Metamateriais de origami mostram auxeticidade reversavel combinada com recuperação de deformação
Embora algumas estruturas de origami em 3D tenham sido produzidas atravanãs da fabricaça£o aditiva, alcana§ar as propriedades de dobragem exibidas no origami de papel ideal permaneceu um desafio.
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)
Va¡rios prota³tipos metamateriais em diferentes escalas, que foram miniaturizados na escala de macrons usando a gravação direta a laser de dois fa³tons. Crédito: Allison L. Carter, Georgia Tech
A simplicidade e a elega¢ncia do origami, uma antiga forma de arte japonesa, motivaram os pesquisadores a explorar sua aplicação no mundo dos materiais.
Novas pesquisas de uma equipe interdisciplinar, incluindo Horacio Espinosa da Northwestern Engineering e Sridhar Krishnaswamy e Glaucio Paulino do Instituto de Tecnologia da Gea³rgia, visam promover a criação e o entendimento dessas estruturas dobradas para aplicações que variam de roba³tica eletra´nica a dispositivos médicos e coletores de energia.
Inspirados no origami, os metamateriais meca¢nicos - estruturas artificiais com propriedades meca¢nicas definidas por sua estrutura e não por sua composição - ganharam considera¡vel atenção devido ao seu potencial de produzir estruturas e materiais implanta¡veis ​​e altamente ajusta¡veis.
O que não se sabia era quais estruturas integram a capacidade de recuperação da forma, propriedades meca¢nicas direcionais pronunciadas e auxicidade reversavel - o que significa que suasDimensões laterais podem aumentar e diminuir quando pressionadas progressivamente. Embora algumas estruturas de origami em 3D tenham sido produzidas atravanãs da fabricação aditiva, alcana§ar as propriedades de dobragem exibidas no origami de papel ideal permaneceu um desafio.
Usando efeitos em nanoescala para um design de origami, a equipe de pesquisadores da Escola de Engenharia McCormick e da Georgia Tech procurou responder a essa pergunta. Eles produziram pequenos metamateriais construados em origami em 3D, mantendo com sucesso as melhores propriedades sem recorrer a artefatos para permitir a dobra.
"As estruturas criadas constituem os menores metamateriais arquitetados de origami fabricados, exibindo uma combinação sem precedentes de propriedades meca¢nicas ", disse Espinosa, o professor de Manufatura e Empreendedorismo James and Nancy J. Farley e professor de engenharia meca¢nica e (por cortesia) engenharia biomédica e engenharia civil e engenharia ambiental .
"Nosso trabalho demonstrou que o design racional de metamateriais, com um alto grau de recuperação da forma e rigidez e deformação dependentes da direção, épossível usando designs de origami, e que a dobrabilidade do origami permite um estado em que o material inicialmente se expande e subsequentemente se contrai lateralmente (auxeticidade reversavel ) ", acrescentou Espinosa, que atua como diretor do programa de pós-graduação em Teoria e Meca¢nica Aplicada da Northwestern. "Tais propriedades prometem influenciar uma sanãrie de aplicações em uma ampla gama de campos, abrangendo as nano, micro e macro escalas, alavancando a escalabilidade intranseca dos conjuntos de origami".
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"Guiados pela geometria, o dimensionamento e a miniaturização do metamaterial do origami são empolgantes em si e pela multifuncionalidade sem precedentes que ele possibilita naturalmente", afirmou Paulino, presidente da Raymond Allen Jones na Escola de Engenharia Civil e Ambiental da Georgia Tech.
"Apenas um esfora§o interdisciplinar que combina design de origami, impressão a laser 3D com resolução em nanoescala e testes meca¢nicos de microscopia eletra´nica in situ pode revelar a combinação sem precedentes de propriedades que nosso trabalho demonstrou e seu potencial impacto em aplicações futuras", acrescentou Paulino, que contribuiu para estabelecendo o programa Fronteiras Emergentes da Fundação Nacional de Ciência em Pesquisa e Inovação chamado ODISSEI (Design de Origami para Integração de Sistemas de Montagem Automa¡tica para Inovação em Engenharia).
"Assim como a natureza arquitetou uma ampla gama de estruturas usando apenas alguns sistemas de materiais, o origami nos permite projetar componentes estruturais resilientes com propriedades físicas distintas em diferentes direções", disse Krishnaswamy, professor de engenharia meca¢nica.
"Podemos imaginar microrobôs macios baseados em origami que são ragidos ao longo de algumas direções para transportar cargas aºteis, mantendo outros graus de flexibilidade de movimento. Os metamateriais de origami que exploram a auxiliaridade reversavel e grande deformação podem levar a aplicações multifuncionais que variam de instrumentos microciraºrgicos implanta¡veis ​​e dispositivos médicos , a direção e colheita de energia ", acrescentou Krishnaswamy, diretor do Centro de Estruturas e Materiais Inteligentes da Northwestern.
O estudo apresenta novos caminhos a serem explorados a longo prazo, disse Espinosa.
"Ha¡ várias possibilidades", disse ele. "Uma éa fabricação de estruturas de origami com materiais cera¢micos e meta¡licos, preservando asDimensões em nanoescala, para explorar efeitos de tamanho na resposta meca¢nica das estruturas, levando a uma dissipação de energia superior por unidade de volume e massa. Outra éo uso de polímeros piezoelanãtricos, que pode resultar em coletores de energia que podem acionar modalidades sensoras ou ferramentas microcirúrgicas de potaªncia ".
A pesquisa, "Dobrando na microescala: habilitando os metamateriais multifuncionais em arquitetura de origami em 3D" foi publicada na Small nesta segunda-feira, 27 de julho.