scholarly journals A closed-form orthotropic constitutive model for fused filament fabrication materials

2019 ◽  
Author(s):  
Ruiqi Chen ◽  
Debbie G. Senesky
Keyword(s):  
Constitutive Model ◽  
Closed Form ◽  
Elastic Constants ◽  
Complex Variable ◽  
Shape Parameter ◽  
Antiplane Shear ◽  
Fused Filament Fabrication ◽  
Effective Elastic Constants ◽  
Out Of Plane ◽  
Simulation Results

We model two common fused filament fabrication mesostructures, square and hexagonal, using an orthotropic constitutive model and derive closed-form expressions for all nine effective elastic constants. The periodic void shapes are modeled using three and four point hypotrochoid curves with a single shape parameter that controls the sharpness of the points. Using the complex variable method of elasticity, we derive the in-plane elastic constants (Exx, Eyy, Gxy, nuxy) as well as out-of-plane antiplane shear constants (Gzx and Gzy). The remaining out-of-plane elastic constants (Ezz, nuzx, nuzy) are derived by directly solving the linearelasticity equations. We compare our results by conducting unit cell simulations on both mesostructures and at various porosity values. The simulations match the closed-form expressions exactly for Ezz, nuzx, and nuzy. For the remaining elastic constants, the simulation results match the closed-form expressions better for the square mesostructure than the hexagonal mesostructure. Differences between simulation and closed-form expressions are less than 10% for porosity values less than 6% (hexagonal mesostructure) and 10% (square mesostructure) for any of the nine elastic constants.

An Analytical Solution to the Electrostatic Actuation of an Asymmetric Combdrive

1999 ◽  
Author(s):  
J.-L. Andrew Yeh ◽  
Norman C. Tien ◽  
Chung-Yuen Hui
Keyword(s):  
Analytical Solution ◽  
Closed Form ◽  
Complex Variable ◽  
Electrostatic Actuation ◽  
Peak Force ◽  
Constant Force ◽  
Electrostatic Forces ◽  
Critical Engagement ◽  
Out Of Plane

Abstract A model for the electrostatic forces generated by an asymmetric combdrive has been developed. Using complex variable techniques, an analytical solution to out-of-plane electrostatic actuation is obtained in closed form. The peak force depends on the thickness of the movable fingers and the amount of overlap between the combs. In addition, the in-plane actuation of an in-plane interdigitated combdrive can also be interpreted using our solution. For an in-plane combdrive, the critical engagement length of the combs, which is required for generating a constant force with variation within 1%, is a factor of 1.24 times the separation gap.

Elastic Constants of Composite Materials by an Inverse Determination Method Based on A Hybrid Genetic Algorithm

2010 ◽  
Vol 26 (3) ◽  
pp. 345-353 ◽  
Author(s):  
S.-F. Hwang ◽  
J.-C. Wu ◽  
Evgeny Barkanovs ◽  
Rimantas Belevicius
Keyword(s):  
Genetic Algorithm ◽  
Elastic Constants ◽  
Hybrid Genetic Algorithm ◽  
Transversely Isotropic ◽  
Determination Method ◽  
Element Analysis ◽  
Plane Shear ◽  
Effective Elastic Constants ◽  
Testing Data ◽  
Out Of Plane

AbstractA numerical method combining finite element analysis and a hybrid genetic algorithm is proposed to inversely determine the elastic constants from the vibration testing data. As verified from composite material specimens, the repeatability and accuracy of the proposed inverse determination method are confirmed, and it also proves that the concept of effective elastic constants is workable. Moreover, three different sets of assumptions to reduce the five independent elastic constants to four do not make clear difference on the obtained results by the proposed method. In addition, to obtain robust values of the five elastic constants for a transversely isotropic material, it is recommended to use the out-of-plane Poisson's ratio instead of the out-of-plane shear modulus as the fifth one.

Design of Frame-Like Periodic Solids for Isotropic Symmetry by Member Sizing

2016 ◽  
Vol 33 (1) ◽  
pp. 41-54 ◽  
Author(s):  
K. Theerakittayakorn ◽  
P. Suttakul ◽  
P. Sam ◽  
P. Nanakorn
Keyword(s):  
Closed Form ◽  
Elastic Constants ◽  
Strain Energy ◽  
Equivalent Strain ◽  
Homogenization Method ◽  
Unit Cell ◽  
Cubic Symmetry ◽  
Effective Elastic Constants ◽  
Common Unit ◽  
2D And 3D

AbstractIn this study, a methodology to design frame-like periodic solids for isotropic symmetry by appropriate sizing of unit-cell struts is presented. The methodology utilizes the closed-form effective elastic constants of 2D frame-like periodic solids with square symmetry and 3D frame-like periodic solids with cubic symmetry, derived using the homogenization method based on equivalent strain energy. By using the closed-form effective elastic constants, an equation to enforce isotropic symmetry can be analytically constructed. Thereafter, the equation can be used to determine relative unit-cell strut sizes that are required for isotropic symmetry. The methodology is tested with 2D and 3D frame-like periodic solids with some common unit-cell topologies. Satisfactory results are observed.

scholarly journals Thermodynamic compatibility conditions of a new class of hysteretic materials

2021 ◽  
Author(s):  
Salvatore Sessa
Keyword(s):  
Constitutive Model ◽  
Dynamic Analysis ◽  
Closed Form ◽  
Iterative Procedure ◽  
Displacement Amplitude ◽  
Compatibility Conditions ◽  
Algebraic Functions ◽  
New Class ◽  
Thermodynamic Compatibility ◽  
Constitutive Parameters

AbstractThe thermodynamic compatibility defined by the Drucker postulate applied to a phenomenological hysteretic material, belonging to a recently formulated class, is hereby investigated. Such a constitutive model is defined by means of a set of algebraic functions so that it does not require any iterative procedure to compute the response and its tangent operator. In this sense, the model is particularly feasible for dynamic analysis of structures. Moreover, its peculiar formulation permits the computation of thermodynamic compatibility conditions in closed form. It will be shown that, in general, the fulfillment of the Drucker postulate for arbitrary displacement ranges requires strong limitations of the constitutive parameters. Nevertheless, it is possible to determine a displacement compatibility range for arbitrary sets of parameters so that the Drucker postulate is fulfilled as long as the displacement amplitude does not exceed the computed threshold. Numerical applications are provided to test the computed compatibility conditions.

scholarly journals Development of Elastoplastic-Damage Model of AlFeSi Phase for Aluminum Alloy 6061

Metals ◽  
2021 ◽  
Vol 11 (6) ◽  
pp. 954
Author(s):  
Hailong Wang ◽  
Wenping Deng ◽  
Tao Zhang ◽  
Jianhua Yao ◽  
Sujuan Wang
Keyword(s):  
Aluminum Alloy ◽  
Constitutive Model ◽  
Material Properties ◽  
Damage Model ◽  
Scratch Test ◽  
Aluminum Alloy 6061 ◽  
Ultra Precision ◽  
Simulation Results ◽  
Alloy 6061 ◽  
Elastoplastic Damage

Material properties affect the surface finishing in ultra-precision diamond cutting (UPDC), especially for aluminum alloy 6061 (Al6061) in which the cutting-induced temperature rise generates different types of precipitates on the machined surface. The precipitates generation not only changes the material properties but also induces imperfections on the generated surface, therefore increasing surface roughness for Al6061 in UPDC. To investigate precipitate effect so as to make a more precise control for the surface quality of the diamond turned Al6061, it is necessary to confirm the compositions and material properties of the precipitates. Previous studies have indicated that the major precipitate that induces scratch marks on the diamond turned Al6061 is an AlFeSi phase with the composition of Al86.1Fe8.3Si5.6. Therefore, in this paper, to study the material properties of the AlFeSi phase and its influences on ultra-precision machining of Al6061, an elastoplastic-damage model is proposed to build an elastoplastic constitutive model and a damage failure constitutive model of Al86.1Fe8.3Si5.6. By integrating finite element (FE) simulation and JMatPro, an efficient method is proposed to confirm the physical and thermophysical properties, temperature-phase transition characteristics, as well as the stress–strain curves of Al86.1Fe8.3Si5.6. Based on the developed elastoplastic-damage parameters of Al86.1Fe8.3Si5.6, FE simulations of the scratch test for Al86.1Fe8.3Si5.6 are conducted to verify the developed elastoplastic-damage model. Al86.1Fe8.3Si5.6 is prepared and scratch test experiments are carried out to compare with the simulation results, which indicated that, the simulation results agree well with those from scratch tests and the deviation of the scratch force in X-axis direction is less than 6.5%.

Effective Elastic Constants of Fiber-Eutectics and Transformation Particles Composite Ceramic

2010 ◽  
Vol 177 ◽  
pp. 182-185 ◽  
Author(s):  
Bao Feng Li ◽  
Jian Zheng ◽  
Xin Hua Ni ◽  
Ying Chen Ma ◽  
Jing Zhang
Keyword(s):  
Elastic Modulus ◽  
Elastic Constant ◽  
Effective Stress ◽  
Elastic Constants ◽  
Transverse Isotropy ◽  
Analytical Formula ◽  
Composite Ceramic ◽  
Phase Model ◽  
Composite Ceramics ◽  
Effective Elastic Constants

The composite ceramics is composed of fiber-eutectics, transformation particles and matrix particles. First, the recessive expression between the effective stress in fiber-eutectic and the flexibility increment tensor is obtained according to the four-phase model. Second, the analytical formula which contains elastic constant of the fiber-eutectic is obtained applying Taylor’s formula. The eutectic is transverse isotropy, so there are five elastic constants. Third, the effective elastic constants of composite ceramics are predicted. The result shows that the elastic modulus of composite ceramic is reduced with the increase of fibers fraction and fibers diameter.

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