundation. The size effect equations of the energy attenuation and energy reflection coefficients in the layered foundation are deduced and the size effect of the energy attenuation is revealed. Based on the nonlinear relationships among the energy attenuation coefficient, the model scale, the loading amplitude and the vibration frequency, the energy attenuation equation of the scale test model is constructed. The reliability of the theoretical and simulation results is verified by the scale test model. The conclusions obtained in this study can provide a reference for a similar engineering practice.

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Size effects in lattice-structured cellular materials: edge softening effects

Cited by 11 publications

References 23 publications

Size effect anomalies in the behaviour of loaded 3D mechanical metamaterials

Size effect anomalies in the behaviour of loaded 3D mechanical metamaterials

Effective strain gradient continuum model of metamaterials and size effects analysis

Size Effect Analysis of Scale Test Model for High-speed Railway Foundation under Dynamic Loading Condition

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