Showing papers in "Mechanics of Time-dependent Materials in 2017"

A study on photothermal waves in an unbounded semiconductor medium with cylindrical cavity

Abstract: The theory of coupled plasma, thermal, and elastic waves was used to investigate the wave propagation on semiconductor material with cylindrical cavity during photo-thermoelastic process. An unbounded material, elastic semiconductor containing a cylindrical cavity with isotropic and homogeneous thermal and elastic properties has been considered. The inner surface of cavity is constrained, and the carrier density is photogenerated by an exponentially decaying pulse boundary heat flux. The eigenvalue approach, together with Laplace transform techniques, was used to obtain the analytical solutions. Numerical computations have been done for a silicon-like semiconductor material, and the results are presented graphically to estimate the effect of the coupling between the plasma, thermal, and elastic waves. The graphical results indicate that the thermal activation coupling parameter is an important phenomenon and has a great effect on the distribution of field quantities.

Nonlinear creep damage constitutive model for soft rocks

Abstract: In some existing nonlinear creep damage models, it may be less rigorous to directly introduce a damage variable into the creep equation when the damage variable of the viscous component is a function of time or strain. In this paper, we adopt the Kachanov creep damage rate and introduce a damage variable into a rheological differential constitutive equation to derive an analytical integral solution for the creep damage equation of the Bingham model. We also propose a new nonlinear viscous component which reflects nonlinear properties related to the axial stress of soft rock in the steady-state creep stage. Furthermore, we build an improved Nishihara model by using this new component in series with the correctional Nishihara damage model that describes the accelerating creep, and deduce the rheological constitutive relation of the improved model. Based on superposition principle, we obtain the damage creep equation for conditions of both uniaxial and triaxial compression stress, and study the method for determining the model parameters. Finally, this paper presents the laboratory test results performed on mica-quartz schist in parallel with, or vertical to the schistosity direction, and applies the improved Nishihara model to the parameter identification of mica-quartz schist. Using a comparative analysis with test data, results show that the improved model has a superior ability to reflect the creep properties of soft rock in the decelerating creep stage, the steady-state creep stage, and particularly within the accelerating creep stage, in comparison with the traditional Nishihara model.

Memory-dependent derivatives for photothermal semiconducting medium in generalized thermoelasticity with two-temperature

Abstract: In this work, a novel generalized model of photothermal theory with two-temperature thermoelasticity theory based on memory-dependent derivative (MDD) theory is performed. A one-dimensional problem for an elastic semiconductor material with isotropic and homogeneous properties has been considered. The problem is solved with a new model (MDD) under the influence of a mechanical force with a photothermal excitation. The Laplace transform technique is used to remove the time-dependent terms in the governing equations. Moreover, the general solutions of some physical fields are obtained. The surface taken into consideration is free of traction and subjected to a time-dependent thermal shock. The numerical Laplace inversion is used to obtain the numerical results of the physical quantities of the problem. Finally, the obtained results are presented and discussed graphically.

Mechanical characterization and modeling of the deformation and failure of the highly crosslinked RTM6 epoxy resin

Abstract: The nonlinear deformation and fracture of RTM6 epoxy resin is characterized as a function of strain rate and temperature under various loading conditions involving uniaxial tension, notched tension, uniaxial compression, torsion, and shear. The parameters of the hardening law depend on the strain-rate and temperature. The pressure-dependency and hardening law, as well as four different phenomenological failure criteria, are identified using a subset of the experimental results. Detailed fractography analysis provides insight into the competition between shear yielding and maximum principal stress driven brittle failure. The constitutive model and a stress-triaxiality dependent effective plastic strain based failure criterion are readily introduced in the standard version of Abaqus, without the need for coding user subroutines, and can thus be directly used as an input in multi-scale modeling of fibre-reinforced composite material. The model is successfully validated against data not used for the identification and through the full simulation of the crack propagation process in the V-notched beam shear test.

Dynamic properties of ultraviolet-exposed polyurea

Abstract: Polyurea is used in military and civilian applications, where exposure to the sun in long durations is imminent. Extended exposure to ultraviolet radiation from the sun can deteriorate its mechanical performance to suboptimal levels. This study reports on the dynamic mechanical properties of polyurea as a function of ultraviolet radiation exposure duration. Six sets of samples were continuously exposed to ultraviolet radiation for different durations up to 18 weeks. Control samples were also tested that did not receive ultraviolet exposure. The dynamic properties were measured using a dynamic mechanical analyzer. Exposed samples exhibited significant color changes from transparent yellow to opaque tan after 18 weeks of exposure. Changes of color were observed as early as 3 weeks of exposure. The dynamic properties showed an initial increase in the dynamic modulus after 3 weeks of exposure, with no further significant change in the stiffness thereafter. The ultraviolet exposure had a significant impact at relatively short loading times or low temperature, for example, up to 6 decades of time. As loading time increases or polyurea operates at high temperature, the effect of ultraviolet exposure and temperature on the performance become highly coupled.

Time-evolving collagen-like structural fibers in soft tissues: biaxial loading and spherical inflation

Abstract: This work considers a previously developed constitutive theory for the time dependent mechanical response of fibrous soft tissue resulting from the time dependent remodeling of a collagen fiber network that is embedded in a ground substance matrix. The matrix is taken to be an incompressible nonlinear elastic solid. The remodeling process consists of the continual dissolution of existing fibers and the creation of new fibers. Motivated by experimental reports on the enzyme degradation of collagen fibers, the remodeling is governed by first order chemical kinetics such that the dissolution rate is dependent upon the fiber stretch. The resulting time dependent mechanical response is sensitive to the natural configuration of the fibers when they are created, and different assumptions on the nature of the fiber’s stress free state are considered here. The response under biaxial loading, a type of loading that has particular significance for the characterization of biological materials, is studied. The inflation of a spherical membrane is then analyzed in terms of the equal biaxial stretch that occurs in the membrane approximation. Different assumptions on the natural configuration of the fibers, combined with their time dependent dissolution and reforming, are shown to emulate alternative forms of creep and relaxation response. This formal similarity to viscoelastic phenomena occurs even though the underlying mechanisms are fundamentally different from the mechanism of macromolecular reconfiguration that one typically associates with viscoelastic response.

Fractional modeling of Pasternak-type viscoelastic foundation

Abstract: In this paper, we propose a fractional Pasternak-type foundation model to characterize the time-dependent properties of the viscoelastic foundation. With varying fractional orders, the proposed model can govern the traditional Winkler model, Pasternak model, and viscoelastic model. We take the four-edge simply supported rectangular thin plate as an example to analyze the viscoelastic foundation reaction, and obtain the solution of the new governing equation. Theoretical results show that the fractional order has a dramatic influence on the deflection and bending moment. It can be further concluded that the softer foundation will become more time-dependent. Subsequently, the difference between fractional Pasternak-type and Winkler foundation model is presented in this work. The existence of constrained boundary is found to definitely affect deflection and bending moment. Such phenomenon, known as the wall effect, is deeply discussed.

Constitutive modeling of polycarbonate over a wide range of strain rates and temperatures

Abstract: The mechanical behavior of polycarbonate was experimentally investigated over a wide range of strain rates ( $10^{-4}\mbox{ to }5\times 10^{3}~\mbox{s}^{-1}$ ) and temperatures (293 to 353 K). Compression tests under these conditions were performed using a SHIMADZU universal testing machine and a split Hopkinson pressure bar. Falling weight impact testing was carried out on an Instron Dynatup 9200 drop tower system. The rate- and temperature-dependent deformation behavior of polycarbonate was discussed in detail. Dynamic mechanical analysis (DMA) tests were utilized to observe the glass ( $\alpha $ ) transition and the secondary ( $\beta $ ) transition of polycarbonate. The DMA results indicate that the $\alpha $ and $\beta $ transitions have a dramatic influence on the mechanical behavior of polycarbonate. The decompose/shift/reconstruct (DSR) method was utilized to decompose the storage modulus into the $\alpha $ and $\beta $ components and extrapolate the entire modulus, the $\alpha$ -component modulus and the $\beta$ -component modulus. Based on three previous models, namely, Mulliken–Boyce, G’Sell–Jonas and DSGZ, an adiabatic model is proposed to predict the mechanical behavior of polycarbonate. The model considers the contributions of both the $\alpha $ and $\beta $ transitions to the mechanical behavior, and it has been implemented in ABAQUS/Explicit through a user material subroutine VUMAT. The model predictions are proven to essentially coincide with the experimental results during compression testing and falling weight impact testing.

Development of a stress-mode sensitive viscoelastic constitutive relationship for asphalt concrete: experimental and numerical modeling

Abstract: Asphalt binder is responsible for the thermo-viscoelastic mechanical behavior of asphalt concrete. Upon application of pure compressive stress to an asphalt concrete specimen, the stress is transferred by mechanisms such as aggregate interlock and the adhesion/cohesion properties of asphalt mastic. In the pure tensile stress mode, aggregate interlock plays a limited role in stress transfer, and the mastic phase plays the dominant role through its adhesive/cohesive and viscoelastic properties. Under actual combined loading patterns, any coordinate direction may experience different stress modes; therefore, the mechanical behavior is not the same in the different directions and the asphalt specimen behaves as an anisotropic material. The present study developed an anisotropic nonlinear viscoelastic constitutive relationship that is sensitive to the tension/compression stress mode by extending Schapery’s nonlinear viscoelastic model. The proposed constitutive relationship was implemented in Abaqus using a user material (UMAT) subroutine in an implicit scheme. Uniaxial compression and indirect tension (IDT) testing were used to characterize the viscoelastic properties of the bituminous materials and to calibrate and validate the proposed constitutive relationship. Compressive and tensile creep compliances were calculated using uniaxial compression, as well as IDT test results, for different creep-recovery loading patterns at intermediate temperature. The results showed that both tensile creep compliance and its rate were greater than those of compression. The calculated deflections based on these IDT test simulations were compared with experimental measurements and were deemed acceptable. This suggests that the proposed viscoelastic constitutive relationship correctly demonstrates the viscoelastic response and is more accurate for analysis of asphalt concrete in the laboratory or in situ.

Generalization of the ordinary state-based peridynamic model for isotropic linear viscoelasticity

Abstract: This paper presents a generalization of the original ordinary state-based peridynamic model for isotropic linear viscoelasticity. The viscoelastic material response is represented using the thermodynamically acceptable Prony series approach. It can feature as many Prony terms as required and accounts for viscoelastic spherical and deviatoric components. The model was derived from an equivalence between peridynamic viscoelastic parameters and those appearing in classical continuum mechanics, by equating the free energy densities expressed in both frameworks. The model was simplified to a uni-dimensional expression and implemented to simulate a creep-recovery test. This implementation was finally validated by comparing peridynamic predictions to those predicted from classical continuum mechanics. An exact correspondence between peridynamics and the classical continuum approach was shown when the peridynamic horizon becomes small, meaning peridynamics tends toward classical continuum mechanics. This work provides a clear and direct means to researchers dealing with viscoelastic phenomena to tackle their problem within the peridynamic framework.

Hyperbolic contraction measuring systems for extensional flow

Abstract: In this paper an experimental method for extensional measurements on medium viscosity fluids in contraction flow is evaluated through numerical simulations and experimental measurements. This measuring technique measures the pressure drop over a hyperbolic contraction, caused by fluid extension and fluid shear, where the extensional component is assumed to dominate. The present evaluative work advances our previous studies on this experimental method by introducing several contraction ratios and addressing different constitutive models of varying shear and extensional response. The constitutive models included are those of the constant viscosity Oldroyd-B and FENE-CR models, and the shear-thinning LPTT model. Examining the results, the impact of shear and first normal stress difference on the measured pressure drop are studied through numerical pressure drop predictions. In addition, stream function patterns are investigated to detect vortex development and influence of contraction ratio. The numerical predictions are further related to experimental measurements for the flow through a 15:1 contraction ratio with three different test fluids. The measured pressure drops are observed to exhibit the same trends as predicted in the numerical simulations, offering close correlation and tight predictive windows for experimental data capture. This result has demonstrated that the hyperbolic contraction flow is well able to detect such elastic fluid properties and that this is matched by numerical predictions in evaluation of their flow response. The hyperbolical contraction flow technique is commended for its distinct benefits: it is straightforward and simple to perform, the Hencky strain can be set by changing contraction ratio, non-homogeneous fluids can be tested, and one can directly determine the degree of elastic fluid behaviour. Based on matching of viscometric extensional viscosity response for FENE-CR and LPTT models, a decline is predicted in pressure drop for the shear-thinning LPTT model. This would indicate a modest impact of shear in the flow since such a pressure drop decline is relatively small. It is particularly noteworthy that the increase in pressure drop gathered from the experimental measurements is relatively high despite the low Deborah number range explored.

Deformation analysis of polymers composites: rheological model involving time-based fractional derivative

Abstract: A modeling approach to time-dependent property of Glass Fiber Reinforced Polymers (GFRP) composites is of special interest for quantitative description of long-term behavior. An electronic creep machine is employed to investigate the time-dependent deformation of four specimens of dog-bond-shaped GFRP composites at various stress level. A negative exponent function based on structural changes is introduced to describe the damage evolution of material properties in the process of creep test. Accordingly, a new creep constitutive equation, referred to fractional derivative Maxwell model, is suggested to characterize the time-dependent behavior of GFRP composites by replacing Newtonian dashpot with the Abel dashpot in the classical Maxwell model. The analytic solution for the fractional derivative Maxwell model is given and the relative parameters are determined. The results estimated by the fractional derivative Maxwell model proposed in the paper are in a good agreement with the experimental data. It is shown that the new creep constitutive model proposed in the paper needs few parameters to represent various time-dependent behaviors.

Linear orthotropic viscoelasticity model for fiber reinforced thermoplastic material based on Prony series

Abstract: Material properties description and understanding are essential aspects when computational solid mechanics is applied to product development. In order to promote injected fiber reinforced thermoplastic materials for structural applications, it is very relevant to develop material characterization procedures, considering mechanical properties variation in terms of fiber orientation and loading time. Therefore, a methodology considering sample manufacturing, mechanical tests and data treatment is described in this study. The mathematical representation of the material properties was solved by a linear viscoelastic constitutive model described by Prony series, which was properly adapted to orthotropic materials. Due to the large number of proposed constitutive model coefficients, a parameter identification method was employed to define mathematical functions. This procedure promoted good correlation among experimental tests, and analytical and numerical creep models. Such results encourage the use of numerical simulations for the development of structural components with the proposed linear viscoelastic orthotropic constitutive model. A case study was presented to illustrate an industrial application of proposed methodology.

Network structure dependence on unconstrained isothermal-recovery processes for shape-memory thiol-epoxy “click” systems

Abstract: The shape-memory response (SMR) of “click” thiol-epoxy polymers produced using latent catalysts, with different network structure and thermo-mechanical properties, was tested on unconstrained shape-recovery processes under isothermal conditions. Experiments at several programming temperatures ( $T_{\mathrm{prog}}$ ) and isothermal-recovery temperatures ( $T_{\mathrm{iso}}$ ) were carried out, and the shape-memory stability was analyzed through various consecutive shape-memory cycles. The temperature profile during the isothermal-recovery experiments was monitored, and it showed that the shape-recovery process takes place while the sample is becoming thermally stable and before stable isothermal temperature conditions are eventually reached. The shape-recovery process takes place in two different stages regardless of $T_{\mathrm{iso}}$ : a slow initial stage until the process is triggered at a temperature strongly related with the beginning of network relaxation, followed by the typical exponential decay of the relaxation processes until completion at a temperature below or very close to $T_{\mathrm{g}}$ . The shape-recovery process is slower in materials with more densely crosslinked and hindered network structures. The shape-recovery time ( $t_{\mathrm{sr}}$ ) is significantly reduced when the isothermal-recovery temperature $T_{\mathrm{iso}}$ increases from below to above $T_{\mathrm{g}}$ because the network relaxation dynamics accelerates. However, the temperature range from the beginning to the end of the recovery process is hardly affected by $T_{\mathrm{iso}}$ ; at higher $T_{\mathrm{iso}}$ it is only slightly shifted to higher temperatures. These results suggest that the shape-recovery process can be controlled by changing the network structure and working at $T_{\mathrm{iso}} < T_{\mathrm{g}}$ to maximize the effect of the structure and/or by increasing $T_{\mathrm{iso}}$ to minimize the effect but increasing the shape-recovery rate.

Stability analysis of arbitrarily shaped moderately thick viscoelastic plates using Laplace–Carson transformation and a simple hp cloud method

Abstract: In this paper, the stability analysis of moderately thick time-dependent viscoelastic plates with various shapes is studied using the Laplace–Carson transformation and simple hp cloud meshless method. The shear effect of the plate is described by the first order shear deformation theory. The mechanical properties of the materials are supposed to be linear viscoelastic based on the constant bulk modulus. The displacement field is assumed to be the product of two functions, one being a function of geometrical parameters and the other a known exponential function of time. The simple hp cloud method is used for discretization which is based on Kronecker-delta properties. Thus, the essential boundary conditions can be imposed directly. A numerical investigation is made by employing the inverse of Laplace–Carson transformation. The time history of buckling coefficients of viscoelastic plates of various shapes with different boundary conditions is considered. Moreover, a number of numerical results are presented to study the effect of thickness, aspect ratio, different boundary conditions, and various shapes on the time history of buckling coefficients of the viscoelastic plate.

Closed-form solution of the Ogden–Hill’s compressible hyperelastic model for ramp loading

Abstract: This article deals with the visco-hyperelastic modelling approach for compressible polymer foam materials. Polymer foams can exhibit large elastic strains and displacements in case of volumetric compression. In addition, they often show significant rate-dependent properties. This material behaviour can be accurately modelled using the visco-hyperelastic approach, in which the large strain viscoelastic description is combined with the rate-independent hyperelastic material model. In case of polymer foams, the most widely used compressible hyperelastic material model, the so-called Ogden–Hill’s model, was applied, which is implemented in the commercial finite element (FE) software Abaqus. The visco-hyperelastic model is defined in hereditary integral form, therefore, obtaining a closed-form solution for the stress is not a trivial task. However, the parameter-fitting procedure could be much faster and accurate if closed-form solution exists. In this contribution, exact stress solutions are derived in case of uniaxial, biaxial and volumetric compression loading cases using ramp-loading history. The analytical stress solutions are compared with the stress results in Abaqus using FE analysis. In order to highlight the benefits of the analytical closed-form solution during the parameter-fitting process experimental work has been carried out on a particular open-cell memory foam material. The results of the material identification process shows significant accuracy improvement in the fitting procedure by applying the derived analytical solutions compared to the so-called separated approach applied in the engineering practice.

Solving viscoelastic problems by combining SBFEM and a temporally piecewise adaptive algorithm

Abstract: A combination of the scaled boundary finite element method (SBFEM) with a temporally piecewise adaptive algorithm is exploited to solve viscoelastic problems. By expanding variables at a discretized time interval, a coupled spatial–temporal problem is decoupled into a series of recursive spatial problems, which are solved by SBFEM, and a piecewise adaptive process in the time domain is realized via the change of expansion powers. Numerical verification, including the cases involving stress singularity, infinite domain, and inhomogeneous medium, are provided in comparison with analytical or ABAQUS-based solutions.

Viscoelastic damped response of cross-ply laminated shallow spherical shells subjected to various impulsive loads

Abstract: In this paper, the viscoelastic damped response of cross-ply laminated shallow spherical shells is investigated numerically in a transformed Laplace space. In the proposed approach, the governing differential equations of cross-ply laminated shallow spherical shell are derived using the dynamic version of the principle of virtual displacements. Following this, the Laplace transform is employed in the transient analysis of viscoelastic laminated shell problem. Also, damping can be incorporated with ease in the transformed domain. The transformed time-independent equations in spatial coordinate are solved numerically by Gauss elimination. Numerical inverse transformation of the results into the real domain are operated by the modified Durbin transform method. Verification of the presented method is carried out by comparing the results with those obtained by the Newmark method and ANSYS finite element software. Furthermore, the developed solution approach is applied to problems with several impulsive loads. The novelty of the present study lies in the fact that a combination of the Navier method and Laplace transform is employed in the analysis of cross-ply laminated shallow spherical viscoelastic shells. The numerical sample results have proved that the presented method constitutes a highly accurate and efficient solution, which can be easily applied to the laminated viscoelastic shell problems.

Effect of mechanical force, rotation and moving internal heat source on a two-temperature fiber-reinforced thermoelastic medium with two theories

Abstract: In the present paper, the three-phase-lag model and Green–Naghdi theory without energy dissipation are used to study the effect of a mechanical force and a rotation on the wave propagation in a two-temperature fiber-reinforced thermoelastic problem for a medium with an internal heat source that is moving with a constant speed. The methodology applied here is the use of the normal mode analysis to solve the problem of a thermal shock problem to obtain the exact expressions of the displacement components, force stresses, thermal temperature, and conductivity temperature. Numerical results for the considered variables are given and illustrated graphically in the absence and presence of a rotation as well as a mechanical force. A comparison is made with the results in the context of the two theories in the absence and presence of a moving internal heat source.

Limit Case Analysis of the "Stable Indenter Velocity" Method for Obtaining Creep Stress Exponents from Constant Load Indentation Creep Tests

Abstract: This study concerns a commonly-used procedure for evaluating the steady state creep stress exponent, $n$ , from indentation data. The procedure involves monitoring the indenter displacement history under constant load and making the assumption that, once its velocity has stabilised, the system is in a quasi-steady state, with stage II creep dominating the behaviour. The stress and strain fields under the indenter are represented by “equivalent stress” and “equivalent strain rate” values. The estimate of $n$ is then obtained as the gradient of a plot of the logarithm of the equivalent strain rate against the logarithm of the equivalent stress. Concerns have, however, been expressed about the reliability of this procedure, and indeed it has already been shown to be fundamentally flawed. In the present paper, it is demonstrated, using a very simple analysis, that, for a genuinely stable velocity, the procedure always leads to the same, constant value for $n$ (either 1.0 or 0.5, depending on whether the tip shape is spherical or self-similar). This occurs irrespective of the value of the measured velocity, or indeed of any creep characteristic of the material. It is now clear that previously-measured values of $n$ , obtained using this procedure, have varied in a more or less random fashion, depending on the functional form chosen to represent the displacement–time history and the experimental variables (tip shape and size, penetration depth, etc.), with little or no sensitivity to the true value of $n$ .

Visco-elastic and thermal-induced damaging in time-dependent reshaping of human cornea after conductive keratoplasty

Abstract: With the aim of investigating the role played by both the radiofrequency-induced thermal damaging and the viscoelasticity of the tissue in human cornea surface reshaping—time dependent key factors for the success of the surgical outcome in the short-term post-intervention period—the Conductive Keratoplasty (CK, a surgical technique used for the correction of farsightedness) has been simulated with reference to the protocol adopted for moderate hyperopia. By means of a transient thermal analysis, the amount of the local thermal-induced tissue damaging has been computed in order to remap the constitutive properties of the corneal tissue. Successively, a mechanical non-linear analysis has been performed for predicting the corneal curvature around the optical zone during the post-surgery period. The study aims to contribute some firm thermo-mechanical roots to better understand the corneal tissue response to thermal insults and its reshaping predictability in a long period.

A viscoelastic Unitary Crack-Opening strain tensor for crack width assessment in fractured concrete structures

Abstract: A post-processing technique which allows computing crack width in concrete is proposed for a viscoelastic damage model. Concrete creep is modeled by means of a Kelvin–Voight cell while the damage model is that of Mazars in its local form. Due to the local damage approach, the constitutive model is regularized with respect to finite element mesh to avoid mesh dependency in the computed solution (regularization is based on fracture energy). The presented method is an extension to viscoelasticity of the approach proposed by Matallah et al. (Int. J. Numer. Anal. Methods Geomech. 34(15):1615–1633, 2010) for a purely elastic damage model. The viscoelastic Unitary Crack-Opening (UCO) strain tensor is computed accounting for evolution with time of surplus of stress related to damage; this stress is obtained from decomposition of the effective stress tensor. From UCO the normal crack width is then derived accounting for finite element characteristic length in the direction orthogonal to crack. This extension is quite natural and allows for accounting of creep impact on opening/closing of cracks in time dependent problems. A graphical interpretation of the viscoelastic UCO using Mohr’s circles is proposed and application cases together with a theoretical validation are presented to show physical consistency of computed viscoelastic UCO.

Determination of relaxation modulus of time-dependent materials using neural networks

Abstract: Health monitoring systems for plastic based structures require the capability of real time tracking of changes in response to the time-dependent behavior of polymer based structures. The paper proposes artificial neural networks as a tool of solving inverse problem appearing within time-dependent material characterization, since the conventional methods are computationally demanding and cannot operate in the real time mode. Abilities of a Multilayer Perceptron (MLP) and a Radial Basis Function Neural Network (RBFN) to solve ill-posed inverse problems on an example of determination of a time-dependent relaxation modulus curve segment from constant strain rate tensile test data are investigated. The required modeling data composed of strain rate, tensile and related relaxation modulus were generated using existing closed-form solution. Several neural networks topologies were tested with respect to the structure of input data, and their performance was compared to an exponential fitting technique. Selected optimal topologies of MLP and RBFN were tested for generalization and robustness on noisy data; performance of all the modeling methods with respect to the number of data points in the input vector was analyzed as well. It was shown that MLP and RBFN are capable of solving inverse problems related to the determination of a time dependent relaxation modulus curve segment. Particular topologies demonstrate good generalization and robustness capabilities, where the topology of RBFN with data provided in parallel proved to be superior compared to other methods.

Creep characterization of solder bumps using nanoindentation

Abstract: Current nanoindentation techniques for the measurement of creep properties are applicable to viscoplastic materials with negligible elastic deformations. A new technique for characterization of creep behavior is needed for situations where the elastic deformation plays a significant role. In this paper, the effect of elastic deformation on the determination of creep parameters using nanoindentation with a self-similar nanoindenter tip is evaluated using finite element analysis (FEA). It is found that the creep exponent measured from nanoindentation without taking into account of the contribution of elastic deformation tends to be higher than the actual value. An effective correction method is developed to consider the elastic deformation in the calculation of creep parameters. FEA shows that this method provides accurate creep exponent. The creep parameters, namely the creep exponent and activation energy, were measured for three types of reflowed solder bumps using the nanoindentation method. The measured parameters were verified using FEA. The results show that the new correction approach allows extraction of creep parameters with precision from nanoindentation data.

Experimental and numerical investigation of energy dissipation in elastomeric rotational joint under harmonic loading

Abstract: This paper focuses on energy losses caused by inner damping and friction in an elastomeric rotational joint. A description of the design of a new experimental device intended to characterize dynamic stiffness in rotational elastomeric joint is presented. An original method based on Lagrange’s equations, which allows accurately measuring forces and torques only with accelerometers, is proposed in order to identify dissipated energy in the rotational elastomeric joint. A rheological model developed taking into account dependence of the torque and the angular displacement (rotation). Experimental results and simulations used to quantify the dissipated energy in order to evaluate the damping ratio are presented and discussed.

Micromechanics of transformation fields in ageing linear viscoelastic composites: effects of phase dissolution or precipitation

Abstract: Transformation fields, in an affine formulation characterizing mechanical behavior, describe a variety of physical phenomena regardless their origin. Different composites, notably geomaterials, present a viscoelastic behavior, which is, in some cases of industrial interest, ageing, i.e. it evolves independently with respect to time and loading time. Here, a general formulation of the micromechanics of prestressed or prestrained composites in Ageing Linear Viscoelasticity (ALV) is presented. Emphasis is put on the estimation of effective transformation fields in ALV. The result generalizes Ageing Linear Thermo- and Poro-Viscoelasticity and it can be used in approaches coping with a phase transformation. Additionally, the results are extended to the case of locally transforming materials due to non-coupled dissolution and/or precipitation of a given (elastic or viscoelastic) phase. The estimations of locally transforming composites can be made with respect to different morphologies. As an application, estimations of the coefficient of thermal expansion of a hydrating alite paste are presented.

Three-dimensional elasticity solution of layered plates with viscoelastic interlayers

Abstract: An analytical solution for simply supported layered plates with viscoelastic interlayers under a transverse load is proposed. The deformation of each plate layer is described by the exact three-dimensional elasticity equations. The viscoelastic property of interlayer is simulated by the generalized Maxwell model. The constitutive relation of the interlayer is simplified by the quasi-elastic approximation, which significantly simplifies the analytical process. The solution of stress and displacement fields with undetermined coefficients is derived by solving a group of ordinary differential equations. The undetermined coefficients can be efficiently deduced by using the recursive matrix technique for the plate with any number of layers. The practical convergence is observed during numerical tests. The comparison analysis indicates that the present solution has a close agreement with the finite element solution. However, the solution based on the Mindlin–Reissner hypothesis is significantly different from the present solution for thick plates. Finally, the effect of interlayer thickness on stress and displacement distributions of a five-layer plate is discussed in detail.

Viscoelastic-damage interface model formulation with friction to simulate the delamination growth in mode II shear

Abstract: In this paper a formulation of a viscoelastic-damage interface model with friction in mode-II is presented. The cohesive constitutive law contains elastic and damage regimes. It has been assumed that the shear stress in the elastic regime follows the viscoelastic properties of the matrix material. The three element Voigt model has been used for the formulation of relaxation modulus of the material. Damage evolution proceeds according to the bilinear cohesive constitutive law combined with friction stress consideration. Combination of damage and friction is based on the presumption that the damaged area, related to an integration point, can be dismembered into the un-cracked area with the cohesive damage and cracked area with friction. Samples of a one element model have been presented to see the effect of parameters on the cohesive constitutive law. A comparison between the predicted results with available results of end-notched flexure specimens in the literature is also presented to verify the model. Transverse crack tension specimens are also simulated for different applied displacement velocities.

Finite element implementation of a thermo-damage-viscoelastic constitutive model for hydroxyl-terminated polybutadiene composite propellant

Abstract: A thermo-damage-viscoelastic model for hydroxyl-terminated polybutadiene (HTPB) composite propellant with consideration for the effect of temperature was implemented in ABAQUS. The damage evolution law of the model has the same form as the crack growth equation for viscoelastic materials, and only a single damage variable $S$ is considered. The HTPB propellant was considered as an isotropic material, and the deviatoric and volumetric strain-stress relations are decoupled and described by the bulk and shear relaxation moduli, respectively. The stress update equations were expressed by the principal stresses $\sigma_{ii}^{R}$ and the rotation tensor $M$ , the Jacobian matrix in the global coordinate system $J_{ijkl}$ was obtained according to the fourth-order tensor transformation rules. Two models having complex stress states were used to verify the accuracy of the constitutive model. The test results showed good agreement with the strain responses of characteristic points measured by a contactless optical deformation test system, which illustrates that the thermo-damage-viscoelastic model perform well at describing the mechanical properties of an HTPB propellant.

A fractional transient model for the viscoplastic response of polymers based on a micro-mechanism of free volume distribution

Abstract: In the present work, the nonlinear viscoelastic/viscoplastic response of polymeric materials is described by introducing essential modifications on a model developed in previous works. A constitutive equation of viscoelasticity, based on the transient network theory, is introduced in a more generalized form, which takes into account volume changes during deformation. This time-dependent equation accounts for the nonlinearity and viscoplasticity at small elastic and finite plastic strain regime. The present description was proved to be more flexible, given that it contains a relaxation function that has been derived by considering instead of first order kinetics a fractional derivative that controls the rate of molecular chain detachment from their junctions. Therefore, the new equation has a more global character, appropriate for cases where heavy tails are expected. On the basis of the distributed nature of free volume, a new functional form of the rate of plastic deformation is developed, which is combined with a proper kinematic formulation and leads to the separation of the total strain into the elastic and plastic part. A three-dimensional constitutive equation is then derived for an isotropic, compressible medium. This analysis was proved to be capable of capturing the main aspects of inelastic response as well as the instability stage taking place at the tertiary creep, related to the creep failure.