Viscoelastic Material Model Research Articles

Treatment of inelastic material models within a dynamic ALE formulation for structures subjected to moving loads

AbstractThis article showcases the development of a dynamic Arbitrary Lagrangian Eulerian (ALE) formulation to account for inelastic material models within a finite element framework. Such a formulation is commonly utilized in research domains like fluid mechanics, fluid‐structure interaction, quasi static remeshing techniques, and quasi static load movement. The work at hand describes the application of the ALE formulation to efficiently analyse structures subjected to moving loads in the field of transient inelastic solid mechanics. In particular, structures such as pavements, gantry crane girders etc., which are subjected to moving loads, can be numerically simulated, and their transient response in the relevant region around the load can be obtained without relying on moving loads. The focus of this article is to facilitate the treatment of history variables stemming from inelastic material models. Of particular interest is the advection procedure required to transport the history variables through the mesh, as the material appears to flow through it. The mathematical framework necessary to treat this advection process is described in detail, considering a nonlinear viscoelastic material model on a neo‐Hookean base at finite deformations. Then, four methods for numerically achieving the advection are implemented within a transient finite element ALE formulation. These methods are compared against each other, and additionally with the conventional Lagrangian method for validation. The results demonstrate satisfactory agreement with conventional simulation methods, while offering a significant improvement in terms of computation speed. With the work at hand, the dynamic response of inelastic materials subjected to moving loads can be numerically simulated in a computationally efficient manner.

Nonlinear mathematical modeling of frequency-temperature dependent viscoelastic materials for tire applications

Understanding and accurately reproducing the realistic response of rubber materials to external stimuli is a crucial research topic that involves all the engineering fields and beyond where these materials are used. This study introduces an innovative nonlinear fractional derivative generalized Maxwell model designed to effectively capture and replicate the experimental behavior of viscoelastic materials. The proposed model addresses the limitations observed in conventional fractional models, providing greater versatility which makes it more suitable for describing the intricate behavior of polymeric materials. Through rigorous mathematical validation, the proposed model demonstrates coherence with the underlying physics of the viscoelastic behavior. To address the identification procedure, the pole-zero formulation is adopted, employing a multi-objective optimization to obtain the optimum, able to replicate the dynamic moduli trends. Satisfying results have been validated over a wide dataset of 10 different materials, demonstrating an extended capability of adapting to different variations than classical widely-used fractional models. Furthermore, the model has proven to be valid even employing a reduced amount of experimental data limited only to low, high-frequency plateaus and around the glass transition temperature, which could be fundamental for optimizing resources in experimental investigations.

Multi-parameter viscoelastic material model for denture adhesives based on time-temperature superposition and multiple linear regression analysis

BackgroundRestorative solutions designed for edentulous patients such as dentures and their accompanying denture adhesives operate in the complex and dynamic environment represented by human oral physiology. Developing material models accounting for the viscoelastic behavior of denture adhesives can facilitate their further optimization within that unique physiological environment. This study aims to statistically quantify the degree of significance of three physiological variables - namely: temperature, adhesive swelling, and pH - on denture adhesive mechanical behavior. Further, based on these statistical significance estimations, a previously-developed viscoelastic material modelling approach for such denture adhesives is further expanded and developed to capture these variables’ effects on mechanical behavior.MethodsIn this study a comparable version of Denture adhesive Corega Comfort was analysed rheologically using the steady state frequency sweep tests. The experimentally derived rheological storage and loss modulus values for the selected physiological variables were statistically analyzed using multi parameter linear regression analysis and the Pearson’s coefficient technique to understand the significance of each individual parameter on the relaxation spectrum of the denture adhesive. Subsequently, the parameters are incorporated into a viscoelastic material model based on Prony series discretization and time-temperature superposition, and the mathematical relationship for the loss modulus is deduced.ResultsThe results of this study clearly indicated that the variation in both the storage and loss modulus values can be accurately predicted using the oral cavity physiological parameters of temperature, swelling ratio, and pH with an adjusted R2 value of 0.85. The R2 value from the multi-parameter regression analysis indicated that the predictor variables can estimate the loss and storage modulus with a reasonable accuracy for at least 85% of the rheologically determined continuous relaxation spectrum with a confidence level of 98%. The Pearson’s coefficient for the independent variables indicated that temperature and swelling have a strong influence on the loss modulus, whereas pH had a weak influence. Based on statistical analysis, these mathematical relationships were further developed in this study.ConclusionsThis multi-parameter viscoelastic material model is intended to facilitate future detailed numerical investigations performed with implementation of denture adhesives using the finite element method.

Viscoelastic-adhesive modeling of hybrid adhesively bonded double-lap joints: analytical and numerical studies

ABSTRACT There are a limited number of studies examining the viscoelastic and viscoplastic behavior of adhesive joints. If there is more than one adhesive in the overlap region, the problem becomes more complex and viscoelastic modeling of the overlap region becomes difficult. There is no study in the literature that covers such a bonding (overlap) scheme and examines the viscoelastic behavior of the double lap joint (DLJ). In this study, the effect of viscoelasticity of polymeric adhesives on shear stress and strain distributions in the hybrid-adhesive layer of a DLJ is studied. Maxwell-Wiechert (MW) viscoelastic material model is used to define the viscoelastic behavior of the adhesives. Analytical and finite element (FE) results are compared for both mono- and hybrid-adhesive joints under the step load. Good matches are observed between the analytical and numerical results. Four different hybrid-adhesive joints with different combinations of the adherend thicknesses are investigated by considering only the analytical method. In order to investigate the effect of the loading type on the viscoelastic behavior, step and ramp loads were applied to the joint separately. It is observed that applying the ramp load to the hybrid-adhesive joints affects the shear stresses occurred at the ends of the overlap more than the mono-adhesive joints.

Mechanical modeling of the petiole-lamina transition zone of peltate leaves

Plant leaves have to deal with various environmental influences. While the mechanical properties of petiole and lamina are generally well studied, only few studies focused on the properties of the transition zone joining petiole and lamina. Especially in peltate leaves, characterised by the attachment of the petiole to the abaxial side of the lamina, the 3D leaf architecture imposes specific mechanical stresses on the petiole and petiole-lamina transition zone. Several principles of internal anatomical organisation have been identified. Since the mechanical characterisation of the transition zone by direct measurements is difficult, we explored the mechanical properties and load-bearing mechanisms by finite-element simulations. We simulate the petiole-lamina transition zone with five different fibre models that were abstracted from CT data. For comparison, three different load cases were defined and tested in the simulation. In the proposed model, the fibres are represented in a smeared sense, where we considered transverse isotropic behavior in elements containing fibres. In a pre-processing step, we determined the fibre content, direction, and dispersion and fed them into our model. The simulations show that initially, matrix and fibres carry the load together. After relaxation of the stresses in the matrix, the fibres carry most of the load. Load dissipation and stiffness differ according to fibre arrangement and depend, among other things, on orientation and cross-linking of the fibres and fibre amount. Even though the presented method is a simplified approach, it is able to show the different load-bearing capacities of the presented fibre arrangements. Statement of significanceIn plant leaves, the petiole-lamina transition zone is an important structural element facilitating water and nutrient transport, as well as load dissipation from the lamina into the petiole. Especially in peltate leaves, the 3D leaf architecture imposes specific mechanical stresses on the petiole-lamina transition zone. This study aims at investigating its mechanical behavior using finite-element simulations. The proposed continuum mechanical anisotropic viscoelastic material model is able to simulate the transition zone under different loads while also considering different fibre arrangements. The simulations highlight the load-bearing mechanisms of different fibre organisations, show the mechanical significance of the petiole-lamina transition zone and can be used in the design of a future biomimetic junction in construction.

Mechanical behaviour of bridge expansion joint interfaces filled with novel polyurethane-modified asphalt

The use of Asphalt Plug Joints (APJs) in bridge construction has rapidly expanded due to their distinct advantages in driving comfort, shock absorption, noise reduction, and maintenance ease. However, prolonged exposure to vehicular loads and environmental factors renders this expansion joint susceptible to interface effects and stress concentration, leading to damage, particularly at the interface layers between the expansion joint pavement and the expansion joint-cross joint plate contact areas. To address issues such as stress concentration, this study proposes a polyurethane-modified asphalt concrete mixture as the joint filling material. Pull-out and inclined shear tests are used to identify a bonding agent with superior adhesive properties. Additionally, a finite element model of pull-out specimens containing bilinear cohesive elements is established to simulate the cohesive damage process of the interface layers. Through parameter design analysis, the study examines the influence of individual parameter variations on interface damage behavior, obtaining comprehensive simulated analysis data on interface crack resistance performance. Based on interface test data, a bilinear cohesive force model and a viscoelastic material model of the asphalt concrete mixture are employed to establish a scaled-down model of the improved geometry design of the new APJ. This model simulates the interface mechanical characteristics of APJs under temperature effects and vehicle loads. The results demonstrate that the bilinear cohesive force model effectively simulates the nonlinear behavior of interface bonding slip. Furthermore, the use of SZ interface bonding agents and improvements in cross joint plate form can effectively mitigate issues such as uneven settlement and low-temperature cracking.

Об идентификации характеристик неоднородных вязкоупругих тел в рамках модели дробного порядка

Nowadays, the development of models of viscoelastic materials with complex inhomogeneous structure is one of the hottest problems of continuum mechanics. Along with classical models, fractional-differential models of viscoelasticity have become increasingly popular. In this paper, we present a model for describing steady-state oscillations of inhomogeneous viscoelastic bodies in terms of fractional-order differential operators. Taking into account the fractional order of the model operators, the corresponding form of the complex module describing the material properties is constructed. The module includes four characteristics: instantaneous and long-term elastic moduli (in the case of material inhomogeneity, they are the functions of coordinates), relaxation time and fractionality parameter. The properties of the complex module are studied, and the ranges of the model parameters, at which the rheological properties are most pronounced, are identified. A general formulation of the inverse problem (IP) on the identification of function-parameters of the model based on the acoustic sounding data is proposed. In the framework of this formulation, the inverse problems for specific objects , namely, an inhomogeneous rod and a round plate, are considered. In both model problems, the influence of the fractionalization parameter on the amplitude-frequency characteristics is analyzed. It has been found that in the vicinity of viscoelastic resonances the fractionality parameter affects the parameters of the oscillatory process most significantly, which is typical for such problems. A solution to the nonlinear IPs under consideration is constructed based on the linearization method, which also serve as basis for the iterative processes supplemented with the elements of the projection approach. This allows one to determine corrections to the required functions in the specified classes of functions using regularization. For both IPs, a series of computational experiments were carried out. The analysis of the experimental results made it possible to formulate recommendations for the selection of optimal sensing modes.

Calibration of Thermal Viscoelastic Material Models for the Dynamic Responses of PVB and SG Interlayer Materials.

Laminated glass interlayer materials polyvinyl butyral (PVB) and SentryGlas® (SG, kuraray, Houstan, TX, USA) exhibit thermal viscoelastic behavior under dynamic tensile loading. Significant temperature and strain rate effects on the behavior of these interlayer materials pose a challenge for accurately modeling the dynamic response of laminated glass. Many researchers have simplified their approaches by modeling the response of the interlayer material using a bilinear approximation or established hyperelastic models. However, temperature and strain rate effects can be captured using the three-network viscoplastic (TNV) model. Therefore, the objective of this study is to calibrate material models for the thermal viscoelastic dynamic responses of PVB and SG interlayer materials. Uniaxial tensile tests were performed at strain rates of 2, 20, and 45 s-1 and temperatures of 0, 23, and 60 °C, and material models were calibrated using the experimental data. Finite element analysis using the calibrated material models successfully predicted the dynamic responses of PVB and SG under the experimental test conditions within a 10% error margin. This suggests that the calibrated models using the TNV model represent significant improvements over existing approaches to modeling the dynamic response of laminated glass. Similar procedures can be applied to other thermoplastics, laying the groundwork for establishing a standard calibration guide.

Characterization of relaxation behaviour of CF/PEKK aerospace composites using the time-temperature-crystallinity superposition principle

In this study, the Time-Temperature-Crystallinity Superposition Principle (TTCSP) was applied to determine the viscoelastic behavior of Thermo-rheological Complex Materials (TCM), specifically Carbon fibre/Poly-Ether-Ketone-Ketone (CF/PEKK) composites. The study investigated the effects of various parameters on the viscoelastic behavior of the composites, such as the degree of crystallinity after different melting temperatures, relaxation, and crystallization times. The TTCSP was utilized on the relaxation data to generate great-grand master curves for the degree of crystallinity for different laminate lay-ups. Hot press forming was employed to manufacture samples under different processing conditions, including various melting and cold crystallization temperatures. Differential Scanning Calorimetry (DSC) was employed to calculate the degree of crystallinity of CF/PEKK composites, while the Dynamic Mechanical Analyzer (DMA) was used to obtain the relaxation data. The generated great-grand master curves proved effective in predicting the relaxation behavior of the composites consolidated using single and double hold cycles at different melting temperatures and crystallization times, respectively. The great-grand master curves presented in this study can serve as valuable tool to calibrate key viscoelastic and/or thermo-viscoelastic material models for aerospace-grade CF/PEKK composites. These models are crucial for simulations aimed at predicting residual stresses and process-induced deformations during the thermoforming process.

Viscoelastic Analysis of Asphalt Concrete with a Digitally Reconstructed Microstructure.

In the finite element analysis of asphalt concrete (AC), it is nowadays common to incorporate the information from the underlying scales to study the overall response of this material. Heterogeneity observed at the asphalt mixture scale is analyzed in this paper. Reliable finite element analysis (FEA) of asphalt concrete comprises a set of complex issues. The two main aspects of the asphalt concrete FEA discussed in this study are: (1) digital reconstruction of the asphalt pavement microstructure using processing of the high-quality images; and (2) FEA of the asphalt concrete idealized samples accounting for the viscoelastic material model. Reconstruction of the asphalt concrete microstructure is performed using a sequence of image processing operations (binarization, removing holes, filtering, segmentation and boundaries detection). Geometry of the inclusions (aggregate) are additionally simplified in a controlled mode to reduce the numerical cost of the analysis. As is demonstrated in the study, the introduced geometry simplifications are justified. Computational cost reduction exceeds of several orders of magnitude additional modeling error occurring due to the applied simplification technique. Viscoelastic finite element analysis of the AC identified microstructure is performed using the Burgers material model. The analysis algorithm is briefly described with a particular focus on the computational efficiency aspects. In order to illustrate the proposed approach, a set of 2D problems is solved. Numerical results confirm both the effectiveness of the self-developed code and the applicability of the Burgers model to the analyzed class of AC analysis problems. Further research directions are also described to highlight the potential benefits of the developed approach to numerical modeling of asphalt concrete.

Viscoelasticty with physics-augmented neural networks: model formulation and training methods without prescribed internal variables

AbstractWe present an approach for the data-driven modeling of nonlinear viscoelastic materials at small strains which is based on physics-augmented neural networks (NNs) and requires only stress and strain paths for training. The model is built on the concept of generalized standard materials and is therefore thermodynamically consistent by construction. It consists of a free energy and a dissipation potential, which can be either expressed by the components of their tensor arguments or by a suitable set of invariants. The two potentials are described by fully/partially input convex neural networks. For training of the NN model by paths of stress and strain, an efficient and flexible training method based on a long short-term memory cell is developed to automatically generate the internal variable(s) during the training process. The proposed method is benchmarked and thoroughly compared with existing approaches. Different databases with either ideal or noisy stress data are generated for training by using a conventional nonlinear viscoelastic reference model. The coordinate-based and the invariant-based formulation are compared and the advantages of the latter are demonstrated. Afterwards, the invariant-based model is calibrated by applying the three training methods using ideal or noisy stress data. All methods yield good results, but differ in computation time and usability for large data sets. The presented training method based on a recurrent cell turns out to be particularly robust and widely applicable. We show that the presented model together with the recurrent cell for training yield complete and accurate 3D constitutive models even for sparse bi- or uniaxial training data.

Additive Manufacturing of Composite Polymers: Thermomechanical FEA and Experimental Study.

This study presents a comprehensive approach for simulating the additive manufacturing process of semi-crystalline composite polymers using Fused Deposition Modeling (FDM). By combining thermomechanical Finite Element Analysis (FEA) with experimental validation, our main objective is to comprehend and model the complex behaviors of 50 wt.% carbon fiber-reinforced Polyphenylene Sulfide (CF PPS) during FDM printing. The simulations of the FDM process encompass various theoretical aspects, including heat transfer, orthotropic thermal properties, thermal dissipation mechanisms, polymer crystallization, anisotropic viscoelasticity, and material shrinkage. We utilize Abaqus user subroutines such as UMATHT for thermal orthotropic constitutive behavior, UEPACTIVATIONVOL for progressive activation of elements, and ORIENT for material orientation. Mechanical behavior is characterized using a Maxwell model for viscoelastic materials, incorporating a dual non-isothermal crystallization kinetics model within the UMAT subroutine. Our approach is validated by comparing nodal temperature distributions obtained from both the Abaqus built-in AM Modeler and our user subroutines, showing close agreement and demonstrating the effectiveness of our simulation methods. Experimental verification further confirms the accuracy of our simulation techniques. The mechanical analysis investigates residual stresses and distortions, with particular emphasis on the critical transverse in-plane stress component. This study offers valuable insights into accurately simulating thermomechanical behaviors in additive manufacturing of composite polymers.

Sampling Points-Independent Identification of the Fractional Maxwell Model of Viscoelastic Materials Based on Stress Relaxation Experiment Data.

Considerable development has been observed in the area of applying fractional-order rheological models to describe the viscoelastic properties of miscellaneous materials in the last few decades together with the increasingly stronger adoption of fractional calculus. The fractional Maxwell model is the best-known non-integer-order rheological model. A weighted least-square approximation problem of the relaxation modulus by the fractional Maxwell model is considered when only the time measurements of the relaxation modulus corrupted by additive noises are accessible for identification. This study was dedicated to the determination of the model, optimal in the sense of the integral square weighted model quality index, which does not depend on the particular sampling points applied in the stress relaxation experiment. It is proved that even when the real description of the material relaxation modulus is entirely unknown, the optimal fractional Maxwell model parameters can be recovered from the relaxation modulus measurements recorded for sampling time points selected randomly according to respective randomization. The identified model is a strongly consistent estimate of the desired optimal model. The exponential convergence rate is demonstrated both by the stochastic convergence analysis and by the numerical studies. A simple scheme for the optimal model identification is given. Numerical studies are presented for the materials described by the short relaxation times of the unimodal Gauss-like relaxation spectrum and the long relaxation times of the Baumgaertel, Schausberger and Winter spectrum. These studies have shown that the appropriate randomization introduced in the selection of sampling points guarantees that the sequence of the optimal fractional Maxwell model parameters asymptotically converge to parameters independent of these sampling points. The robustness of the identified model to the measurement disturbances was demonstrated by analytical analysis and numerical studies.

Performance Evaluation of Nonlinear Viscoelastic Materials using Finite Element Method

This research paper applies the finite element method as a methodology to evaluate the structural performance of nonlinear viscoelastic solids. A finite element algorithm was built and developed to simulate the mathematical nonlinear viscoelastic material behavior based on incremental constitutive equations. The derived Equation of the incremental constitutive included the complete strain and stress histories. The Schapery’s nonlinear viscoelastic material model was integrated within the displacement-based finite element environment to perform the analysis. A modified Newton-Raphson technique was used to solve the nonlinear part in the resultant equations. In this work, the deviatoric and volumetric strain–stress relations were decoupled, and the hereditary strains were updated at the end of each time increment. It is worth mentioning that the developed algorithm can be effectively employed for all the permissible values of Poisson’s ratio by using a selective integration procedure. The algorithm was tested for a number of applications, and the results were compared with some previously published experimental results. A small percentage error of (1%) was observed comparing the published experimental results. The developed algorithm can be considered a promising numerical tool that overcomes convergence issues, enhancing equilibrium with high-accuracy results.

Viscoelastic material properties determine the contact mechanics of hydrogel spheres

Granular materials are ubiquitous in nature and industry; their mechanical behavior has been a subject of academic and engineering interest for centuries. One of the reasons for their rather complex mechanical behavior is that stresses exerted on a granular material propagate only through contacts between the grains. These contacts can change as the packing evolves. This makes any deformation and mechanical response from a granular packing a function of the nature of contacts between the grains and the material response of the material the grains are made of. We present a study in which we isolate the role of the grain material in the contact forces acting between two particles sliding past each other. By using hydrogel particles, we find that a viscoelastic material model, in which the shear modulus decays with time, coupled with a simple Coulomb friction model, captures the experimental results. The results suggest that particle material evolution itself may play a role in the collective behavior of granular materials.

Anisotropic evolution of viscous strain in soft biological materials

We propose a model for anisotropic viscoelastic biological materials that can handle large deformations, based on the kinematic assumption that the reinforcing fibre structure undergoes affine deformation with the underlying matrix. A generalized orientation tensor approach is used to account for the dispersion of the fibres. Moreover, we consider a strain energy function that features both an elastic and an overstress component, corresponding to distinct natural states. As a consequence of this choice, the remodelled state is not necessarily stress-free, and the material does not completely relax the stress. Notably, we consider that viscous remodelling also alters the fibre distribution, leading to a dependence of the overstress energy on the remodelled orientation tensor. An anisotropic evolution equation for the viscous strain is then derived, which has five distinct characteristic times if a single fibre family is considered and requires no additional assumptions on the viscous spin. To implement the model, we prove that the evolution of the viscous strain can be recast in a variational form by an Onsager variational principle. Finally, we discuss the algorithm used for the simulations and show numerical examples that serve as benchmark test cases for viscoelastic materials.

The generalized Kelvin chain-based model for an orthotropic viscoelastic material

We propose a constitutive material model to describe the rheological (viscoelastic) mechanical response of timber. The viscoelastic model is based on the generalized Kelvin chain applied to the orthotropic material and is compared to the simple approach given by standards. The contribution of this study consists of the algorithmization of the viscoelastic material model of the material applied to the orthotropic constitutive law and implementation into the FEM solver. In the next step, the fitting of the input parameters of the Kelvin chain is described, and at least a material model benchmark and comparison to the approach given by standards were done. The standardized approach is based on the reduction of the material rigidity at the end of the loading period using a creep coefficient, whereas the loading history state variables are not considered when establishing the result for a specific time step. The paper presents the benefits of the rheological model. It also demonstrates the fitting algorithm based on particle swarm optimization and the least squares method, which are essential for the use of the generalized Kelvin chain model. The material model based on the orthotropic generalized Kelvin chain was implemented into the FEM solver for the shell elements. This material model was validated on the presented benchmark tasks, and the influence of the time step size on the accuracy of model results was analyzed.

A hybrid constitutive model of high-damping viscoelastic materials used for vibration control of civil structures

The dynamic mechanical properties of high-damping viscoelastic (VE) materials exhibit significant frequency and temperature dependences in the glass transition zone. However, the current state of VE constitutive models face a challenge in balancing the accuracy, simplicity, and ease of structural dynamic analysis. In this study, a power-law and exponent-law hybrid model is proposed to model the frequency-dependent and temperature-dependent complex modulus of VE materials. The equivalence of hybrid model and existing VE constitutive models is presented. A total of 12 groups of experimental data are collected to validate the accuracy of hybrid model. An efficient numerical method for the hybrid model is proposed and then validated through a viscoelastically damped frame. Results show that the hybrid model is equivalent to two rheological models or fractional derivative models owning to the unshared model coefficients. The hybrid model is superior to the eight-parameter fractional derivative model in predicting the complex modulus over a wide equivalent frequency range. The proposed numerical method performs quite well in calculating seismic responses of proportional and non-proportional damped frames.

The influence of oral cavity physiological parameters: temperature, pH, and swelling on the performance of denture adhesives - in vitro study

BackgroundThe various physical and chemical conditions within the oral cavity are hypothesized to have a significant influence on the behavior of denture adhesives and therefore the overall comfort of denture wearers. As such, this study aims to understand the influence of oral cavity physiological parameters such as temperature (17 to 52 °C), pH (2, 7, 10), and denture adhesive swelling due to saliva (20–120%) on the behavior of denture adhesives. This study further aims to emphasize the need for a collective approach to modelling the in-situ behavior of denture adhesives.MethodsRheological measurements were carried out using the Super Polygrip Ultra fresh brand denture adhesive cream to evaluate its storage modulus (G´) and loss modulus (G´´) values at a range of physiologically relevant temperatures, pH values, and degrees of swelling, to represent and characterize the wide variety of conditions that occur within the oral cavity.ResultsRheological data was recorded with respect to variation of temperature, pH, and swelling. Overall, it can be seen that the physiological conditions of the oral cavity have an influence on the rheological properties of the denture adhesive cream. Specifically, our data indicates that the adhesive’s mechanical properties are weakly influenced by pH, but do change with respect to the temperature in the oral cavity and the swelling rate of the adhesive.ConclusionsOur results suggest that the collective inter-play of the parameters pH, temperature and swelling ratio have an influence on the behavior of the denture adhesive. The results clearly highlight the need for developing a multi-parameter viscoelastic material model to understand the collective influence of physiological parameters on the performance of denture adhesives. Multi-parameter models can also potentially be utilized in numerically simulating denture adhesives using finite element simulations.

A new approach to the fractional Abel k−integral equations and linear fractional differential equations in a fuzzy environment

This paper introduces some recent approaches to the fuzzy fractional Abel integral equations with respect to another function, which is called the fuzzy fractional Abel k−integral equations. The problem proposed here allows for the interpolation of different types of fuzzy classical fractional Abel integral equations, and the solvability of each type of integral equation is also discussed. Additionally, a new approach to the linear fuzzy fractional differential equations in the space of generalized fuzzy functions is introduced. Unlike previous approaches with gH-differentiability, this approach avoids making any prior assumptions about the solution's monotonic behavior during the solving process. It also overcomes the problem of multiple solutions for fuzzy fractional differential equations. To demonstrate the benefits of this approach, two initial value problems of linear fuzzy differential equations are compared using two different concepts of fractional derivatives: the Caputo fractional gH-differentiability and the Caputo fractional derivative in the generalized fuzzy space. Furthermore, some applications are provided in a viscoelastic material model and a population growth with harvesting model.