Metamaterial design in the hyperelastic regime
The design of metamaterials relies on numerical simulations to both obtain the basic distribution of displacements, stresses and strains throughout the domain, and to find structures that handle the loads optimally. Linear elasticity theory is often employed for these simulations; however, this form...
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| Tipo de documento: | dissertação |
| Data de publicação: | 2024 |
| País: | España |
| Recursos: | Universitat Politècnica de Catalunya (UPC) |
| Repositório: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglês |
| OAI Identifier: | oai:upcommons.upc.edu:2117/411651 |
| Acesso em linha: | https://hdl.handle.net/2117/411651 |
| Access Level: | Acceso aberto |
| Palavra-chave: | Metamaterials--Design Elasticity Finite element method Topology Hyperelasticity Neo-hookean Nearly-incompressible Metamaterials Topology optimization Metamaterials--Disseny Elasticitat Elements finits, Mètode dels Topologia Àrees temàtiques de la UPC::Enginyeria dels materials::Materials compostos |
| Resumo: | The design of metamaterials relies on numerical simulations to both obtain the basic distribution of displacements, stresses and strains throughout the domain, and to find structures that handle the loads optimally. Linear elasticity theory is often employed for these simulations; however, this formulation fails to capture large displacements, and the results obtained in highly deformed structures may not be as efficient as possible. In this present work, the goal is to solve hyperelastic problems using Neo-hookean materials, using a formulation geared towards the field of topology optimization for further later implementations. Hyperelasticity is posed as a minimization problem, which is discretized using the finite element method, and solved using a Newton-Raphson algorithm implemented in a MATLAB-based topology optimization toolbox. After showing that the formulation is consistent with the small displacements theory, four tests are carried out to validate the implementation. The results obtained are promising from a physical meaning perspective, but a lack of quadratic convergence in the Newton-Raphson algorithm suggests the presence of an error in the calculation of the tangent operator. |
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