| In recent years,with the rapid development of additive manufacturing technology,nanoporous metallic martials and metamaterials have attracted extensive attentions from academia and industry,both at domestic and abroad.Although nanoporous metallic materials and metamaterials are very similar to conventional porous metals in terms of structural morphology,they have a much smaller pore structure and higher specific surface area.Therefore,the physical properties of nanoporous metallic materials and metamaterials are drastically different from their macroscopic counterparts.Surface effects should no longer be neglected when studying the properties of nanostructures.It is therefore important to understand the mechanical properties of nanoporous metallic materials and metamaterials from the fundamental level.Motived by such needs,nanoporous metallic materials and metamaterials are selected as the research object of the study presented in this dissertation.Finite element numerical simulation is chosen as the main research methodology.By developing user-defined finite element subroutines for capturing surface effects,this dissertation systematically investigates the mechanical properties of nanoporous metallic materials and metamaterials,in the order of one-dimensional nanobeams to twodimensional(2D)and three-dimensional(3D)nanostructures.The main focus of this work is to examine the effects of quite a few factors,such as computational models,surface material parameters,surface constitutive laws,boundary conditions,porosity,shape of nanopores,distribution of nanopores and topology,on the mechanical properties of nanoporous metallic materials and metamaterials.In summary,the research content and main conclusions of this dissertation can be drawn as follows.(1)As the basic building blocks of nanoporous metallic materials,nanobeams are the first research object of this dissertation.Based on the Young-Laplace equation,a theoretical model describing the bending deformation of nanobeams is first derived in detail.After that,a finite element model based on the Galerkin weighted residual method is also developed.The theoretical predictions and numerical simulation results are then compared and contrasted.The effects of Young’s modulus,surface residual stress,cross-sectional area,shape,and the ratio between the radius of a circular crosssection and the thickness of the surface shell layer on the bending deformation behavior of nanobeams are finally investigated in detail.The results show that the bending deformation behavior of nanobeams is dependent on both the Young’s modulus and residual stress of the surface shell layer.A certain amount of mutual competition between these two factors can be identified.Their relative importance is up to the cross-section radius-to-thickness ratio as well as the supporting conditions of the nanobeams.(2)Based on the energy minimization principle,user-defined finite element subroutines are developed for 2D nano-surfaces.For a few 2D nanoporous models,the pore surface mechanical response,stress concentration effects and equivalent mechanical properties are investigated in detail.The results show that stress concentrations in 2D representative volume elements containing superhyperelliptic pores are significantly affected by the pore geometry,loading conditions and surface mechanical models.In the presence of surface effects,the mechanical properties of nanoporous materials with randomly distributed pores exhibit significant size-effects,when compared to the corresponding classical models.(3)By extending 2D nanoporous metallic materials to 3D,user-defined finite element subroutines for general 3D nanoporous metallic materials are further developed.Finite element simulations are sequentially performed for a 1/8 cubic representative volume element containing a single spherical pore subjected to tensile loading and a full cubic element embedded with multiple randomly distributed voids under quasi-static compressive loading.The effects of surface material parameters,porosity,pore size and pore distribution on the mechanical properties of 3D nanoporous metallic materials are subsequently analyzed.It is found that surface bending stiffness can effectively enhance the equivalent Young’s modulus,yield strength and strain energy density under the condition of same porosity level.It can also change the trend of energy absorption rate.Similar to the 2D case,the material near the pores is found to be more susceptive to stress concentrations,in the presence of Steigmann-Ogden surface mechanical model.(4)By using the developed user-defined finite element subroutines,the mechanical properties of low-porosity 2D nanoporous metallic metamaterials and general 3D nanoporous metallic metamaterials are also investigated.The influence of pore geometry on negative Poisson’s ratio effects of 2D nanoporous metallic metamaterials is first studied.The results show that the mechanical properties of low-porosity 2D nanoporous metallic metamaterials are significantly influenced by the pore geometry.Due to incorporation of pore surface flexural rigidity,the Steigmann-Ogden surface effects are able to increase the equivalent Young’s modulus and equivalent Poisson’s ratio for any pore shapes.As a result,the Steigmann-Ogden surface effects weaken the negative Poisson’s ratio effects of low-porosity 2D nanoporous metallic metamaterials.After that,the influence of topology on the equivalent Young’s modulus of 3D nanoporous metallic metamaterials with the consideration of surface effects are explored.The effects of pore surface elasticity on the elastic-mechanical properties of general 3D nanoporous metallic metamaterials are mainly influenced by the topology of the model.Compared with the cubic family topology,the deformation mode of the basic unit of the octahedron family,especially the tetrakaidecahedron topology,is dominated by the bending deformation.Therefore,the equivalent elastic modulus of the structure can be significantly enhanced by the surface effects.Compared with the cubic,octahedron families and the triply period minimal surface topology has a higher specific surface area.As a result,the effects of pore surface elasticity are more pronounced.In this dissertation,the mechanical properties of nanoporous metallic materials and metamaterials are systematically investigated by coupling user-defined finite element subroutines and commercial simulation software.The research results of this paper can not only extend the application scenarios of theoretical studies but also provid a validation pathway for the emerging experimental studies of nanoporous metallic materials and metamaterials.Ultimately,it can provide effective ideas for the structural design and optimization of nanoporous metallic materials and metamaterials. |
