Lattice structures as thermoelastic strain gradient metamaterials: Evidence from full-field simulations and applications to functionally step-wise-graded beams

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@article{3636f4043ea54b41af07fa7d6db8d339,
title = "Lattice structures as thermoelastic strain gradient metamaterials: Evidence from full-field simulations and applications to functionally step-wise-graded beams",
abstract = "The present work investigates the mechanical and thermomechanical bending response of beam structures possessing a triangular lattice microarchitecture. The validity of generalized continuum models, in general, and the associated dimensionally reduced models for functionally step-wise-graded microarchitectural beams, in particular, is approved by full-field finite element simulations. Most importantly, the necessity of the temperature gradient in the Helmholtz free energy is substantiated. The corresponding strong and weak forms for the associated Bernoulli–Euler and Timoshenko models of functionally graded beams are derived. The effective classical thermoelastic properties of a metamaterial with a triangular lattice microarchitecture are defined by means of computational homogenization. The additional length scale parameter involved in the generalized beam models, and associated to the particular triangular microarchitecture, is calibrated by fitting the mechanical bending responses of a series of lattice beams to the analytical solutions of the corresponding theoretical models. Strongly size-dependent mechanical and size-independent thermal bending responses are observed for both thin and thick beams with triangular lattice microarchitectures. Finally, different lattice beams with varying microarchitectures are introduced and shown to behave as generalized functionally step-wise-graded beams with respect to the higher-order elastic modulus, i.e., the length scale parameter varying in the direction of the beam axis.",
keywords = "Bernoulli–Euler beam, Microarchitecture, Second grade thermoelasticity, Size effect, Temperature gradient, Timoshenko beam, Triangular lattice metamaterial",
author = "Sergei Khakalo and Jarkko Niiranen",
year = "2019",
month = "11",
day = "15",
doi = "10.1016/j.compositesb.2019.107224",
language = "English",
volume = "177",
journal = "Composites Part B: Engineering",
issn = "1359-8368",
publisher = "Elsevier Limited",

}

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TY - JOUR

T1 - Lattice structures as thermoelastic strain gradient metamaterials

T2 - Evidence from full-field simulations and applications to functionally step-wise-graded beams

AU - Khakalo, Sergei

AU - Niiranen, Jarkko

PY - 2019/11/15

Y1 - 2019/11/15

N2 - The present work investigates the mechanical and thermomechanical bending response of beam structures possessing a triangular lattice microarchitecture. The validity of generalized continuum models, in general, and the associated dimensionally reduced models for functionally step-wise-graded microarchitectural beams, in particular, is approved by full-field finite element simulations. Most importantly, the necessity of the temperature gradient in the Helmholtz free energy is substantiated. The corresponding strong and weak forms for the associated Bernoulli–Euler and Timoshenko models of functionally graded beams are derived. The effective classical thermoelastic properties of a metamaterial with a triangular lattice microarchitecture are defined by means of computational homogenization. The additional length scale parameter involved in the generalized beam models, and associated to the particular triangular microarchitecture, is calibrated by fitting the mechanical bending responses of a series of lattice beams to the analytical solutions of the corresponding theoretical models. Strongly size-dependent mechanical and size-independent thermal bending responses are observed for both thin and thick beams with triangular lattice microarchitectures. Finally, different lattice beams with varying microarchitectures are introduced and shown to behave as generalized functionally step-wise-graded beams with respect to the higher-order elastic modulus, i.e., the length scale parameter varying in the direction of the beam axis.

AB - The present work investigates the mechanical and thermomechanical bending response of beam structures possessing a triangular lattice microarchitecture. The validity of generalized continuum models, in general, and the associated dimensionally reduced models for functionally step-wise-graded microarchitectural beams, in particular, is approved by full-field finite element simulations. Most importantly, the necessity of the temperature gradient in the Helmholtz free energy is substantiated. The corresponding strong and weak forms for the associated Bernoulli–Euler and Timoshenko models of functionally graded beams are derived. The effective classical thermoelastic properties of a metamaterial with a triangular lattice microarchitecture are defined by means of computational homogenization. The additional length scale parameter involved in the generalized beam models, and associated to the particular triangular microarchitecture, is calibrated by fitting the mechanical bending responses of a series of lattice beams to the analytical solutions of the corresponding theoretical models. Strongly size-dependent mechanical and size-independent thermal bending responses are observed for both thin and thick beams with triangular lattice microarchitectures. Finally, different lattice beams with varying microarchitectures are introduced and shown to behave as generalized functionally step-wise-graded beams with respect to the higher-order elastic modulus, i.e., the length scale parameter varying in the direction of the beam axis.

KW - Bernoulli–Euler beam

KW - Microarchitecture

KW - Second grade thermoelasticity

KW - Size effect

KW - Temperature gradient

KW - Timoshenko beam

KW - Triangular lattice metamaterial

UR - http://www.scopus.com/inward/record.url?scp=85071955919&partnerID=8YFLogxK

U2 - 10.1016/j.compositesb.2019.107224

DO - 10.1016/j.compositesb.2019.107224

M3 - Article

VL - 177

JO - Composites Part B: Engineering

JF - Composites Part B: Engineering

SN - 1359-8368

M1 - 107224

ER -

ID: 36886178