A viscoelastic–viscoplastic modeling approach for amorphous polymers in vacuum forming simulation

In this study, the simulation of a vacuum forming process employing a micromechanical inspired viscoelastic–viscoplastic model is investigated. In the vacuum forming process, a plastic sheet is heated above the glass transition temperature and subsequently forced into a mold by applying a vacuum. The model consists of a generalized Maxwell model combined with an dissipative element in series. Each Maxwell element incorporates a hyperelastic element in series with a viscous element based on a hyperbolical law. While the generalized Maxwell model considers the relaxation due to molecular alignment, the additional viscous element is a modification based on the approach of Bergström and thus considers molecular chain reptation. The model is designed with the aim to converge to the generalized linear Maxwell model in the limit of small deformation. Furthermore, the viscous modeling is temperature activated and follows the Williams–Landel–Ferry approach in the limit of linear viscoelasticity. To simulate rheological standard experiments, a physical-network-based implementation into Simscape is presented. To validate the performance of the model in thermoforming, it is implemented into Fortran programming language for finite element simulation with Abaqus/Explicit. It can be shown that the simulation is able to predict the thickness in high correlation with experimental results.     

Modeling creep behavior in ceramic matrix composites

In this work, a three-dimensional viscoplasticity formulation with progressive damage is developed and used to investigate the complex time-dependent constituent load transfer and progressive damage behavior in ceramic matrix composites (CMCs) subjected to creep. The viscoplasticity formulation is based on Hill's orthotropic plastic potential, an associative flow rule, and the Norton-Bailey creep power law with Arrhenius temperature dependence. A fracture mechanics-informed isotropic matrix damage model is used to account for CMC brittle matrix damage initiation and propagation, in which two scalar damage variables capture the effects of matrix porosity as well as matrix property degradation due to matrix crack initiation and propagation. The Curtin progressive fiber damage model is utilized to simulate progressive fiber failure. The creep-damage formulation is subsequently implemented as a constitutive model in the generalized method of cells (GMC) micromechanics formulation to simulate time-dependent deformation and material damage under creep loading conditions. The developed framework is used to simulate creep of single fiber SiC/SiC microcomposites. Simulation results are in excellent agreement with experimental and numerical data available in the literature.     

A Method for the Stress Analysis of Lap Joints

A theory is presented for the adhesive stresses in single and double lap joints under tensile loading, while subjected to thermal stress. The formulation includes the effects of bending, shearing, stretching and hygrothermal deformation in both the adherend and adhesive. All boundary conditions, including shear stress free surfaces, are satisfied. The method is general and therefore applicable to a range of material properties and joint configurations including metal-to-metal, metal-to-CFRP or CFRP-to-CFRP. The solution is numerical and is based on an equilibrium finite element approach. Through the use of an iterative procedure, the solution has been extended to cater for non-linear adhesive materials.     

A Method for the Stress Analysis of Lap Joints

A theory is presented for the adhesive stresses in single and double lap joints under tensile loading, while subjected to thermal stress. The formulation includes the effects of bending, shearing, stretching and hygrothermal deformation in both the adherend and adhesive. All boundary conditions, including shear stress free surfaces, are satisfied. The method is general and therefore applicable to a range of material properties and joint configurations including metal-to-metal, metal-to-CFRP or CFRP-to-CFRP. The solution is numerical and is based on an equilibrium finite element approach. Through the use of an iterative procedure, the solution has been extended to cater for non-linear adhesive materials.     

Creep Resistance of Pressure Sensitive Mounting Tapes

The first part of the paper deals with an approach towards a systematic testing procedure to evaluate the creep behavior of single lap shear specimens bonded with PSA mounting tapes under the influence of temperature and humidity. The study includes commercial tapes as well as self-formulated pressure sensitive adhesives based on styrene block copolymers. The second part of the paper relates the obtained data, consisting of the time-dependent sample deformation and time-to-failure, to the observed failure modes. The results show that the creep behavior of a pressure sensitive adhesive is not only dependent on the environmental, conditions but also on the substrate material and its surface composition. The results for the self-formulated adhesives reveal the possibility of enhancing creep resistance of PSA's by adding fillers to the formulation. The paper closes with a modification of the Burgers model that is suitable for describing the creep/creep recovery behavior of tested lap shear specimens. The effect of nonlinear behavior in cyclic loading experiments is described and a thesis for the relation of nonlinear creep behavior to damaging processes in the adhesive bond is presented.     

Development of a curvilinear viscoelastic constitutive relationship for time dependent materials. Part B: Example problems

The boundary value problem of a two‐dimensional viscoelastic beam clamped at two ends and subjected to both a dead load and normal surface traction is solved using a finite element method here in Part B. The constitutive relationship between stress and strain developed in Part A uses a convected coordinate system and body tensor mathematics. Maxwell elements (springs and dashpots) describe the material for both fluid and solid characterizations. The overall finite element results calculated were physically reasonable. However, the assumed boundary conditions produce a stress singularity at the boundary, a singularity that is also seen in small deformation elastic theory.     

Modeling of visco‐hyperelastic behavior of transversely isotropic functionally graded rubbers

In this article, visco‐hyperelastic constitutive model is developed to describe the rate‐dependent behavior of transversely isotropic functionally graded rubber‐like materials at finite deformations. Zener model that consists of Maxwell element parallel to a hyperelastic equilibrium spring is used in this article. Steady state response is described by equilibrium hyperelastic spring and rate‐dependence behavior is modeled by Maxwell element that consists of a hyperelastic intermediate spring and a nonlinear viscous damper. Modified and reinforced neo‐Hookean strain energy function is proposed for the two hyperelastic springs. The mechanical properties and material constants of strain energy function are graded along the axial direction based on exponential function. A history‐integral method has been used to develop a constitutive equation for modeling the behavior of the model. The applied history integral method is based on the Kaye‐BKZ theory. The material constant parameters appeared in the formulation have been determined with the aid of available uniaxial tensile experimental tests for a specific material and the results are compared to experimental results. It is then concluded that, the proposed constitutive equation is quite proficient in forecasting the behavior of rubber‐like materials in different deformation and wide ranges of strain rate. POLYM. ENG. SCI., 56:342–347, 2016. © 2016 Society of Plastics Engineers     

Micromorphic theory: a gateway to nano world

Micromorphic theory (MMT) envisions a material body as a continuous collection of deformable particles; each possesses finite size and inner structure. It is considered as the most successful top-down formulation of a two-level continuum model, in which the deformation is expressed as a sum of macroscopic continuous deformation and internal microscopic deformation of the inner structure. In this work, the kinematics including the objective Eringen tensors is introduced. Balance laws are derived by requiring the energy equation to be form-invariant under the generalized Galilean transformation. The concept of material force and the balance law of pseudomomentum are generalized for MMT. An axiomatic approach is demonstrated in the formulation of constitutive equations for a generalized micromorphic thermoviscoelastic solid, generalized micromorphic fluid, micromorphic plasticity, and micromorphic electromagnetic–thermoelastic solid. Applications of MMT in micro/nanoscale are discussed.     

Experimental and numerical investigation on flexural behavior of acrylonitrile-butadiene-styrene polymer

Acrylonitrile-butadiene-styrene (ABS) is an extensively utilized rubber-toughened amorphous thermoplastic in industry. Compared to other amorphous thermoplastics, the most promising mechanical quantity of ABS is its high impact resistance. Thus, understanding the mechanical response of ABS to multiaxial loads is of the great industrial concern. The primary objective of this study was to characterize the flexural response of ABS by conducting three-point bending tests at two distinct deformation rates of 5 and 10 mm/s to figure out the deformation rate effect on the flexural response of ABS. It was observed that the ABS act stiffer with an increased deformation rate. Numerical implementation of three-point bending tests for each deformation rate was performed using the semi-analytical material model (SAMP-1) available in Ls-Dyna finite element code. The simulations for each deformation rate were run depending on SAMP-1 and Von-Misses yield surface formulations to figure out the effect of nonidentical material behavior of ABS in tension, compression, and shear on flexural response. The percentage error in the predicted peak force values considering the compression and shear test data (SAMP-1) and without it (Von Misses) was 3% and 7% for deformation rate of 5 mm/s and 5% and 12% for deformation rate of 10 mm/s. Hence, predicting the flexural behavior of ABS accurately, dissimilar material behavior needs to be taken into consideration. Moreover, associated and nonassociated flow rule effects on the flexural response of ABS were numerically investigated and there was no significant influence observed on the flexural response of ABS.     

计入横向剪切时层合梁的弯曲弹性解

本文根据一阶横向剪切变形理论,导出了对称层合梁的挠曲线微分方程,求解了层合染在简单载荷作用下的挠度曲线和应力,横向剪切对挠度和应力的影响依赖于层合梁的材料常数,约束类型,载荷种类和跨高比,计算结果表明,横向剪切对层合梁挠度影响颇为显著,且当层合梁跨高比大于18时,可忽略横向剪切效应。     

Numerical study on the electromechanical behavior of dielectric elastomer with the influence of surrounding medium

The considerable electric-induced shape change, together with the attributes of lightweight, high efficiency, and inexpensive cost, makes dielectric elastomer, a promising soft active material for the realization of actuators in broad applications. Although, a number of prototype devices have been demonstrated in the past few years, the further development of this technology necessitates adequate analytical and numerical tools. Especially, previous theoretical studies always neglect the influence of surrounding medium. Due to the large deformation and nonlinear equations of states involved in dielectric elastomer, finite element method (FEM) is anticipated; however, the few available formulations employ homemade codes, which are inconvenient to implement. The aim of this work is to present a numerical approach with the commercial FEM package COMSOL to investigate the nonlinear response of dielectric elastomer under electric stimulation. The influence of surrounding free space on the electric field is analyzed and the corresponding electric force is taken into account through an electric surface traction on the circumstances edge. By employing Maxwell stress tensor as actuation pressure, the mechanical and electric governing equations for dielectric elastomer are coupled, and then solved simultaneously with the Gent model of stain energy to derive the electric induced large deformation as well as the electromechanical instability. The finite element implementation presented here may provide a powerful computational tool to help design and optimize the engineering applications of dielectric elastomer.     

Theoretical and finite element studies of interfacial stresses in reinforced concrete beams strengthened by externally FRP laminates plate

The paper presents the results of an analytical and numerical solution for interfacial stresses in carbon fiber reinforced plastic (CFRP)–reinforced concrete (RC) hybrid beams studied by the finite element method. The analytical analysis is based on the deformation compatibility approach where both the shear and normal stresses are assumed to be invariant across the adhesive layer thickness. The adherend shear deformations are taken into account by assuming a parabolic shear stress through the thickness of both the concrete beam and the bonded plate. In numerical analysis, the mesh sensitivity test shows that the finite element results for interfacial stresses are not sensitive to the finite element mesh. The finite element analysis then is used to calculate the interfacial stress distribution and evaluate the effect of the structural parameters on the interfacial behavior. It is shown that both the normal and shear stresses at the interface are influenced by the material and geometry parameters of the composite beam. Numerical results from the present analysis are presented both to demonstrate the advantages of the present solution over existing ones and to illustrate the main characteristics of interfacial stress distributions. We can conclude that this research is helpful for the understanding the mechanical behavior of the interface and design of the FRP–RC hybrid structures.     

ANALYTIC SOLUTIONS FOR THE UNSTEADY LONGITUDINAL FLOW OF AN OLDROYD-B FLUID WITH FRACTIONAL MODEL

The unsteady flow of an Oldroyd-B fluid with fractional derivative model, between two infinite coaxial circular cylinders, is studied by using finite Hankel and Laplace transforms. The motion is produced by the inner cylinder that, at time t = 0⁺, is subject to a time-dependent longitudinal shear stress. The solutions that have been obtained, presented under series form in terms of the generalized G and R functions, satisfy all imposed initial and boundary conditions. The corresponding solutions for ordinary Oldroyd-B and generalized and ordinary Maxwell and Newtonian fluids, performing the same motion, are obtained as limiting cases of our general solutions. Finally, the influence of the pertinent parameters on the fluid motion, as well as a comparison between models, is shown by graphical illustrations.     

Master Sintering Curve Formulated from Constitutive Models

The classical master sintering curve (MSC) is derived from empirical sintering model and is applicable over a range of heating rates and temperatures. For simplicity, the MSC approach was modified by assuming one dominant densification mechanism to evaluate and predict densification response. However, the concept of MSC can be extended well beyond the original formulation or the subsequent simplifications. To this effect, generalized formulations are proposed based on several constitutive equations including both grain growth and densification. These formulations can be used very effectively to obtain material properties that in turn can be used in finite-element method to improve the accuracy of the simulations.     

Tensile stress measurements on linear and branches low-density polyethylene melts. Interpretation of results with a generalized Maxwell model

Dynamic shear experiments in the linear range of deformation and extensional tests at constant strain rate have been carried out on a linear low-density polyethylene (LLDPE) melt and on two branched low-density polyethylene (LDPE) melts with different amounts of long-chain branching. Both the dynamic shear moduli and the tensile stress obey the time–temperature superposition principle. A simple model based on a nonaffine generalized Maxwell model with two relaxation times is proposed to describe the rheological behavior in elongation of these melts. Close agreement between the model and the experimental data can be obtained by adjusting the two relaxation times and the “slip parameter” of entanglements. The variations of these parameters with strain rate and their relationship with molecular structure are discussed.     

Caractérisation viscoélastique du comportement d'une membrane thermoplastique et modélisation numérique de thermoformage

In this work, we are interested, on the one hand in the characterization of circular polymeric ABS membrane under biaxial deformation using the bubble inflation technique, on the other hand in modelling and numerical simulation of the thermoforming of ABS materials using the dynamic finite element method. The viscoelastic behaviour of the Lodge model is considered. First, the governing equations for the inflation of a flat circular membrane are solved using a variable‐step‐size‐finite difference method and a modified Levenberg‐Marquardt algorithm to minimize the difference between the calculated and measured inflation pressure. This will determine the material constants embedded within the model used. For dynamic finite elements method, we consider a nonlinear load in air flow which obeys the Redlich‐Kwong equation of state of the real gases. For numerical simulation, the lagrangian formulation together with the assumption of the membrane theory is used. Moreover, the influence of the viscoelastic model on the thickness and on the stress distribution in the thermoforming sheet are analysed for ABS material.     

Modeling nonlinear viscoelastic response

We present a model for calculating nonlinear viscoelastic response which we call the “phases model” (PHM). In terms of a mechanical model representation the PHM is a generalized Maxwell model with nonlinear elements where each Maxwell element is referred to as a phase. The viscous material properties are represented in the model in terms of flow curves of the individual phases. The collection of flow curves form the flow diagram. We show how to calibrate the flow diagram from a family of constant rate test curves by means of a simple straightforward procedure. We give an example of such a calibration for a certain rigid polyurethane. We applied our model to the calculation of nonlinear viscoelastic response to varius loading programs in uniaxial tension, and to the creep of a simply supported beam, and obtained good agreement with experimental data.     

INFLUENCE OF DRYING CONDITIONS ON THE RHEOLOGICAL PROPERTIES OF PRUNES

Rheological properties of rehydrated prunes were obtained applying compression-relaxation tests by using a Texture Analyzer TAXT2i. A mathematical development was adopted to determine the stress and area, along the deformation. Experimental data of stress versus time was fitted by using three different rheological models: generalized Maxwell, Normand & Peleg and Maxwell. Results showed that generalized Maxwell model can be used to describe the viscoelastic behavior of the samples. The rheological parameters obtained indicated that prunes exhibited elastic behavior more pronounced at low moisture content and drying air temperature. At high moisture content and temperature the sample became a more viscous and less rigid.     

High temperature internal friction measurements of 3YTZP zirconia polycrystals. High temperature background and creep

This work focuses on the high-temperature mechanic properties of a 3 mol% yttria zirconia polycrystals (3YTZP), fabricated by hot-pressureless sintering. Systematic measurements of mechanical loss as a function of temperature and frequency were performed. An analytical method, based on the generalized Maxwell rheological model, has been used to analyze the high temperature internal friction background (HTB). This method has been previously applied to intermetallic compounds but never to ceramics, except in a preliminary study performed on fine grain and nano-crystalline zirconia. The HTB increases exponentially and its analysis provides an apparent activation enthalpy which correlates well with that obtained from creep experiments. This fact shows on the one hand the plausibility of applying the generalized Maxwell model to ceramics, and on the other hand indicates the possibility of using mechanical spectroscopy as a complementary helpful technique to investigate the high temperature deformation mechanism of materials.     

Effect of shear deformation on interfacial stresses in plated beams subjected to arbitrary loading

Bonding a fibre reinforced polymer (FRP) composite or metallic plate to the soffit of a reinforced concrete (RC), timber or metallic beam can significantly increase its strength and other aspects of structural performance. These hybrid beams are often found to fail due to premature debonding of the plate from the original beam in a brittle manner. This has led to the development of many analytical solutions over the last two decades to quantify the interfacial shear and normal stresses between the adherends. The adherends are subjected to axial, bending and shear deformations. However, most analytical solutions have neglected the influence of shear deformation of the adherends. For the few solutions which consider this effect in an approximate manner, their applicability is limited to one or two specific load cases. This paper presents a general analytical solution for the interfacial stresses in plated beams under an arbitrary loading with the shear deformation of the adherends duly considered. The shear stress distribution is assumed to be parabolic through the depth of the adherends in predicting the interfacial shear stress and Timoshenko's beam theory is adopted in predicting interfacial normal stress to account for the shear deformation. The solution is applicable to a beam of arbitrary prismatic cross-section bonded symmetrically or asymmetrically with a thin or thick plate, both having linear elastic material properties. The effect of shear deformation is illustrated through an example beam. The influence of material and geometric parameters of the adherends and adhesive on the interfacial stress concentrations at the plate end is discussed.