Modeling of the viscoelastic mechano-sorptive behavior in wood

This paper focuses on the modeling of linearly viscoelastic, mechano-sorptive behavior and its effects during moisture content changes in timber. A generalized Kelvin?CVoigt model integrating specific hygro-lock springs is developed and associated, in series, with a shrinkage?Cswelling element. The coupling between moisture content state and mechanical state implies an evolution in rheological parameters. This alternative approach leads to incorporating strain blockings during the drying period as well as memory effects during wetting phases after unloading. An incremental formulation is also established using a finite-element software, and, moreover, an experimental validation from tensile creep-recovery tests is presented.     

A maximum dissipation thermodynamic multi-scale model for the dynamic response of the arterial elastin–water system

The mechanical response of the elastin–water system in an artery wall is viscoelastic. Elastin in vivo must operate in the rubbery region, i.e., above the glass transition, that depends on moisture content. A dynamic multi-scale time-dependent evolution equation is presented for the mechanical response of the elastin–water system that captures the effect of moisture content on the glass transition of the elastin. To define non-equilibrium evolution processes, the construction requires only a hyperelastic strain energy density function describing the long-term behavior and the thermodynamic relaxation modulus that describes the relaxation speed of non-equilibrium processes. The thermodynamic relaxation modulus also relates spatial scales, the molecular scale including moisture bonding to the bulk material scale. The model reproduces published experimental data on the elastin glass transition behavior with respect to load frequency and to ambient relative humidity but is not merely empirical in the sense of being a fit to such data because it predicts dynamic responses such as non-physiological creep and physiological rate-dependent stress–stretch relations. The new viscoelastic model predicts the influence of moisture content and the glass transition of the elastin on the time-dependent response of the circumferential stretch and the change in radius of a hydrated arterial cylindrical elastin lamella under cyclic radial pressure loads in the hemodynamic range. Such an elastin cylinder approximates the behavior of the elastin substructure in an elastic artery wall.     

A variational framework for fiber‐reinforced viscoelastic soft tissues

The mechanical properties of soft biological tissues vary depending on how the internal structure is organized. Classical examples of tissues are ligaments, tendons, skin, arteries, and annulus fibrous. The main element of such tissues is the fibers which are responsible for the tissue resistance and the main mechanical characteristic is their viscoelastic anisotropic behavior. The objective of this paper is to extend an existing model for isotropic viscoelastic materials in order to include anisotropy provided by fiber reinforcement. The incorporation of the fiber allows the mechanical behavior of these tissues to be simulated. The model is based on a variational framework in which its mechanical behavior is described by a free energy incremental potential whose local minimization provides the constraints for the internal variable updates for each load increment. The main advantage of this variational approach is the ability to represent different material models depending on the choice of suitable potential functions. Finally, the model is implemented in a finite‐element code in order to perform numerical tests to show the ability of the proposed model to represent fiber‐reinforced materials. The material parameters used in the tests were obtained through parameter identification using experimental data available in the literature. Copyright © 2011 John Wiley & Sons, Ltd.     

Elastic response in wood under moisture content variations: analytic development

Creep evolution of timber structures results from the interaction between mechanical stresses due to different loads and hydric stresses due to moisture content variations. This paper deals with a thermodynamic approach in order to take into account a realistic elastic behavior under moisture content variations. In this context, memory effect, experimentally observed, is introduced employing a mechano-sorptive stress driven by a function dependent of the moisture content variations. This new internal thermodynamic variable enables to define an original separation of the free energy into an instantaneous recoverable part and a stored part during the last drying phase. This energy enables the modeling of the nonreversible strain process during the unloading phase. The locate state method is employed in order to define the thermodynamic function which traduces an indirect hereditary behavior between moisture content history and the stress state in the material.     

Identification of viscoelastic behavior for early-age concrete based on measured strain and stress histories

In order to accurately predict the stress of concrete structures that undergo variations of temperature and moisture, a compliance function is required that considers the fast development of material properties in early-age concrete. The purpose of present study is to identify the viscoelastic behavior in actual concrete structures at early ages. To this end, a numerical method to identify the viscoelastic properties from measured strain and stress histories was investigated and a series of full-scale test members was fabricated, from which the behavior of early-age concrete was directly measured. The relaxation function was identified from measured data in the full-scale members and the existing compliance model, which is based on the solidification theory, was modified for incorporation into the early-age behavior. The modified compliance model described the highly viscoelastic behavior of concrete at very early ages and thus allowed more accurate evaluation of deformation and stress in early-age concrete.     

Viscoelastic behaviour of macro-defect-free cement

The viscoelastic behaviour of macro-defect-free (MDF) cement was studied by dynamic mechanical analysis. MDF specimens with various moisture contents in the range 1.70%–3.20% moisture, were measured at 1 Hz as a function of temperature from 34–96 °C and as a function of frequency from 0.05–5 Hz at 34°C. The viscoelasticity of MDF was found to be affected by moisture content through its plasticizing effect on the PVA binder. Time-moisture and temperature-moisture superposition of the shear moduli were found to be possible for MDF, and linear relationships between log time and linear moisture and between temperature and moisture were found. How the microstructure of MDF affects the viscoelastic response is also discussed through mechanical models. A comparison of the models with known experimental data suggests that the viscoelastic response arises from both direct connections between the inorganic particles and from connections through the polymer binder. Inorganic links are estimated to connect 45% of the inorganic phase.     

Observations of anomalous mass-loss behavior in SRM coals and cokes on drying

The determination of moisture content in coal and coke is required for the accurate reporting of physical and chemical constituents on a dry mass basis. Interlaboratory comparisons are reported on a dry mass basis and require reproducible assessments of moisture content to minimize differences among laboratories. Comparability between laboratories is necessary to ensure equity in trade and to avoid costly disputes between buyer and seller. Moisture loss was measured as mass (M) loss as a function of time (t) at constant temperature in a dynamic inert nitrogen atmosphere on 10 SRM coals (7 bituminous and 3 subbituminous) and 4 SRM cokes. Three different patterns of mass-loss were observed-ideal (dM/dt = 0), and two anomalous behaviors, negative deviation (dM/ dt < 0) and positive deviation (dM/dt > 0). Bituminous coals with lower moisture (1-4%) and volatile content (33-38%) tend to display either ideal or positive behavior while subbituminous coals with higher moisture (12-17%) and volatile content (41-47%) display negative behavior. The identification of these different mass-loss patterns demonstrates the potential for method bias depending on the drying end-point definition (ASTM and LECO) used.     

Rheological parameters and characteristics of bamboo in compression perpendicular to grain under hot-pressing process

Bamboo with high specific strength is a renewable biomaterial. Studying the rheological properties of bamboo is helpful to improve the performance and quality of bamboo products. In this paper, four-element Burgers model was applied to describe the creep behavior of moso bamboo (Phyllostachs pubescens) in compression perpendicular to grain under hot-pressing process. The relationship between creep components and experimental factors (temperature, moisture content and stress level) was investigated. More importantly, four rheological parameters in Burgers model were also determined at different temperatures, moisture contents and stress levels. And the effect of experimental factors on rheological parameters was quantitatively explored. The results showed that, when compressive stress was below the yield limit, the amount of three components of creep was proportional to experimental factors, but the increase in temperature and moisture content could reduce the proportion of elastic deformation, and improve the proportion of viscoelastic deformation and viscous deformation. Besides, rheological parameters were insensitive to stress level when temperature and moisture content remained unchanged. But they were greatly affected by temperature and moisture content, presenting a linear inverse proportion to them.

     

Nonlinear viscoelastic analysis of orthotropic beams using a general third-order theory

The displacement based finite element model of a general third-order beam theory is developed to study the quasi-static behavior of viscoelastic rectangular orthotropic beams. The mechanical properties are considered to be linear viscoelastic in nature with a scope to undergo von Kármán nonlinear geometric deformations. A differential constitutive law is developed for an orthotropic linear viscoelastic beam under the assumptions of plane-stress. The fully discretized finite element equations are obtained by approximating the convolution integrals using a trapezoidal rule. A two-point recurrence scheme is developed that necessitates storage of data from the previous time step only, and not from the entire deformation history. Full integration is used to evaluate all the stiffness terms using spectral/hp lagrange polynomials. The Newton iterative scheme is employed to enhance the rate of convergence of the nonlinear finite element equations. Numerical examples are presented to study the viscoelastic phenomena like creep, cyclic creep and recovery for thick and thin beams using classical mechanical analogues like generalized n-parameter Kelvin-Voigt solids and Maxwell solids.     

Constitutive equations for orthotropic nonlinear viscoelastic behaviour using a generalized Maxwell model Application to wood material

This paper presents a nonlinear viscoelastic orthotropic constitutive equation applied to wood material. The proposed model takes into account mechanical and mechanosorptive creep via a 3D stress ratio and moisture change rate for a cylindrical orthotropic material. Orthotropic frame is based on the grain direction (L), radial (R) and hoop (T) directions, which are natural wood directions. Particular attention is taken to ensure the model to fulfill the necessary dissipation conditions. It is based on a rheological generalized Maxwell model with two elements in parallel in addition with a single linear spring taking into account the long term response. The proposed model is implemented in the finite element code ABAQUS/Standard^® via a user subroutine UMAT and simple example is shown to demonstrate the capability of the proposed model. Future works would deal with damage and fracture prediction for wooden structures submitted to climate variations and mechanical loading.     

Resilient modulus–moisture content relationships for pavement engineering applications

In recent years, there has been an increased interest in determining the influence of moisture changes on the resilient modulus (M_R) of subgrade soils beneath pavement structures. Efforts have also been made to develop mathematical models that predict the change in M_R values with moisture. These models are expected to account for seasonal variations in subgrade moisture content. This study evaluates the variation of resilient modulus with post-compaction moisture content of soils in the State of Oklahoma and the State of Pennsylvania. A series of specimens was compacted at optimum moisture content and then tested for resilient modulus; other series of specimens were prepared at optimum moisture content and then either wetted or dried prior to M_R testing. Employed wetting and drying procedures are time-efficient in developing the M_R–moisture relationships. Results showed that M_R–moisture content relationships varied with soil types and M_R values varied inversely with changes of moisture content. In addition, an M_R–moisture model predicting the variation of resilient modulus with moisture contents is proposed. This model can be used to predict changes in the bearing capacity of pavements due to seasonal variations of moisture content.     

A time-domain boundary element method for quasistatic thermoviscoelastic behavior modeling of the functionally graded materials

In the present paper, a boundary element formulation is presented for two-dimensional thermoviscoelasticity analysis of components fabricated from the functionally graded materials (FGMs). In this regard, a graded viscoelastic element capable of tracing gradual variations of the material properties is developed. Several attempts have been made so far to employ the integral equation approach for the heterogeneous viscoelastic materials. In the present research, Somigliana’s displacement identity is considered and implemented numerically for analyzing the two-dimensional exponentially graded viscoelastic components. Employing the common assumptions of the viscoelastic constitutive equations and the weighted residual technique, an efficient boundary element formulation is developed for the heterogeneous Kelvin–Voigt solid viscoelastic models. Finally, three numerical examples are provided to verify the proposed formulation and present practical conclusions.     

Effect of processing variables on the durability of epoxy resins for composite systems

The Flory approach has been used to described the molecular characteristics of the non-linear polymerization of tetraglycidyl diamino diphenyl methane (TGDDM) cured with diphenyl sulfone (DDS).The cure behavior of commercial grade TGDDM-DDS mixtures was analyzed by means of differential scanning calorimetry (DSC), high-pressure liquid chromatography (HPLC), and steady and dynamic viscosity measurements. The gelation limits and molecular distribution measured in isothermal tests were in good agreement with experimental determinations. The gelation theory was further combined with the WLF treatment of the temperature dependency of the viscoelastic behavior for the reacting system in order to describe the viscosity profiles during complex cure cycles.Furthermore, this work relates moisture sorption and plasticization of two epoxy systems to hydrothermal and processing variables. A low cross-linked diglycidyl ether of bisphenol-A (DGEBA) cured with linear amines, such as ethylene diamine (EDA), diethylene triamine (DETA) and triethylene tetramine (TETA), and the highly cross-linked TGDDM-DDS system, have been studied. An increase in the equilibrium moisture content was observed as a result of thermal cycling in liquid environments. The hydrothermal interactions are shown to produce changes in the epoxy network structures and in the moisture sorption behavior.     

A continuous threshold model for the visco-elasto-plastic behavior of PET based multi-layer polymeric films

The envelopes of the super-pressure balloons fabricated by the French space agency (CNES) are made of a multi-layer polymeric film that shows substantial viscoelastic and viscoplastic behavior, both depending nonlinearly on stress. A model is presented that takes into account stress depending viscoelastic and viscoplastic strain response functions observed in uniaxial creep experiments. For easy numerical implementation, the strain response functions are represented by a Prony series, whose coefficients form a continuous spectrum on the logarithmic retardation time scale. The observed response functions are generated by an exponential power law distribution of the Prony coefficients with exponent 3. The distribution is fully characterized by three stress dependent parameters: its center, width, and an intensity factor, corresponding to the maximum coefficient. Creep and recovery experiments show that both viscoelastic and viscoplastic strain are highly stress dependent over a limited stress range and are approximately linear at low stresses and around the maximum stress reached during flight. A continuous threshold function is proposed that approximates well the observed stress dependence of the intensities. It is assumed that the other viscoelastic (viscoplastic) parameters change around the same threshold as the viscoelastic (viscoplastic) intensity and are approximately constant elsewhere. The model reproduces very well the strain response observed in creep and recovery experiments with different creep stresses.     

Limits of linear viscoelastic behavior of polymers

In the present study different approaches for determination of the limits of linear viscoelastic (LVE) behavior are considered on examples of some thermoplastic and thermosetting polymers. Stress or strain level, commonly considered as a limit of LVE behavior, are interrelated time-dependent functions strongly influenced by action of external factors. The concept of energy threshold has an advantage of combining into one physical function the effects of both stress and strain in initiating nonlinear behavior. The value of the stored deviatoric energy is considered as a limit of LVE behavior and is a material characteristic. The experimental data on tension at various constant strain rates and tensile creep at various stresses, temperatures, and moisture conditions are considered. It is proved for some polymers that LVE limits in stress-strain representation fall on a common curve that is an energy curve independent of time. Decrease of the test rate or growth of temperature or moisture content appears only in a shift down along the energy curve to the lower limit stresses and higher limit strains.     

Influence of humidity on creep response of sandwich beam with a viscoelastic soft core

Polymer foam cored sandwich beams are widely used in load-bearing components due to their high strength to weight ratio. To improve the reliability in using sandwich beams, it is essential to understand their long-term creep response in terms of variation of stresses and deformations with time under external mechanical and environmental stimuli. This paper presents an analytical model for investigating the creep response of sandwich beams made with a viscoelastic soft core, including the effect of the variable ambient humidity under the sustained load and its influence on the creep behavior. The model is based on a high-order viscoelastic structural modeling. The soft core is modeled as a viscoelastic material using differential-type constitutive relations that are based on the linear Boltzman’s principle of superposition and accounting for the deformability of the core in shear and through its thickness. Several numerical examples are presented in order to show the capability of the model and to investigate the effect of moisture on the creep behavior of sandwich beams. Finite element simulations of the creep response of sandwich beams are also performed using ABAQUS software to validate the proposed theoretical model. The results show the concentrations of shear and transverse normal stresses near the edges and their variation in time and with the change of humidity.     

A phenomenological constitutive model for the nonlinear viscoelastic responses of biodegradable polymers

We formulate a constitutive framework for biodegradable polymers that accounts for nonlinear viscous behavior under regimes with large deformation. The generalized Maxwell model is used to represent the degraded viscoelastic response of a polymer. The large-deformation, time-dependent behavior of viscoelastic solids is described using an Ogden-type hyperviscoelastic model. A deformation-induced degradation mechanism is assumed in which a scalar field depicts the local state of the degradation, which is responsible for the changes in the material’s properties. The degradation process introduces another timescale (the intrinsic material clock) and an entropy production mechanism. Examples of the degradation of a polymer under various loading conditions, including creep, relaxation and cyclic loading, are presented. Results from parametric studies to determine the effects of various parameters on the process of degradation are reported. Finally, degradation of an annular cylinder subjected to pressure is also presented to mimic the effects of viscoelastic arterial walls (the outer cylinder) on the degradation response of a biodegradable stent (the inner cylinder). A general contact analysis is performed. As the stiffness of the biodegradable stent decreases, stress reduction in the stented viscoelastic arterial wall is observed. The integration of the proposed constitutive model with finite element software could help a designer to predict the time-dependent response of a biodegradable stent exhibiting finite deformation and under complex mechanical loading conditions.     

Micromechanical modeling and experimental characterization on viscoelastic behavior of 1–3 active composites

A study on the temperature-dependent viscoelastic behavior of (1–3 active composites) 1–3 piezocomposites and bulk piezoceramic subjected to electromechanical loading is carried out. The temperature-dependent effective properties are obtained experimentally using resonance based measurement technique. Experiments are also preformed for various fiber volume fractions of 1–3 piezocomposites subjected to constant compressive prestress and cyclic electric field at elevated temperature to understand the time-dependent behavior. Based on the measurements it is observed that the viscoelastic behavior has a significant influence on the electromechanical responses of 1–3 piezocomposites. Hence a viscoelastic based numerical model (unit cell approach) is proposed to predict the time-dependent effective properties of 1–3 piezocomposites. The evaluated effective properties are incorporated in a finite element based 3-D micromechanical model to predict the time-dependent thermo-electro-mechanical behavior of 1–3 piezocomposites and compared with the experimental observations.     

2-D elasticity solution of layered composite beams with viscoelastic interlayers

This paper focuses on the mechanical properties of layered composite beams with viscoelastic interlayers. The exact two-dimensional elasticity theory is used to represent the deformation of each beam layer. The viscoelastic interlayer is described by the Maxwell–Wiechert model through the quasi-elastic approximation, which greatly simplifies the analytical process. The stress function with a series of undetermined coefficients depending on the time variable is derived for each beam layer. No matter how many layers the beam includes, the total solution can be obtained rapidly and efficiently by using the recursive matrix technique. The present method can give the exact stress and deformation distributions in the beam, which cannot be predicted by the approximate theories such as the one-dimensional Euler–Bernoulli theory. The convergence of the solution is numerically verified. A comparison study indicates that the present results are in agreement with those obtained from the finite element method; however, they have obvious differences from the results based on the Euler–Bernoulli theory for thick beams. Finally, the variations of stresses and displacements with respect to time in a five-layer beam are discussed in detail.     

Multiscale design of a rectangular sandwich plate with viscoelastic core and supported at extents by viscoelastic materials

This work presents a multiscale model of viscoelastic constrained layer damping treatments for vibrating plates/beams. The approach integrates a finite element (FE) model of macroscale vibrations and a micromechanical model to include effects of microscale structure and properties. The FE model captures the shear deformation of the viscoelastic core, rotary inertial effects of all layers, and viscoelastic boundaries of the plate. Comparison with analytical and FE results validates the proposed FE model. A self-consistent (SC) model makes the micro to macro scale transition to approximate the effective behavior a heterogeneous core. Modal damping resulting from the presence of voids and negative stiffness regions in the core material is modeled. Results show that negative stiffness regions in the viscoelastic core material, even at low volume fractions, yield superior macroscopic damping behavior. The coupled SC and FE models provide a powerful multiscale predictive design tool for sandwich beams and plates.