Drop-weight impact tests and finite element modeling of cast acrylic/aluminum plates

As an extension of a previous study [1], drop-weight impact tests on cast acrylic (PMMA) plates reinforced by aluminum face sheets were carried out using an instrumented drop weight impact tester. The PMMA and aluminum layers were adhered by epoxy cured at room temperature. Depending on the impact velocity and the type of top surface (acrylic or aluminum) struck by the impactor, damage caused by impact included partial or full delamination at the interface and radial cracks in the acrylic layer. The higher the impact velocity, the more damage was induced. More severe damage occurred if the bi-layer plate was impacted on the aluminum side. The ultrasonic C-scan technique was adopted to detect the damage. The pulse-echo technique with a focused transducer provided very good C-scan results for detecting damage patterns. The transducer with higher frequency gave better resolution and showed more details of damage. Finally, the finite element program, LS-DYNA, implemented with maximum strength criterion for radial cracking and mixed mode strength criterion for interfacial fracture, was used to simulate the drop weight impact tests. Impact force history, energy partition and delamination were predicted assuming various boundary conditions according to experimental results. The finite element simulations were in very good agreement with the experimental data.     

A critical assessment of finite element modeling approach for protein dynamics

Finite element (FE) modeling approach has emerged as an efficient way of calculating the dynamic properties of supramolecular protein structures and their complexes. Its efficiency mainly stems from the fact that the complexity of three-dimensional shape of a molecular surface dominates the computational cost rather than the molecular size or the number of atoms. However, no critical evaluation of the method has been made yet particularly for its sensitivity to the parameters used in model construction. Here, we make a close investigation on the effect of FE model parameters by analyzing 135 representative protein structures whose normal modes calculated using all-atom normal mode analysis are publicly accessible online. Results demonstrate that it is more beneficial to use a contour surface of electron densities as the molecular surface, in general, rather than to employ a solvent excluded surface, and that the solution accuracy is almost insensitive to the model parameters unless we avoid extreme values leading to an inaccurate depiction of the characteristic shapes.     

3D finite element analysis and mathematical modeling for estimation of material dissolution rate in the electrochemical machining processes

Journal of Solid State Electrochemistry - Electrochemical machining (ECM) operating with mechanism of electrochemical dissolution during an electrolysis process is one of the most crucial...     

Finite element modeling of syntactic foam

A decomposition model has been developed to predict the response of removable syntactic foam (RSF) exposed to fire-like heat fluxes. RSF consists of glass micro-balloons (GMB) in a cured epoxy polymer matrix. A chemistry model is presented based on the chemical structure of the epoxy polymer, mass transport of polymer fragments to the bulk gas, and vapor-liquid equilibrium. Thermophysical properties were estimated from measurements. A bubble nucleation, growth, and coalescence model was used to describe changes in properties with the extent of reaction. Decomposition of a strand of syntactic foam exposed to high temperatures was simulated.     

FTIR studies of conformational energies of poly(acrylic acid) in cast films

Fourier transform infrared (FTIR) spectroscopic measurements have been undertaken to estimate the conformational energies of poly(acrylic acid) (PAA) cast films in the temperature range of 40–130°C. The temperature dependence of the IR spectra in the C=O stretching region has been analyzed to yield the side-chain and backbone conformational energies. The estimated energies are close to those previously obtained by polarized Raman spectroscopic measurements for PAA solutions. Combining the FTIR value of conformational energy with the simplified rotational isomeric state (RIS) model proposed in the Raman analysis provides a persistence length in accordance with earlier SAXS experiments. The data also agree with the Gibbs-DiMarzio predictions, further substantiating the validity of the analysis. © 1997 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys, 35: 507–515, 1997     

A finite element formulation of frequency-dependent electro-osmosis

In this paper, we model frequency-dependent electro-osmosis in a capillary using the fully nonlinear Navier-Stokes equation (NSE) for viscous, incompressible, and homogeneous flow. We simulate the NSE using the finite element method, computing the solution for a closed capillary and compare it to the closed form solutions. It is confirmed that the second velocity zero crossing is dependent of the capillary radius. The distance of the zero velocity crossing decreases with decreasing capillary radius. It is also shown that the AC electro-osmosis causes a circulation of fluid within the capillary with low frequencies generating the greatest net flow.     

X-ray computed tomography-based modeling of polymeric foams: The effect of finite element model size on the large strain response

A hybrid numerical–experimental approach is used to characterize the macroscopic mechanical behavior of polymeric foams. The method is based on microstructural characterization of foams with X-ray computed tomography (CT) and conversion of the data to finite element (FE) models. The 2D models are created from a 3D close-celled foam and subjected to compression loads. Since the large strain regime is explored, contact between elements is incorporated. It is shown that, for calculating the effective Young's modulus, a model consisting of at least 11²–12² cells in the model should be used, whereas for the large strain regime 12²–14² cells in the model are needed. Discretization had a significant influence on the results, where relatively coarse elements caused loss of connectivity in the cell walls and thickening of the cell walls. It is shown that at least three to four elements should be taken over the thickness of the cell walls for these structures. Finally, a good qualitative agreement is observed between the deformations found with the FE models and in situ compression experiments of an open-celled foam during X-ray CT. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 1473–1482, 2010     

Computation of dynamic adsorption with adaptive integral,finite difference,and finite element methods

Analysis of diffusion-controlled adsorption and surface tension in one-dimensional planar coordinates with a finite diffusion length and a nonlinear isotherm, such as the Langmuir or Frumkin isotherm, requires numerical solution of the governing equations. This paper presents three numerical methods for solving this problem. First, the often-used integral (I) method with the trapezoidal rule approximation is improved by implementing a technique for error estimation and choosing time-step sizes adaptively. Next, an improved finite difference (FD) method and a new finite element (FE) method are developed. Both methods incorporate (a). an algorithm for generating spatially stretched grids and (b). a predictor-corrector method with adaptive time integration. The analytical solution of the problem for a linear dynamic isotherm (Henry isotherm) is used to validate the numerical solutions. Solutions for the Langmuir and Frumkin isotherms obtained using the I, FD, and FE methods are compared with regard to accuracy and efficiency. The results show that to attain the same accuracy, the FE method is the most efficient of the three methods used.     

Formation and finite element analysis of tethered bilayer lipid structures

Rapid solvent exchange of an ethanolic solution of diphytanoyl phosphatidylcholine (DPhyPC) in the presence of a mixed self-assembled monolayer (SAM) [thiolipid/β-mercaptoethanol (βME) (3/7 mol/mol) on Au] shows a transition from densely packed tethered bilayer lipid membranes [(dp)tBLMs], to loosely packed tethered bilayer lipid membranes [(lp)tBLMs], and tethered bilayer liposome nanoparticles (tBLNs) with decreasing DPhyPC concentration. The tethered lipidic constructs in the aqueous medium were analyzed by atomic force microscopy (AFM) and electrochemical impedance spectroscopy (EIS). Finite element analysis (FEA) was applied to interpret spectral EIS features without referring to equivalent circuit modeling. Using structural data obtained earlier from neutron reflectometry and dielectric constants of lipid bilayers, we reproduced experimentally observed features of the electrochemical impedance (EI) spectra of complex surface constructs involving small pinhole defects, large membrane-free patches, and bound liposomes. We demonstrated by FEA that highly insulating (dp)tBLMs with low-defect density exhibit EI spectra in the shape of a perfect semicircle with or without low-frequency upward "tails" in the Cole-Cole representation. Such EI spectra were observed at DPhyPC concentrations of >5 × 10(-3) mol L(-1). While AFM was not able to visualize very small lateral defects in such films, EI spectra unambiguously signaled their presence by increased low frequency "tails". Using FEA we demonstrate that films with large diameter visible defects (>25 nm by AFM) produce EI spectral features consisting of two semicircles of comparable size. Such films were typically obtained at DPhyPC concentrations of <5 × 10(-3) mol L(-1). At DPhyPC concentrations of <1.0 × 10(-3) mol L(-1) the planar bilayer structures were replaced by ellipsoidal liposomes with diameters ranging from 50 to 500 nm as observed in AFM images. Despite the distinct surface morphology change, the EI curves exhibited two semicircle spectral features typical for the large size defects in planar tBLMs. FEA revealed that, to account for these EI features for bound liposome systems (50-500 nm diameter), one needs to assume much lower tBLM conductivities of the submembrane space, which separates the electrode surface and the phospholipid bilayer. Alternatively, FEA indicates that such features may also be observed on composite surfaces containing both bound liposomes and patches of planar bilayers. Triple semicircular features, observed in some of the experimental EI curves, were attributed to an increased complexity of the real tBLMs. The modeling demonstrated that such features are typical for heterogeneous tBLM surfaces containing large patches of different defectiveness levels. By integrating AFM, EIS, and FEA data, our work provides diagnostic criteria allowing the precise characterization of the properties and the morphology of surface supported bilayer systems.     

Hybrid finite element and Brownian dynamics method for diffusion-controlled reactions

Diffusion is often the rate determining step in many biological processes. Currently, the two main computational methods for studying diffusion are stochastic methods, such as Brownian dynamics, and continuum methods, such as the finite element method. This paper proposes a new hybrid diffusion method that couples the strengths of each of these two methods. The method is derived for a general multidimensional system, and is presented using a basic test case for 1D linear and radially symmetric diffusion systems.     

Adaptive finite element simulation of chronoamperometry at microdisc electrodes

In this paper we shall introduce a transient finite element algorithm by considering the simplest problem of numerical simulation of the chronoamperometric current for an E reaction mechanism at a microdisc electrode. Such a numerical simulation is made difficult by the presence of a boundary singularity where the electrode meets the insulator (often known as the ‘edge-effect’) and by a time-singularity caused by the impulsive start of the experiment. We attempt to overcome these problems by using an adaptive finite element algorithm in which we derive an a posteriori bound on the error in the computed current. This is used to guide mesh refinement and adaptive time-stepping, resulting in a fully automated algorithm which is both accurate and efficient.     

Differential capacitance of liquid/liquid interfaces of finite thicknesses: a finite element study

Finite element simulations were used to investigate the effect of a smooth variation of permittivity across a polarized liquid/liquid interface on the differential capacitance. The results show that a relative permittivity profile can account for the variation of ion solvation in the interfacial region, and therefore upon the diffuse double layer itself. The width and the symmetry of this profile across the interface are shown to be crucial parameters for interfacial distributions and fitting of capacitance data has been used to estimate the width of the interfacial region.     

Thermoforming process of semicrystalline polymeric sheets: Modeling and finite element simulations

A micromechanically-based elastic-viscoplastic model for the thermoforming process of semicrystalline polymer materials is proposed and implemented in a finite element code. This model takes into account the temperature and strain rate dependence. In this process the applied temperature is taken uniform throughout the sheet and its variation is due only to the adiabatic heating. The simulations are conducted for isotactic polypropylene using the finite element method. The polymer sheet thickness, the orientation of the polymer molecular chains, and the percent crystallinity show an important dependence on the process temperature (polymer softening) and the geometry of the mold. Based on recent experimental results in the literature, amorphization (decrease of crystallinity) is taken into account. Published in Russian in Vysokomolekulyarnye Soedineniya, Ser. A, 2008, Vol. 50, No. 5, pp. 841–849. This article was submitted by the authors in English.     

Application of the finite element method to molecular quantum mechanics

We present a general formalism of the finite element method and its computational aspects that influence the solution accuracy of spectral quantum mechanical problems. The possibilities of the method are demonstrated using as an example inversion vibrational spectra of structurally non-rigid complexes.High Energy Physics Institute, Protvino. I. V. Kurchatov, Atomic Energy Institute, Moscow. Translated from Teoreticheskaya i Eksperimental'naya Khimiya, Vol. 27, No. 4, pp. 442–446. July–August, 1991. Original article submitted April 4, 1991.     

Preparation and artificial ageing tests in stone conservation of fluorosilicone vinyl acetate/acrylic/epoxy polymers

In this work, a series of fluorosilicone vinyl acetate/acrylic/epoxy (FVAE) polymers for protection of stone relics were prepared with different content of hexafluorobutyl methacrylate (HFBMA) by the seed emulsion polymerization process. Properties and structure of FVAE materials were characterized by Fourier transform infrared spectroscopy (FTIR), thermogravimetric analysis (TG), and transmission electron microscopy (TEM). Viscosity, particle size, surface tension, gel content, adhesion and surface hardness of polymer materials were also determined. Surface morphology of the stone sample was observed by scanning electron microscopy (SEM). Compared with a commercial copolymer, ethyl methacrylate/methyl acrylate (EM/MA, Paraloid B72), protection ability of the prepared FVAE polymer was investigated using artificial ageing tests such as the freeze-thaw aging test, acid aging test and the soluble salts aging test. It was found that the FVAE polymers prepared can effectively prevent corrosion caused by H⁺, formation of an interface crack and further weathering, which indicates their possible application in stone protection.     

Generalized finite element method applied to the calculation of continuum states

A new method for the calculation of continuum energy eigenfunctions in one dimension is presented. It is based on a numerical coupling method first exploited in the so-called finite element method which does not require explicit fitting of boundary conditions. Results from simple test calculations for square well and Morse potentials show the method to be highly accurate and efficient.     

Effect of aging time on properties of acrylic impact modifier modified bisphenol A polycarbonate

Polycarbonate (PC) was blended with acrylic impact modifiers (AIMs). The effects of modifiers weight fraction on the Izod impact strength and yield strength of PC/AIM blends were investigated. The samples with 4% modifiers were aged under the T_g of PC in an air‐circulating oven, and the effects of aging time on impact strength, yield strength, modulus, elongation at break, post yield stress drop (PYSD) values, and morphology of fracture surface were investigated. The effects of aging time on the shape of stress–strain curve were also investigated. The aged samples were heat‐treated over the T_g of PC to erase the effects of physical aging. It was found that the drop of impact strength caused by physical aging can be recovered, the increment of yield strength and PYSD value caused by physical aging can only be partly recovered, and the heat‐treatment over the T_g of PC caused further increment of modulus. © 2005 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 43: 2715–2724, 2005     

Hybrid boundary element and finite difference method for solving the nonlinear Poisson-Boltzmann equation

A hybrid approach for solving the nonlinear Poisson-Boltzmann equation (PBE) is presented. Under this approach, the electrostatic potential is separated into (1) a linear component satisfying the linear PBE and solved using a fast boundary element method and (2) a correction term accounting for nonlinear effects and optionally, the presence of an ion-exclusion layer. Because the correction potential contains no singularities (in particular, it is smooth at charge sites) it can be accurately and efficiently solved using a finite difference method. The motivation for and formulation of such a decomposition are presented together with the numerical method for calculating the linear and correction potentials. For comparison, we also develop an integral equation representation of the solution to the nonlinear PBE. When implemented upon regular lattice grids, the hybrid scheme is found to outperform the integral equation method when treating nonlinear PBE problems. Results are presented for a spherical cavity containing a central charge, where the objective is to compare computed 1D nonlinear PBE solutions against ones obtained with alternate numerical solution methods. This is followed by examination of the electrostatic properties of nucleic acid structures.