Design of Kinematic Connectors for Microstructured Materials Produced by Additive Manufacturing

Miguel R. Silva; João A. Dias-de-Oliveira; António M. Pereira; Nuno M. Alves; Álvaro M. Sampaio; António J. Pontes

doi:10.3390/polym13091500

Design of Kinematic Connectors for Microstructured Materials Produced by Additive Manufacturing

Polymers ◽

10.3390/polym13091500 ◽

2021 ◽

Vol 13 (9) ◽

pp. 1500

Author(s):

Miguel R. Silva ◽

João A. Dias-de-Oliveira ◽

António M. Pereira ◽

Nuno M. Alves ◽

Álvaro M. Sampaio ◽

...

Keyword(s):

Young’S Modulus ◽

Functionally Graded Materials ◽

Cellular Structure ◽

Young's Modulus ◽

Functionally Graded ◽

Graded Materials ◽

Mean Values ◽

Shear Moduli ◽

Young’S Moduli ◽

Unit Cells

The main characteristic of materials with a functional gradient is the progressive composition or the structure variation across its geometry. This results in the properties variation in one or more specific directions, according to the functional application requirements. Cellular structure flexibility in tailoring properties is employed frequently to design functionally-graded materials. Topology optimisation methods are powerful tools to functionally graded materials design with cellular structure geometry, although continuity between adjacent unit-cells in gradient directions remains a restriction. It is mandatory to attain a manufacturable part to guarantee the connectedness between adjoining microstructures, namely by ensuring that the solid regions on the microstructure’s borders i.e., kinematic connectors) match the neighboring cells that share the same boundary. This study assesses the kinematic connectors generated by imposing local density restrictions in the initial design domain (i.e., nucleation) between topologically optimised representative unit-cells. Several kinematic connector examples are presented for two representatives unit-cells topology optimised for maximum bulk and shear moduli with different volume fractions restrictions and graduated Young’s modulus. Experimental mechanical tests (compression) were performed, and comparison studies were carried out between experimental and numerical Young’s modulus. The results for the single maximum bulk for the mean values for experimental compressive Young’s modulus (Ex¯) with 60%Vf show a deviation of 9.15%. The single maximum shear for the experimental compressive Young’s modulus mean values (Ex¯) with 60%Vf, exhibit a deviation of 11.73%. For graded structures, the experimental mean values of compressive Young’s moduli (Ex¯), compared with predicted total Young’s moduli (ESe), show a deviation of 6.96 for the bulk graded structure. The main results show that the single type representative unit-cell experimental Young’s modulus with higher volume fraction presents a minor deviation compared with homogenized data. Both (i.e., bulk and shear moduli) graded microstructures show continuity between adjacent cells. The proposed method proved to be suitable for generating kinematic connections for the design of shear and bulk graduated microstructured materials.

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Inversion of Functionally Graded Materials to Improve the Elastic Ultimate Bearing Capacity of Thick-Walled Hollow Cylinder

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.378-379.116 ◽

2011 ◽

Vol 378-379 ◽

pp. 116-120 ◽

Cited By ~ 1

Author(s):

Ai Zhong Lu ◽

Ning Zhang

Keyword(s):

Bearing Capacity ◽

Young’S Modulus ◽

Hollow Cylinder ◽

Functionally Graded Materials ◽

Young's Modulus ◽

Ultimate Bearing Capacity ◽

Functionally Graded ◽

The Body ◽

Graded Materials ◽

Homogeneous Materials

Thick-walled hollow cylinder is an important class of engineering structure, the stress state of which depends on the loads and properties of the body materials. Under the assumptions of σθ-σr=c (σθ and σr denote the hoop stress and radial stress, respectively, c is a constant), inverse analysis of thick-walled hollow cylinder composed of functionally graded materials with uniform pressure acting on the outer surface is carried out. Analytical solutions for the Young’s modulus variation in the radial direction are obtained. It is found that only when the Young’s modulus E(r) is a specific monotone increasing function of the radius r, the pre-specified stress distribution can be satisfied. Comparing with classical homogeneous materials, stress concentration at the inner surface of hollow cylinder composed of functionally graded materials can be alleviated. Hence the elastic ultimate bearing capacity of hollow cylinder can be improved strikingly. For functionally graded materials, the elastic ultimate bearing capacity can be improved strikingly by increasing the thickness of cylinder, which is not so obvious for classical homogeneous materials.

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On the Effect of Functionally Graded Materials on Resonances of Rotating Beams

Shock and Vibration ◽

10.1155/2012/395782 ◽

2012 ◽

Vol 19 (6) ◽

pp. 1315-1326 ◽

Cited By ~ 4

Author(s):

Arnaldo J. Mazzei Jr.

Keyword(s):

Young’S Modulus ◽

Functionally Graded Materials ◽

Young's Modulus ◽

Ritz Method ◽

Turbine Blades ◽

Functionally Graded ◽

Graded Materials ◽

Rotating Beams ◽

Helicopter Blades ◽

Aerospace Applications

Radially rotating beams attached to a rigid stem occur in several important engineering applications. Some examples include helicopter blades, turbine blades and certain aerospace applications. In most studies the beams have been treated as homogeneous. Here, with a goal of system improvement, non-homogeneous beams made of functionally graded materials are explored. The effects on the natural frequencies of the system are investigated. Euler-Bernoulli theory, including an axial stiffening effect and variations of both Young's modulus and density, is employed. An assumed mode approach is utilized, with the modes taken to be beam characteristic orthogonal polynomials. Results are obtained via Rayleigh-Ritz method and are compared for both the homogeneous and non-homogeneous cases. It was found, for example, that allowing Young's modulus and density to vary by approximately 2.15 and 1.15 times, respectively, leads to an increase of 23% in the lowest bending rotating natural frequency of the beam.

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On the Effect of Functionally Graded Materials on Resonances of Rotating Beams

Shock and Vibration ◽

10.1155/2012/529429 ◽

2012 ◽

Vol 19 (4) ◽

pp. 707-718 ◽

Cited By ~ 2

Author(s):

Arnaldo J. Mazzei Jr.

Keyword(s):

Young’S Modulus ◽

Functionally Graded Materials ◽

Young's Modulus ◽

Ritz Method ◽

Turbine Blades ◽

Functionally Graded ◽

Graded Materials ◽

Rotating Beams ◽

Helicopter Blades ◽

Aerospace Applications

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Numerical Model of Instrumented Indentation by a Rounded Cone Indenter Using Finite Element Method

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.606.73 ◽

2014 ◽

Vol 606 ◽

pp. 73-76 ◽

Cited By ~ 2

Author(s):

Lenka Kocmanová ◽

Petr Haušild ◽

Aleš Materna ◽

Jiří Matějíček

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Young’S Modulus ◽

Numerical Solutions ◽

Young's Modulus ◽

Numerical Models ◽

Functionally Graded ◽

Indentation Modulus ◽

Young’S Moduli ◽

Element Method

The paper serves as an introduction to investigation of mechanical properties of functionally graded materials and deals with elastic nanoindentation numerical models. The models were based on the finite element method. Young's moduli were estimated by Oliver-Pharr method. The indenter geometry for which numerical solutions were accomplished was a rounded cone indenter. The effect of tip sharpness was examined by applying an increasing spherical tip radius. The results show that the apparent Young's modulus and the hardness increase linearly with increasing radius of the tip. The effect of approaching interface between two elastic materials on the apparent hardness and indentation modulus was identified in 3D model. The specimen consisted of two materials. First, the interface was linear and parallel to the direction of indentation, so that the Young's modulus changed suddenly. Second, the Young's modulus was continuously changing. The dependence on various boundary conditions of the specimen was also considered.

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Measurement Model for Young's Modulus of Axially Functionally Graded Materials

Key Engineering Materials ◽

10.4028/www.scientific.net/kem.748.391 ◽

2017 ◽

Vol 748 ◽

pp. 391-395

Author(s):

Xiao Liang Chen ◽

Long Zhang ◽

Ding Yu Li

Keyword(s):

Elastic Modulus ◽

Young’S Modulus ◽

Young's Modulus ◽

Beam Theory ◽

Measurement Model ◽

Functionally Graded ◽

The Finite Element Method ◽

Graded Materials ◽

Experiment Method ◽

Euler Bernoulli Beam

For axially functionally graded beams with elastic modulus varying through the longitudinal directions, a measurement model for Young's modulus is presented based on the classic Euler-Bernoulli beam theory. When the force and deflection of cantilever beams are measured by the experiment method, the Young's modulus of axially functionally graded beams can be obtained by the measurement model. By the derivation rule of compound functions, the validity of the measurement model is proved. For the axially functionally graded beams with elastic modulus varying according to the power law and the exponential law respectively, the deflection is simulated by the finite element method. The simulated elastic modulus by the model is in accord with the theoretical value well.

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Surface Effects on Effective Young’s Modulus of Nanoporous Structures

International Journal of Structural Stability and Dynamics ◽

10.1142/s021945542050073x ◽

2020 ◽

Vol 20 (07) ◽

pp. 2050073

Author(s):

Tao Fan

Keyword(s):

Young’S Modulus ◽

Surface Stress ◽

Young's Modulus ◽

Surface Elasticity ◽

Cross Sectional ◽

Residual Surface Stress ◽

Young’S Moduli ◽

Unit Cells ◽

The Cross ◽

Nanoporous Structures

Nanoporous materials and structures have attracted widespread attention due to their excellent mechanical properties. Based on the surface elasticity, the effective Young’s moduli are derived for four typical nanoporous structures with periodic unit cells. When the cross-sectional size reduces to nanoscale, the effective Young’s modulus is revealed to be strongly size-dependent. Both the effects of residual surface stress and effective-surface Young’s modulus are examined. The results indicate that negative effective Young’s modulus can be achieved when the residual surface stress is less than zero. The influences of the cross-sectional shape on the relationship between the overall deformation and applied loads are examined. The relative density also plays an important role to the mechanical characteristics not only at macroscales, but also at nanoscales.

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