Inhomogeneous Material Parameters Research Articles

Considering inhomogeneous material properties for stiffness and failure prediction of thin-walled additively manufactured parts

By overcoming manufacturing constraints imposed by traditional production technologies, additive manufacturing enables engineers to realize highly optimized lightweight components of unmatched geometrical complexity. However, the common dependency of the mechanical material properties on build orientation and wall thickness constitutes a challenge for valid structural analyses of thin-walled parts. Hence within this research, a previously proposed strategy to improve the structural simulations by mapping inhomogeneous material properties into finite shell element models is extended for failure prediction. Therefore, coupons in various build orientations and thicknesses were produced of short fiber-reinforced polyamid 12 via laser sintering and the mechanical properties evaluated by means of digital image correlation-assisted tensile testing. Consequently, the obtained data is utilized for modeling of the thickness dependent and anisotropic material behavior. The inhomogeneous material parameters are automatically mapped in the finite element models and ultimately, numeric simulations are validated by experimental testing of thin-walled parts. The comparisons of finite element analyses with mapped inhomogeneous and conventional constant properties disclosed considerably improved prediction of stiffness and failure. For the latter, however, substantial deviations between simulation and physical experiment remained, indicating that further research is necessary to effectively asses the load bearing capacity of thin-walled additively manufactured structures.

Self-similar solitons in optical waveguides with dual-power law refractive index

We consider the propagation of optical beams in an inhomogeneous nonlinear waveguide whose refractive index exhibits a dual power law dependence on the electric field amplitude. Self-similar evolution of the beams is studied within the framework of a generalized nonlinear Schrödinger equation with distributed diffraction, dual power-law nonlinearity, and gain or loss. The propagation properties and formation conditions of self-similar solitons in such a waveguide is studied by means of an improved homogeneous balance principle and an extended hyperbolic function method. A variety of new self-similar bright solitons are found and their characteristics are explored in terms of the inhomogeneous material parameters. A class of self-similar kink solitons is also identified, featuring another type of the self-similar evolution in the nonlinear waveguide. Dynamical behaviors of these self-similar structures are studied for a periodic distributed amplification system. It is shown that the parameters associated with the group velocity enable one to control the self-similar wave structure and dynamical behavior more efficiently, while the gain parameter affects just the evolution of the self-similar soliton’s peak. Unlike the case of homogeneous dual power-law materials, soliton structures in inhomogeneous systems show novel and interesting features due to their distributed parameters which allow effective control of their dynamics.

Homogeneous external cloak with arbitrarily symmetric or asymmetric structures

A novel external cloak with homogeneous properties is proposed and designed based on the coordinate transformation. By contrast with the reported external cloaks, the homogeneous properties make the cloak designed here applicable to practical fabrication. Both symmetric and asymmetric structured polygonal external cloaks are investigated here, which provides a new perspective to designing arbitrary transformation based devices, breaking through the limitation of previously reported cloak designs with symmetric structures and inhomogeneous material parameters. It represents important progress toward the practical fabrication of the metamaterial-assisted invisible external cloak.

Anisotropic Locally Conformal Perfectly Matched Layer for Higher Order Curvilinear Finite-Element Modeling

A perfectly matched layer (PML) method is proposed for electrically large curvilinear meshes based on a higher order finite-element modeling paradigm and the concept of transformation electromagnetics. The method maps the non-Maxwellian formulation of the locally conformal PML to a purely Maxwellian implementation using continuously varying anisotropic and inhomogeneous material parameters. An approach to the implementation of a conformal PML for higher order meshes is also presented, based on a method of normal projection for PML mesh generation around an already existing convex volume mesh of a dielectric scatterer, with automatically generated constitutive material parameters. Once the initial mesh is generated, a PML optimization method based on gradient descent is implemented to most accurately match the PML material parameters to the geometrical interface. The numerical results show that the implementation of a conformal PML in the higher order finite-element modeling paradigm dramatically reduces the reflection error when compared to traditional PMLs with piecewise constant material parameters. The ability of the new PML to accurately and efficiently model scatterers with a large variation in geometrical shape and those with complex material compositions is demonstrated in examples of a dielectric almond and a continuously inhomogeneous and anisotropic transformation-optics cloaking structure, respectively.

Theoretical study of time-resolved luminescence in semiconductors. IV. Lateral inhomogeneities

In the fourth part of this series, we study the impact of lateral inhomogeneities on the time-resolved luminescence decay (TRL) after a pulsed excitation by means of simulation with Synopsys® TCAD and analytical approximation. This work consists of two parts: In the first part, the effect of excitations being inhomogeneous on a lateral scale is investigated. It turns out that for localized excitations there may be a strong lateral diffusion of charge carriers, thereby limiting the resolution of a micro-TRL experiment. In this case, a replacement of the inhomogeneous excitation in the simulation by a homogeneous excitation and an average photon density is not possible, especially due to defect saturation depending non-linearly on the excitation. In the second part, we consider a homogeneous excitation and study inhomogeneous material parameters, namely, inhomogeneous charge carrier lifetimes, band gaps, and doping densities. We find that their effects strongly depend on their characteristic lengths of variation. For length scales smaller than the diffusion length, inhomogeneous material parameters can lead to curved luminescence decays.

TIME–HARMONIC BEHAVIOUR OF CRACKED PIEZOELECTRIC SOLID BY BOUNDARY INTEGRAL EQUATION METHOD

Abstract Anti-plane cracked functionally graded finite piezoelectric solid under time-harmonic elecromechanical load is studied by a non-hypersingular traction boundary integral equation method (BIEM). Exponentially varying material properties are considered. Numerical solutions are obtained by using Mathematica. The dependance of the intensity factors (IF) - mechanical stress intensity factor (SIF) and electrical field intensity factor (FIF) on the inhomogeneous material parameters, on the type and frequency of the dynamic load and on the crack position are analyzed by numerical illustrative examples

Simulating material inhomogeneities and defects in CIGS thin‐film solar cells

AbstractThin‐film CIGS solar cells are simulated using a hybrid model consisting of a distributed form of the analytical one diode model paired with a numerical finite element model of the d.c. conduction in the front contact layers. Variations in material quality over the substrate surface, from measured J–V curves, are incorporated into the model and the effects of cell width and window layer thickness are evaluated for homogeneous and inhomogeneous material quality. Furthermore, the effects of discrete shunt defects of different sizes are modelled, and in different positions on the cell surface. The results from optimizing cell width and window layer thickness show that the effects of material inhomogeneities include a small shift of the optimal parameters together with a less pronounced maximum. As expected, the defect size is important to the shunt conductance parameter of the resulting J–V curves. The passivating effect of the highly resistive ZnO layer is confirmed. Copyright © 2009 John Wiley & Sons, Ltd.

Influence from front contact sheet resistance on extracted diode parameters in CIGS solar cells

AbstractThe extraction of one‐diode model parameters from a current–voltage (J–V) curve is problematic, since the model is one‐dimensional while real devices are indeed three‐dimensional. The parameters obtained by fitting the model curve to experimental data depend on how the current is collected, and more specifically the geometry of the contact. This is due to the non‐uniform lateral current flow in the window layers, which leads to different parts of the device experiencing different front contact voltage drop, and hence different operating points on the ideal J–V curve. In this work, finite element simulations of three‐dimensional contact structures are performed and compared to experimental data on Cu(In,Ga)Se2‐based solar cell devices. It is concluded that the lateral current flow can influence the extracted parameters from the one‐diode model significantly if the resistivity of the front contact material is high, or if there is no current collecting grid structure. These types of situations may appear in damp heat‐treated cells and module type cells, respectively. Copyright © 2007 John Wiley & Sons, Ltd.

Characterization of near- and far-field radiation from ultrafast electronic systems

Accurate and computationally efficient characterization of near- and far-field radiation from a class of microwave, millimeter wave, and ultrafast systems is presented. A numerical technique is utilized which combines the finite-difference time domain method with a spatial transformation, the Kirchhoff surface integral. Included in the analysis are inhomogeneous material parameters, small feature size relative to wavelengths of interest, and the wide-band nature of the radiation. Based on simulation results, a simple model of the radiation from an inhomogeneous structure is developed. Finally, the technique is applied to accurately characterize the radiation from a photoconducting structure.

Analysis of bianisotropic layered structures with laterally periodic inhomogeneities-an eigenoperator formulation

A method of analysis for electromagnetic wave phenomena in multilaiyered media consisting of bianisotropic slabs with periodically inhomogeneous material parameters is presented. The analysis relies on a transformation of Maxwell's equations into an equivalent eigenoperator equation for the transverse components of the field vectors, which is Fourier transformed into an algebraic eigenvalue equation in spectral domain. The fields in the inhalmogeneous layers are then expressed in terms of eigenmodes, where the expansion coefficients are determined by imposing internal and external boundary conditions. The proposed method lis verified by comparing numerical results for ordinary isotropic-media problems with corresponding results obtained previously by different methods. The applicability and convergence behavior of the approach is illustrated for typical sample applications involving scattering- and guided-wave problems.