Arruda Boyce Eight-chain Model Research Articles

Multiscale Network Modeling of Fibrin Fibers and Fibrin Clots with Protofibril Binding Mechanics.

The multiscale mechanical behavior of individual fibrin fibers and fibrin clots was modeled by coupling atomistic simulation data and microscopic experimental data. We propose a new protofibril element composed of a nonlinear spring network, and constructed this based on molecular simulations and atomic force microscopy results to simulate the force extension behavior of fibrin fibers. This new network model also accounts for the complex interaction of protofibrils with one another, the effects of the presence of a solvent, Coulombic attraction, and other binding forces. The network model was formulated to simulate the force–extension mechanical behavior of single fibrin fibers from atomic force microscopy experiments, and shows good agreement. The validated fibrin fiber network model was then combined with a modified version of the Arruda–Boyce eight-chain model to estimate the force extension behavior of the fibrin clot at the continuum level, which shows very good correlation. The results show that our network model is able to predict the behavior of fibrin fibers as well as fibrin clots at small strains, large strains, and close to the break strain. We used the network model to explain why the mechanical response of fibrin clots and fibrin fibers deviates from worm-like chain behavior, and instead behaves like a nonlinear spring.

A Mechanism-Based Four-Chain Constitutive Model for Enthalpy-Driven Thermoset Shape Memory Polymers With Finite Deformation

Abstract Chemically cross-linked thermoset shape memory polymers (TSMPs) are an important branch of smart materials due to their potentially wide applications in deplorable structures, soft robots, damage self-healing, and 4D printing. Further development and design of TSMP structures call for constitutive models. Although the Arruda–Boyce eight-chain model has been very successful and widely used for entropy-driven TSMPs, recent studies found that some new TSMPs, such as those using enthalpy as the primary driving force, show unit cells different from the eight-chain model. Considering that these new epoxy-based TSMP networks consist of a plenty of four-chain features, this study proposes a four-chain tetrahedron structure as the unit cell of the network to construct the constitutive model. In this model, Gibbs free energy is used to formulate the thermodynamic driving force. Then, by introducing a transition of the molecule deformation mechanism from that dominated by bond stretch to that dominated by bond angle opening, the traditional Langevin chain model is modified. It is found that this model can well capture the dramatic modulus change for the new TSMP in the thermomechanical experiments. Moreover, it shows that the original Treloar four-chain model and Arruda–Boyce eight-chain model underestimate the driving force for the enthalpy-driven TSMPs, and thus cannot well capture the thermomechanical behaviors. It is also found that under certain conditions, our four-chain model produces the same Cauchy stress as the eight-chain model does. This study may help researchers understand the thermomechanical response and design a special category of TSMPs with high recovery stress.

A unified modeling approach for amorphous shape memory polymers and shape memory polymer based syntactic foam

Shape memory polymers (SMPs) and shape memory polymer composites have drawn considerable attention in recent years for their shape memory effects. A unified modeling approach is proposed to describe thermomechanical behaviors and shape memory effects of thermally activated amorphous SMPs and SMP-based syntactic foam by using the generalized finite deformation multiple relaxation viscoelastic theory coupled with time–temperature superposition property. In this paper, the thermoviscoelastic parameters are determined from a single dynamic mechanical analysis temperature sweep at a constant frequency. The relaxation time strongly depends on the temperature and the variation follows the time–temperature superposition principle. The horizontal shift factor can be obtained by the Williams–Landel–Ferry equation at temperatures above or close to the reference temperature (Tr), and by the Arrhenius equation at temperatures below Tr. As the Arruda–Boyce eight-chain model captures the hyperelastic behavior of the material up to large deformation, it is used here to describe partial material behaviors. The thermal expansion coefficient of the material is regarded as temperature dependent. Comparisons between the model results and the thermomechanical experiments presented in the literature show an acceptable agreement. Copyright © 2016 John Wiley & Sons, Ltd.

A finite deformation constitutive model for thermally activated amorphous shape memory polymers

A thermoviscoelastic–thermoviscoplastic finite deformation constitutive model incorporating structural and stress relaxation is developed for thermally activated amorphous shape memory polymers. In this study, the nonlinear Adam–Gibbs model is used to describe the structural relaxation. Furthermore, a modified Argon scalar equation is proposed for the viscous flow as the temperature crosses Tg. In addition, as the Arruda–Boyce eight-chain model captures the hyperelastic behavior of the material up to large stretches, it is used here to represent the partial material behavior of shape memory polymers. To further feature the macroscopic post-yield strain softening behavior, the phenomenological evolution rule is also implemented. Comparisons of numerical simulations and the thermomechanical experiments conducted on an ether-based polyurethane shape memory polymer show acceptable agreement.

Orthotropic cyclic stress-softening model for pure shear during repeated loading and unloading

We derive an orthotropic model to describe the cyclic stress-softening of a carbon-filled rubber vulcanizate through multiple stress-strain cycles with increasing values of the maximum strain. We specialize the deformation to pure shear loading. As a result of strain-induced anisotropy following on from initial primary loading, the material may subsequently be described as orthotropic because in pure shear there are three different principal stretches so that the strain-induced anisotropy of the stress response is different in each of these three directions. We derive non-linear orthotropic models for the elastic response, stress relaxation and residual strain in order to model accurately the inelastic features associated with cyclic stress softening. We then develop an orthotropic version of the Arruda-Boyce eight-chain model of elasticity and then combine it with the ideas previously developed in this paper to produce an orthotropic constitutive relation for the cyclic stress-softening of a carbon-filled rubber vulcanizate. The model developed here includes the widely-occurring effects of hysteresis, stress-relaxation and residual strain. The model is found to compare well with experimental data. } {Mullins effect, stress-relaxation, hysteresis, residual strain, orthotropy.}

A model for the Mullins effect during multicyclic equibiaxial loading

In this paper, we derive a model to describe the cyclic stress softening of a carbon-filled rubber vulcanizate through multiple stress–strain cycles with increasing values of the maximum strain, specializing to equibiaxial loading. Since the carbon-filled rubber vulcanizate is initially isotropic, we can show that following initial equibiaxial loading the material becomes transversely isotropic with preferred direction orthogonal to the plane defined by the equibiaxial loading. This is an example of strain-induced anisotropy. Accordingly, we derive nonlinear transversely isotropic models for the elastic response, stress relaxation, residual strain and creep of residual strain in order to model accurately the inelastic features associated with cyclic stress softening. These ideas are then combined with a transversely isotropic version of the Arruda–Boyce eight-chain model to develop a constitutive relation for the cyclic stress softening of a carbon-filled rubber vulcanizate. The model developed includes the effects of hysteresis, stress relaxation, residual strain and creep of residual strain. The model is found to compare extremely well with experimental data.

Multicyclic modelling of softening in biological tissue

In this paper we derive a model to describe the important inelastic features associated with the cyclic softening, often referred to as stress-softening, of soft biological tissue. The model developed here includes the notion of multiple stress-strain cycles with increasing values of the maximum strain. The model draws upon the similarities between the cyclic softening associated with carbon-filled rubber vulcanizates and soft biological tissue. We give non-linear transversely isotropic models for the elastic response, stress relaxation, residual strain and creep of residual strain. These ideas are then combined with a transversely isotropic version of the Arruda-Boyce eight-chain model to develop a constitutive relation that is capable of accurately representing the multicyclic softening of soft biological tissue. To establish the validity of the model we have compared it with experimental data from three cyclic uniaxial test samples, one taken from the \textit{Manduca sexta} (tobacco hornworm) caterpillar and the other two samples taken from the human aorta, one in the longitudinal and the other in the circumferential direction. The model was found to fit these experimental data extremely well. {Keywords:} Mullins effect, stress relaxation, creep of residual strain, biological tissue, transverse isotropy. {MSC codes:} 74B20, 74D10, 74L15, 92C10

Cyclic stress-softening model for the Mullins effect in compression

This paper models the cyclic stress softening of an elastomer in compression. After the initial compression the material is described as being transversely isotropic. We derive non-linear transversely isotropic constitutive equations for the elastic response, stress relaxation, residual strain, and creep of residual strain in order to model accurately the inelastic features associated with cyclic stress softening. These equations are combined with a transversely isotropic version of the Arruda–Boyce eight-chain model to develop a constitutive relation that is capable of accurately representing the Mullins effect during cyclic stress softening for a transversely isotropic, hyperelastic material, in particular a carbon-filled rubber vulcanizate. To establish the validity of the model we compare it with two test samples, one for filled vulcanized styrene–butadiene rubber and the other for filled vulcanized natural rubber. The model is found to fit this experimental data extremely well.

Transversely isotropic cyclic stress-softening model for the Mullins effect

This paper models stress softening during cyclic loading and unloading of an elastomer. The paper begins by remodelling the primary loading curve to include a softening function and goes on to derive nonlinear transversely isotropic constitutive equations for the elastic response, stress relaxation, residual strain and creep of residual strain. These ideas are combined with a transversely isotropic version of the Arruda–Boyce eight-chain model to develop a constitutive relation that is capable of accurately representing the Mullins effect during cyclic stress softening for a transversely isotropic, hyperelastic material, in particular, a carbon-filled rubber vulcanizate.

A cyclic stress softening model for the Mullins effect

In this paper the inelastic features of stress relaxation, hysteresis and residual strain are combined with the Arruda–Boyce eight-chain model of elasticity, in order to develop a model that is capable of describing the Mullins effect for cyclic stress-softening of an incompressible hyperelastic material, in particular a carbon-filled rubber vulcanizate. We have been unable to identify in the literature any other model that takes into consideration all the above inelastic features of the cyclic stress-softening of carbon-filled rubber. Our model compares favourably with experimental data and gives a good description of stress-softening, hysteresis, stress relaxation, residual strain and creep of residual strain.

Nanoscale characterization of the biomechanical hardening of bovine zona pellucida

The zona pellucida (ZP) is an extracellular membrane surrounding mammalian oocytes. The so-called zona hardening plays a key role in fertilization process, as it blocks polyspermy, which may also be caused by an increase in the mechanical stiffness of the ZP membrane. However, structural reorganization mechanisms leading to ZP's biomechanical hardening are not fully understood yet. Furthermore, a correct estimate of the elastic properties of the ZP is still lacking. Therefore, the aim of the present study was to investigate the biomechanical behaviour of ZP membranes extracted from mature and fertilized bovine oocytes to better understand the mechanisms involved in the structural reorganization of the ZP that may lead to the biomechanical hardening of the ZP. For that purpose, a hybrid procedure is developed by combining atomic force microscopy nanoindentation measurements, nonlinear finite element analysis and nonlinear optimization. The proposed approach allows us to determine the biomechanical properties of the ZP more realistically than the classical analysis based on Hertz's contact theory, as it accounts for the nonlinearity of finite indentation process, hyperelastic behaviour and material heterogeneity. Experimental results show the presence of significant biomechanical hardening induced by the fertilization process. By comparing various hyperelastic constitutive models, it is found that the Arruda-Boyce eight-chain model best describes the biomechanical response of the ZP. Fertilization leads to an increase in the degree of heterogeneity of membrane elastic properties. The Young modulus changes sharply within a superficial layer whose thickness is related to the characteristic distance between cross-links in the ZP filamentous network. These findings support the hypothesis that biomechanical hardening of bovine ZP is caused by an increase in the number of inter-filaments cross-links whose density should be higher in the ZP inner side.

Biaxial stress–strain behavior of chemical and physical gels of poly(vinyl alcohol)

In a recent paper, Urayama K, Ogasawara S, Takigawa T [Polymer 2006;47:6868–73.] found significant differences in the pure shear behavior of the poly(vinyl alcohol) gels with similar initial modulus but with different types of crosslinks, physical crosslinks formed by microcrystallites and chemical crosslinks made of covalent bonds. The non-Gaussian three-chain model was found to give but a limited explanation of the data. In this paper we show that the constitutive equation that we proposed and tested previously (Polymer 2006) for filler-reinforced rubber networks gives equally good description and reasonable interpretation of the stress–strain data on poly(vinyl alcohol) gels in different geometrical modes. The Arruda–Boyce eight-chain model combined with the Gaylord–Douglas theory of tube-like topological constraints describes well the stress–strain properties of chemical gels in pure shear and in uniaxial and equibiaxial extensions. The pure shear behavior of physical gels can be reasonably explained and described by taking into account the amplification of local strain in the presence of inextensible particles (crystalline domains).

A constitutive model for protein-based materials

Protein-based materials are critical to the construction of tissue substitutes that exhibit precisely defined mechanical properties. Under physiologically relevant conditions, materials derived from natural or synthetic structural proteins are characterized by nonlinear elastic responses at medium and large deformations, time-dependent or viscoelastic behavior, and display the effects of strain-induced structural changes. Although a constitutive model that accurately describes mechanical behavior is essential for the rational design of tissue constructs, few models account for all of these characteristics. In this report, we present a new constitutive model for protein based materials, in which nonlinear elasticity is captured by the Arruda-Boyce eight-chain model, time dependant viscoelasticity is described by a generalized Maxwell model, and the effect of strain-induced structural change is incorporated using a network alteration theory originally proposed by Tobolsky. The model was applied to a number of protein-based materials and cell containing constructs, including recombinant elastin-mimetic protein polymers and fibroblast populated collagen gel matrices. Significantly, numerical implementation of this model is straightforward and mechanical behavior accurately described under a variety of loading conditions. Moreover, when calibrated using stress relaxation data alone, the model accurately predicted cyclic loading responses. Although limitations exist, this model provides a convenient tool to correlate viscoelastic data obtained by different testing modes and may assist in reducing the number of experimental tests required to fully capture the range of viscoelastic responses of protein-based materials.