Large Viscoelastic Deformations Research Articles

Phase field modeling of fracture mechanics for ion-exchanged glass considering large viscoelastic deformation, mechanic–electrochemical coupling

A phase field model is proposed to investigate the fracture mechanics of ion-exchanged glass, which involves significant viscoelastic deformation and stress-diffusion interaction. Based on this theoretical model, the fracture behavior of both double-sided and single-sided ion exchange processes was studied. The results indicate that, compared to single-sided ion exchange, the double-sided process is more likely to induce crack initiation and propagation, ultimately resulting in a notable reduction in glass strength. For both cases, increasing the glass thickness and interfacial energy density will significantly improve the fracture resistance of the glass. Notably, when the glass thickness or interfacial energy density is large enough, the crack can be completely closed, ensuring the integrity of the glass during the ion exchange process. Furthermore, the study conducted a preliminary investigation of two industrially relevant conditions: edging and impurities. The impacts of edging parameters, glass interfacial energy density, and covering radius on glass stress evolution, mechanical deformation, crack initiation, and crack propagation during chemical strengthening were summarized. These findings offer valuable theoretical support and a reference for optimizing chemical strengthening process parameters and enhancing the strength of glass products.

Large viscoelastic deformation of hard-magnetic soft beams

This work aims at developing a viscoelastic formulation for the time-dependent finite deformation analysis of beams made of hard-magnetic soft materials (HMSMs) under magnetic loading. After introducing the basic kinematic quantities, a viscoelasticity formulation for the analysis of HMSMs is developed, which is general in the sense that it can be used for 2D and 3D geometries beside the beam, plate, and shell-type structures. Next, the expression for the consistent fourth-order tangent tensors for 3D bodies and beams made of HMSMs are presented. Due to the highly nonlinear nature of the governing equations, a finite element formulation for the numerical solution of beam problems with various loading and boundary conditions is developed. To demonstrate the applicability of the developed formulation, several numerical examples are provided. It is observed that for the case of elastic deformations, the results of the present formulation are very close to those previously reported in the literature. For the case of viscoelastic deformations, the creep response of beams is simulated and the effect of viscoelastic parameters is studied. It is shown that the obtained results are qualitatively in agreement with the basic properties of viscoelastic deformations.

Modeling of ion exchange in glass considering large viscoelastic deformation and mechano–electrochemical coupling

AbstractThis work proposes a theoretical description of ion exchange in glass involving mechano–electrochemical coupling, distinct from the previous models. The generalized Maxwell viscoelastic constitutive relation and large‐deformation formulae are employed, which is indispensable for thin glass panels widely used in consumer electronics. With the theory, two‐dimensional numerical simulations based on axisymmetric and plan‐strain models are conducted. The numerical results signify lateral deformation in a double‐side ion‐exchanged glass and bending caused by single‐side or electric‐field‐assisted ion exchange. With the decrease in glass thickness, the increase in time, or applied electric potential, these deformations become more significant, leading to the relief of in‐plane stresses in the ion‐exchanged layer and the increase in stresses in other parts. This could lead to a remarkable decrease in fracture strength or cracking of an ultrathin glass panel. As the stress and diffusion are coupled, the decrease in stress in the ion‐exchanged layer leads to the increase in the depth of layer of invading ions. These numerical results clearly show the necessity to incorporate the mechano–electrochemical coupling and large deformation in modeling ion exchange, which is uninvolved in previous theoretical models. Moreover, the proposed theoretical model is directly extendable to three‐dimensional scenarios, such as curved or foldable ultrathin glass panels.

The generalized viscoelastic spring

A spring/rod model is presented that describes one-dimensional behaviour of solids susceptible to large or small viscoelastic deformation. Derivation of its constitutive equation is underpinned by the fact that the internal energy, which the elastic part of deformation stores in the spring, changes in time with the observed strain as well as with some, unknown part of the strain-rate. The latter emerges through the action of a viscous flow potential and is the source of inelastic deformation. Thus, unlike its conventional viscoelasticity counterparts, the model does not postulate a priori a rule that relates strain with viscous flow formation. Instead, it considers that such a rule, as well as other important features of combined elastic and inelastic material response, should become known a posteriori through the solution of a relevant, well-posed boundary value problem. This paper begins with considerations compatible with large viscoelastic deformations and gradually progresses through simpler modelling situations. The latter also include the case of small viscoelastic strain that underpins formulation of classical, spring-dashpot viscoelastic models. In an example application, a relevant closed-form solution is obtained for a spring undergoing small viscoelastic deformation under the influence of a viscous flow potential which is quadratic in the stress.

A diffusion, oxidation reaction and large viscoelastic deformation coupled model with applications to SiC fiber oxidation

In this paper, we present a continuum-level thermodynamically consistent oxidation model that couples large viscoelastic deformation, diffusion and oxidation reaction. Constitutive equations are derived by means of the free energy inequality. The Eyring model for the shear stress dependence of viscosity is adopted to describe the viscous deformation. Subsequently, this model is applied to study the oxidation processes of SiC fibers. A sharp interface between the oxide and substrate naturally develops and propagates forward during the oxidation process. Furthermore, the stresses at the outer surface change from the initial compressive state to tensile due to the viscous deformation and significant volumetric swelling at the interface, which may explain the surface cracking observed in experiments. Notably, the present model can be conveniently used to simulate the oxidation processes that involve complex geometrical shapes without the need to mark and track the interface artificially.

Experimental method for wear assessment of sealing elastomers

Elastomeric dynamic seals are components to prevent or to limit lubricant leakage in machinery. Nevertheless, they wear away under certain working conditions. Mostly, wear exists by starvation of lubricant film (two-body abrasion) and interaction with hard debris (three-body abrasion). This work aims to propose a suitable test methodology toward determining two-body and three-body abrasive wear rates of elastomers by using a TE66 Micro-Scale Abrasion Tester. In the tests, sections of silicone rubber were used. The experiments were divided in two parts. Firstly, dry runs were carried out replicating the two–body abrasion mechanism. Secondly, trials were run using two different media (contaminated oil and slurry) to reproduce three-body abrasive wear. Large viscoelastic deformations were generated in the samples and then they were considered for the wear estimation. In conclusion, the method shows advantages which make it suitable as an alternative test to obtain the wear behavior of sealing elastomers.

Analysis of a viscous soft dielectric elastomer generator operating in an electrical circuit

AbstractDielectric Elastomer Generators (DEGs) are able to convert mechanical work into electric energy. A soft dielectric elastomer generator can be modelled as a strain‐dependent variable capacitor undergoing large viscoelastic deformation. In this work we analyze an electrical circuit for energy harvesting in which the DEG is stretched periodically by a source of mechanical work. Since these devices undergo a high number of electro‐mechanical loading cycles at large deformation, it turns out that viscous effects must be carefully taken into account as they strongly affect the generator performance. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

A constitutive model for coupled fluid permeation and large viscoelastic deformation in polymeric gels

A polymeric gel is a cross-linked polymer network swollen with a solvent. Much of the literature concerning the constitutive response of these materials is limited to elasticity coupled with fluid permeation. We have developed a continuum-level theory to describe the coupled fluid permeation and large viscoelastic deformation of polymeric gels. In discussing special constitutive equations we limit our attention to isothermal conditions, isotropic gels, and consider a model based on a Flory–Huggins model for the free energy change due to mixing of the fluid with the polymer network, coupled with a non-Gaussian statistical–mechanical model for the change in configurational entropy—a model which accounts for the limited extensibility of polymer chains, paired with a linear viscosity. We have numerically implemented our theory in a finite element program. We show that our theory is capable of qualitatively reproducing the experimentally observed behavior of a polymeric gel in simple compression and a fixed depth indentation experiment.

B23 粘弾性材の高速切削特性(OS6 切削加工(1))

High-speed cutting experiment of a natural rubber was carried out in order to clarify the characteristic of high-speed cutting of viscoelastic materials. Cutting speeds ranging from 1 m/s to 150 m/s were examined. The influence of the rake angle was also examined. The following findings were obtained. Large viscoelastic deformation ahead of the cutting edge degrades the geometrical accuracy of the machined surface regardless of the cutting speed and rake angel. Higher rake angle, however, diminishes the tear defects on the machined surface. Shear stress on the shear zone rises as the cutting speed increases. This is attributed to the increase of the viscous drag of a viscoelastic material.

A Finite Element Analysis of Coupling Between Water Absorption and Swelling of Foodstuffs During Soaking

Most foodstuffs are viscoelastic in nature and they experience volume change when soaked. Moisture transport affects the volume change of foodstuffs in a soaking process and vice versa. Studies of soaking of foodstuffs that involve rigorous two way coupling between simultaneous moisture transport and large viscoelastic deformation of the material are missing, to the best of the authors’ knowledge. In this article, these two important phenomena, i.e., swelling and moisture transport during a soaking process of foodstuffs are coupled non-empirically based on a fundamental mathematical model developed by Zhu et al. (Transp Porous Media 84:335–369, 2010). A finite element analysis is performed to study boiling of plane sheet pasta at 100°C. This coupling of the transport and deformation problems is carried out using a Newton scheme based on a Lagrangian description of the spatial domains. In this study, the dependence of relaxation modulus of pasta on the moisture content is investigated, starting from data in the literature, and it is found from the results that pasta can be considered as a hydro-rheologically simple viscoelastic material as analogous to a thermo-rheologically simple material. A novel theoretically determined expression of the diffusion coefficient is also used to completely separate the viscoelastic effect from diffusion. Sorption curves are calculated and the predictions agree well with experimental results obtained by Cafieri et al. (J Cereal Sci 48:857–862, 2008). Thickness change of plane sheet pasta and the stress field at different times are also calculated. The numerical model presented here can be successfully used to predict simultaneous moisture migration and swelling of viscoelastic food materials during a soaking process.

The Effect of Evolving Damage on the Finite Strain Response of Inelastic and Viscoelastic Composites

A finite strain micromechanical model is generalized in order to incorporate the effect of evolving damage in the metallic and polymeric phases of unidirectional composites. As a result, it is possible to predict the response of composites with ductile and brittle phases undergoing large coupled inelastic-damage and viscoelastic-damage deformations, respectively. For inelastic composites, both finite strain elastoplastic (time-independent) and viscoplastic (time-dependent) behaviors are considered. The ductile phase exhibits initially a hyperelastic behavior which is followed by an inelastic one, and its analysis is based on the multiplicative split of its deformation gradient into elastic and inelastic parts. The embedded damage mechanisms and their evolutions are based on Gurson’s (which is suitable for the modeling of porous materials) and Lemaitre’s finite strain models. Similarly, the polymeric phase exhibits large viscoelastic deformations in which the damage evolves according to a suitable evolution law that depends on the amount of accumulated deformation. Evolving damage in hyperelastic materials can be analyzed as a special case by neglecting the viscous effects. The micromechanical analysis is based on the homogenization technique for periodic multiphase materials, which establishes the strong form of the Lagrangian equilibrium equations. These equations are implemented together with the interfacial and periodic boundary conditions, in conjunction with the current tangent tensor of the phase. As a result, the instantaneous strain concentration tensor that relates the local deformation gradient of the phase to the externally applied deformation gradient is established. This provides also the instantaneous effective stiffness tangent tensor of the composite as well as its current response. Results are given that exhibit the effect of damage on the initial yield surfaces, response and possible failure of the composite.

Application of Rosenbrock‐type methods to a finite element formulation based on large strain viscoelasticity

AbstractThe present paper is focused on the solution of differential–algebraic equation systems (DAE), which arise in large viscoelastic deformations within the quasi–static finite element context. For this purpose linearly implicit methods of Rosenbrock–type are used, which avoid completely the solution of non–linear equations. This article investigates a possible treatment of the new global approach with respect to expense and achievable accuracy. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Molded geometry and viscoelastic behavior of film insert molded parts

AbstractVirgin injection‐molded tensile specimens without any inserted film and four kinds of film insert molded (FIM) tensile specimens were prepared. They were annealed at 80°C to investigate the effect of residual stresses and thermal shrinkage of the inserted film on thermal deformation of tensile specimens. The FIM specimens with the unannealed film were bent after ejection in such a way that the film side was protruded and the warpage was reversed gradually during annealing and the film side was intruded. Warpage of the FIM specimen with the film annealed at 80°C for 20 days was not reversed during annealing. Processing of the FIM specimens have been modeled numerically to predict thermoviscoelastic deformation of the part and to understand the warpage reversal phenomenon (WRP). Nonisothermal three‐dimensional flow analysis was carried out for filling, packing, and cooling stages. The flow analysis results were transported to a finite element stress analysis program for prediction of deformation of the FIM part. The WRP was caused by the combined effect of thermal shrinkage of the inserted film and relaxation of residual stresses in the FIM specimen during annealing. It is expected that this study will contribute towards the improvement of the FIM product quality and prevention of large viscoelastic deformation of the molded part. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2009

Kidney damage in extracorporeal shock wave lithotripsy: a numerical approach for different shock profiles

In shock-wave lithotripsy--a medical procedure to fragment kidney stones--the patient is subjected to hypersonic waves focused at the kidney stone. Although this procedure is widely applied, the physics behind this medical treatment, in particular the question of how the injuries to the surrounding kidney tissue arise, is still under investigation. To contribute to the solution of this problem, two- and three-dimensional numerical simulations of a human kidney under shock-wave loading are presented. For this purpose a constitutive model of the bio-mechanical system kidney is introduced, which is able to map large visco-elastic deformations and, in particular, material damage. The specific phenomena of cavitation induced oscillating bubbles is modeled here as an evolution of spherical pores within the soft kidney tissue. By means of large scale finite element simulations, we study the shock-wave propagation into the kidney tissue, adapt unknown material parameters and analyze the resulting stress states. The simulations predict localized damage in the human kidney in the same regions as observed in animal experiments. Furthermore, the numerical results suggest that in first instance the pressure amplitude of the shock wave impulse (and not so much its exact time-pressure profile) is responsible for damaging the kidney tissue.

A 3‐D Model for Finite Viscoelsatic Swelling of Charged Tissues and Gels

AbstractMaterials like soft biological tissues undergo large viscoelastic deformations during the swelling process. Following this, it is the goal of this contribution to merge the advances of finite viscoelasticity laws and the state of the art in electrochemical swelling theories within a well‐founded multiphasic concept. The numerical treatment is carried out fully 3‐d in the framework of the FEM.

Long-Term Stability of a Circular Roadway Subjected to Inner Pressure

It is the purpose of this study to clarify long-term stability of a circular roadway subjected to inner pressure σr (ri)together with rock pressure σr (r0). Circumferential stress at the wall σθ(ri ) obtained by the elastic analysis is equal to {2σr(r0) -σr (ri)}. Therefore, it is natural to consider that tensile failure possibly develops into the surrounding rock starting at the wall if σr (ri ) is larger than 2σr(r0). A question arises whether it can be properly applied to a circular roadway where large visco-elastic deformation is expected.A non-linear rheological model proposed by this authors was used to simulate time-dependent behaviour of rock around a circular roadway. It was assumed that inner pressure gradually increases. Results of computer simulation indicate that, at first, the failed region develops and the roadway converges. As time goes by, inner pressure gradually increases, then convergence ceases and finally the roadway diameter starts to increase. We obtained interesting results as follows；1. Even if σr(ri) is larger than 2σr (r0), σθ(ri) is still remained in compression provided that Poisson's ratio increases with failure of rock.2. Post-failure characteristics of rock, that is, slope of descending portion of stress-strain curve in the post-failure region is not so important.3. Time-dependency of rock is very important, and affects long-term stability of a circular roadway. Right now, we have only limited information concerning time-dependent behaviour of rock. It is especially important to obtain accurate knowledge concerning Poisson's ratio and behaviour of rock in tension.

Leukocyte deformability: Finite element modeling of large viscoelastic deformation

An axisymmetric deformation of a viscoelastic sphere bounded by a prestressed elastic thin shell in response to external pressure is studied by a finite element method. The research is motivated by the need for understanding the passive behavior of human leukocytes (white blood cells) and interpreting extensive experimental data in terms of the mechanical properties. The cell at rest is modeled as a sphere consisting of a cortical prestressed shell with incompressible Maxwell fluid interior. A large-strain deformation theory is developed based on the proposed model. General non-linear, large strain constitutive relations for the cortical shell are derived by neglecting the bending stiffness. A representation of the constitutive equations in the form of an integral of strain history for the incompressible Maxwell interior is used in the formulation of numerical scheme. A finite element program is developed, in which a sliding boundary condition is imposed on all contact surfaces. The mathematical model developed is applied to evaluate experimental data of pipette tests and observations of blood flow.

Constitutive model for large viscoelastic deformations of elastomeric materials

An evolving internal stress variable is introduced as the macroscopic manifestation of the molecular chain network resistance to deform affinely instantaneously. The inelastic response is obtained by the corotational rate equation of evolution for the internal stress, with respect to a properly defined constitutive spin