Poynting Effect Research Articles

Combined extension and torsion of hydrogels with chemo-mechanical coupling: Revealing positive poynting effect

In this paper, combined extension and torsion of hydrogel subject to a chemo-mechanical coupled loading is described in the framework of continuum mechanics, where the free energy density consists of the elastic, mixing and chemical contributions. A simplified, closed-form and exactly analytical solution to the mechanical response is obtained, which accounts for the coupling effect of external loading, chemical potential and microstructural parameters, such as crosslinking degree, Flory-Huggins parameter, etc. In particular, the effect of free swelling and microscopic diffusion on deformation of the hydrogel at equilibrium state is discussed, reaching some fundamental conclusions. Negative axial forces are captured, revealing the typical positive Poynting effect where the cylinder tends to elongate on twisting, and an inhomogeneous deformation, induced by torsion, along the radial direction is demonstrated. Furthermore, the dynamic competition between external loading and solvent environment is revealed and investigated, where the direct connection between internal micro-physical parameters and macroscopic deformation is demonstrated. The theoretical results presented in this paper may provide predictions and guidance for the mechanical analysis and design of hydrogel cylinder subject to extension and torsion in a solvent.

The cross-sectional geometry regulated Poynting effect in ribbed silicone rubber tubes

The cross-sectional geometry regulated Poynting effect in ribbed silicone rubber tubes

Programmable nonreciprocal Poynting effect enabled by lattice metamaterials.

Shear nonreciprocity, implying unequal shear forces in opposite shear directions, can be achieved by arranging structures asymmetrically. However, the nonreciprocal Poynting effect, i.e., unequal normal stresses induced by the same shear displacements to the left and right, has not been fully explored. We discover the nonreciprocal Poynting effect using a generalized directional truss model. Inspired by this discovery, the cylindrical lattice metamaterials constructed from antisymmetric curled microstructures are used as a case study to generate the nonreciprocal Poynting effect. We develop a design framework that integrates digital generation, finite deformation theory, finite element modeling, and three-dimensional printing to program the nonreciprocal Poynting effect. Applications such as bionic Poynting effect matching, wave energy converter, and unidirectional motion limitation are demonstrated. This framework allows the one-to-one mapping between the torque and normal forces, paving the way for designing soft devices with precise force transmission capabilities.

WAX PRECIPITATION PREDICTIVE MODEL MODIFICATION ON THE EXAMPLE OF A KAZAKHSTAN OIL

Currently, the oil and gas segment of Kazakhstan is facing such a problem as paraffin deposits. The problem associated with the deposition and crystallization of paraffin causes large-scale difficulties, and models for predicting wax precipitation are limited to specific types of oil, and therefore there is a need to improve them. The authors of this article analyzed and developed a predictive model of paraffin deposition from crude oil for Kazakhstani fields. The work is based on the study of Lira-Galeana et al., which considers the multicomponent deposition of immiscible solids from an oil mixture - a multi-solid model. During the study, it was found out that the Lira-Galeana model uses the equation of state, the volatility properties of the components and the activity coefficient. The Poynting effect was considered at high pressures in the system. For experimental studies, oil samples were taken from two fields. The component composition of the oil, the pour point and loss of fluidity of the oil, as well as the melting point temperatures were determined in laboratory conditions. The amount of paraffin sludge from the oil was estimated experimentally. The results obtained are fully consistent with the analytical solution. During laboratory tests, it was found that the oil from the second field was heavier, and the degree of crystallization of paraffin was more significant than that of oil from the first field under the same conditions. Using this predictive model, the authors were able to predict the amount of solid precipitation from crude oil during the year, depending on changes in ambient temperature.

An Ogden hyperelastic 3D micromechanical model to depict Poynting effect in brain white matter

Shear and torsional load on soft solids such as brain white matter purportedly exhibits the Poynting Effect. It is a typical nonlinear phenomenon associated with soft materials whereby they tend to elongate (positive Poynting effect) or contract (negative Poynting effect) in a direction perpendicular to the shearing or twisting plane. In this research, a novel 3D micromechanical Finite Element Model (FEM) has been formulated to describe the Poynting effect in bi-phasic modeled brain white matter (BWM) representative volume element (RVE) with axons tracts embedded in surrounding extracellular matrix (ECM) for simulating brain matter's response to pure and simple shear. In the presented BWM 3D FEM, nonlinear Ogden hyper-elastic material model is deployed to interpret axons and ECM material phases. The modeled bi-phasic RVEs have axons tied to the surrounding ECM. In this proof-of-concept (POC) FEM, three simple shear loading configurations and a pure shear case were analyzed. Root mean square deviation (RMSD) was calculated for stress and deformation response plots to understand the effect of axon-ECM orientations and loading conditions on the degree of Poynting behavior. Variations in normal stresses (S11, S22, or S33) perpendicular to the shear plane underscored the significance of axonal fiber-matrix interactions. From the simulated ensemble of cases, a transitional dominance trend was noticed, as simple sheared axons showed pronounced Poynting behavior, but shear deformation build-up in the purely sheared brain model exhibited the highest Poynting behavior at higher strain % limits. At lower strain limits, simple shear imparted across and perpendicular to axonal tract directions emerged as the dominant Poynting effect configurations. At high strains, the stress-strain% plots manifested mild strain stiffening effects and bending stresses in purely sheared axons, substantiated the strong non-linearity in brain tissues’ response.

Poynting effect in fluid-saturated poroelastic soft materials in torsion

This work studies the Poynting effect in fluid-saturated poroelastic soft materials in torsion. The Poynting effect is a nonlinear mechanical phenomenon commonly observed in soft solids such as biological soft tissues, gels and rubber. When sheared or twisted, such materials tend to either expand or contract in the direction perpendicular to the plane of shearing or twisting. Thus, to maintain a constant height, a compressive (positive Poynting effect) or tensile (negative Poynting effect) normal force must be applied to the material’s sheared face or twisted end. The mechanical response of fluid-saturated poroelastic soft materials can be described using mixture theory. Although both of its constituents are intrinsically incompressible, the biphasic material as a whole is compressible since it may gain or lose fluid through its pores. Our model—an extension of the single-constituent, incompressible solid models found in anterior studies—allows one to quantify the effect of the fluid and the solid on the normal force and torque required to maintain the torsion deformation and shows that the anomalous negative Poynting effect cannot be attributed to the poroelastic nature of the material alone. We use finite element simulations to predict the normal force and torque for biphasic materials with weakly-compressible and fully-compressible Mooney–Rivlin skeletons and Holmes–Mow-type hydraulic permeability. We also approximate analytical expressions for the normal force and torque for a weakly-compressible Mooney–Rivlin solid, which set a benchmark for the numerical simulations.

Unified and accurate simulation for large elastic strain responses of rubberlike soft materials under multiple modes of loading

AbstractA new and explicit form of the multi-axial elastic potential for elastic soft materials is constructed by means of two invariants of the Hencky strain. The new elasticity model with this form can bypass coupling complexities and uncertainties usually involved in parameter identification. Namely, exact closed-form solutions of decoupled nature are obtainable for stress responses under multiple benchmark modes. Unlike usual solutions with numerous coupled parameters, such new solutions are independent of one another and, as such, data sets for multiple benchmark modes can be separately matched with mutually independent single-variable functions. A comparative study is presented between a few well-known models and the new model. Results show that predictions from the former agree well with uniaxial and biaxial data, as known in the literature, but would be at variance with data for the constrained stress response in the plane-strain extension. In contrast, predictions from the new model agree accurately with all data sets. Furthermore, exact solutions for the Poynting effect of freely twisted elastic thin-walled tube are obtained from the new model.

Effect of fiber properties and orientation on the shear rheology and Poynting effect in meat and meat analogues

The development of plant-based meat analogues is an important aspect of the transition towards using more plant proteins. Production of such products with texture (and rheology) adequate for consumer acceptance like meats is a great challenge. However, there is a current lack in quantitative methods to compare whole cut meats and plant-based analogues that also consider its fibrous structures. We tackled this problem by combining non-linear shear rheology and shear-induced normal stress measurements on whole cut meats (beef and chicken) and plant-based fibrous model systems for meat analogues (soy and pea protein isolates combined with wheat gluten). We found different response in the linear viscoelastic regime for different samples, and the non-linear viscoelastic regime provided a deeper understanding into the role of structural components. Meat samples showed rearrangements at small strains and lower energy dissipation, higher intracycle strain stiffening, and a larger normal stress response at large strains than plant-based fibrous products, due to more elastic fibers. The plant-based fibrous products behave more solid-like until a larger strain, but the fibrous structures break down at large deformations resulting in higher energy dissipation, and show a lower normal stress response than meat. We therefore explore the importance of fiber properties and orientation on the nonlinear rheology of fibrous model systems for meat analogues, and provide a robust methodology to quantitatively compare different mechanical responses of meat and plant-based fibrous meat analogues. These results thereby allow comparison and tuning mechanical responses of plant-based meat analogue products towards real meat.

An accurate and parameter‐free analysis for the converse Poynting effect in large constrained torsion of highly elastic soft tubes

AbstractNew exact solutions to large constrained torsion of highly elastic soft tubes are obtained from a new hyper‐elastic constitutive model. This new model is established with a new form of the multiaxial elastic potential toward simultaneously matching multiple data sets for three benchmark modes, including the uniaxial extension of a bar, the equi‐biaxial extension of a thin plate and the plane‐strain extension of a plate strip. With the new model, exact closed‐form solutions to the stress responses for these benchmark modes are first derived and shown to be of decoupled nature, and, then, an accurate analysis for the converse Poynting effect of twisted highly elastic tubes with fixed ends is presented with a new technique in treating nonlinear coupling complexities. The main novelties are incorporated as follows. First, multiple data sets for three benchmark modes can be accurately and automatically matched with no need to identify any unknown parameters; next, the nonlinear coupled system of the governing equations for four variables in a twisted tube, including the averaged radius and the wall‐thickness as well as the axial constrained stress and the shear stress, can be reduced to treating a single nonlinear equation; and, accordingly, the nonlinear coupling complexities can be worked out and exact results are obtainable.

A perturbation analysis of pure torsion of incompressible hyperelastic cylinders

The stretch-based formulation of basic problems for incompressible isotropic hyperelastic materials has been the subject of renewed recent attention largely motivated by application to modelling the mechanical response of soft tissues. Here we are concerned with the classical problem of simple torsion of a circular cylinder which has in the past been primarily investigated by employing the classical approach of Rivlin in terms of invariants of the Cauchy–Green deformation tensors. Here we propose a perturbation approach to the pure torsion problem for thin (but not necessarily infinitesimally thin) cylindrical specimens motivated by potential applications to rubber-like or biological filaments and for the infinitesimal twisting of thick cylinders. The advantage of this approach is that the results are valid for all strain–energy functions whether based in terms of the principal stretches or in terms of the classical deformation invariants. The asymptotic results obtained for the resultant force and moment are applied to the special case of the one-term stretch-based Ogden model. In particular, a prediction of a transition in the Poynting effect for values of the Ogden parameter α>6 is obtained. Other illustrative examples for both invariant and stretch-based strain energies are described. In view of the complexity of a general analysis of torsion for arbitrary strain energies, the perturbation approach provides a viable alternative for assessing the resultant force and moment.

The mechanics of embedded fiber networks

Fiber networks underlie the mechanical behavior of a wide range of natural and engineered materials. Interestingly, these networks are often embedded within amorphous matrices rather than appearing in isolation. However, despite their frequent occurrence as embedded rather than isolated networks, few prior studies have focused on investigating the role of embedding on the emergent mechanical behavior of these systems. To address this, we adopt a mortar-type embedding approach within the finite element framework and perform simulations to systematically fill this knowledge gap. Within this study, we focus on soft tissues as an exemplary class of materials where embedded fiber networks are essential to mechanical function. Specifically, we investigate the role of embedding on the strain energy distribution within the networks across the bending, stretching, torsional, and shear fiber-level loading modes. Therein, we specifically focus on semi-flexible fiber networks. In addition to revealing the role of embedding on the networks themselves, we also investigate how the networks affect the mechanics of the matrix material. Together, we find that embedding fundamentally alters the mechanics of semi-flexible fiber networks and the surrounding matrices. Most importantly, we find that embedding semi-flexible fiber networks leads to strain-stiffening and negative Poynting effect of the resulting composite material. Furthermore, semi-flexible fiber networks induce stress heterogeneity in their host material and increase its resistance to compression. Overall, our work improves our fundamental understanding of an important class of materials. By making our implementation openly available, we also hope to help others learn more about embedded semi-flexible fiber networks in the context of materials other than soft tissues.

A model for residually stressed viscoelastic bodies and its application to some boundary value problems

A model for residually stressed viscoelastic bodies undergoing finite deformations is developed and applied to the study of time-dependent responses of spheres and cylinders to various stress and strain controlled tests. An approach based on the notion of natural configurations is employed. An appropriate free energy function is used, and a suitable dissipation function is adopted to obtain a constitutive model. This constitutive model is applied to the study of different boundary value problems of thick spheres and cylinders. The responses to various strain controlled tests are investigated, which includes the stress-relaxation test and a test for a time-dependent inflation–deflation cycle. Also, the response to creep test and step-stress test in thick viscoelastic spheres is investigated. Furthermore, the stretch-controlled responses of residually stressed viscoelastic cylinders to pure torsion and axial stretch are studied. Pure torsion involves an axial extension or compression known as the Poynting effect. The Poynting effect in residually stressed viscoelastic bodies, which does not appear to be studied in the literature, is investigated in detail here. It is noted that the magnitude of the angle of twist has a significant influence (sometimes involving a change of sign) on the observed Poynting effect.

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Nonlinear viscoelastic damping in a Poynting oscillator

This work considers a cylindrical rod, acting as a nonlinear viscoelastic spring, with an attached mass that can displace along and rotate about the rod’s axis, thereby inducing an extension and twist in the rod. The coupling between them produces the Poynting effect in the body. The material is modeled by the nonlinear single integral Pipkin–Rogers constitutive equation. The mass has been assumed to be at rest in a long-time equilibrium state and then given a small axial or rotational disturbance and released (plucked). The subsequent motion is governed by a linear Volterra integro-differential equation. For a particular choice of material parameters, analytical expressions for the time-dependent decay of the disturbance are obtained in terms of the extension/torsion coupling, material stiffness, the amount and rate of stress relaxation, and the inertia of the mass. For other choices of material parameters, the results provide insight into how these quantities affect the time-dependent decay. A number of plucking scenarios are treated such as extensional or rotational disturbances from the undeformed state, rotational plucking after a finite axial stretch, and extensional plucking after a finite rotation. Simultaneous rotational and extensional plucking leads to a system of Volterra integro-differential equations whose treatment is deferred to later work.

Canceling the elastic Poynting effect with geometry.

The Poynting effect is a paragon of nonlinear soft matter mechanics. It is the tendency (found in all incompressible, isotropic, hyperelastic solids) exhibited by a soft block to expand vertically when sheared horizontally. It can be observed whenever the length of the cuboid is at least four times its thickness. Here we show that the Poynting effect can be easily reversed and the cuboid can shrink vertically, simply by reducing this aspect ratio. In principle, this discovery means that for a given solid, say one used as a seismic wave absorber under a building, an optimal ratio exists where vertical displacements and vibrations can be completely eliminated. Here we first recall the classical theoretical treatment of the positive Poynting effect, and then show experimentally how it can be reversed. Using finite-element simulations, we then investigate how the effect can be suppressed. We find that cubes always provide a reverse Poynting effect, irrespective of their material properties (in the third-order theory of weakly nonlinear elasticity).

Pure torsion for incompressible hyperelastic materials of Valanis–Landel form

The stretch-based formulation of basic problems for incompressible isotropic hyperelastic materials has been the subject of renewed recent attention largely motivated by application to modelling the mechanical response of soft tissues. Here, we are concerned with this formulation of the classic problem of simple torsion of a circular cylinder that has been primarily in the past investigated by employing the classical approach of Rivlin in terms of invariants of the Cauchy–Green strain tensor. Attention is focused on examining the resultant axial force necessary to sustain pure torsion, thereby investigating the Poynting effect, and the resultant moment needed to generate the twist. General results for the resultant force and moment are obtained for all hyperelastic materials that can be modelled in the celebrated separable Valanis–Landel form. These expressions are specialized for the one-term Ogden model to provide explicit results valid for all strain-stiffening exponents in this model. Some particular examples are provided, mainly for even values of the exponent. A notable result obtained for the Ogden model is that for values of the hardening exponent n in that model for which n ≤ 6 , one obtains the classical Poynting effect, whereas for n > 6 , a reverse Poynting effect always occurs for sufficiently small twist.

Exact large strain analysis for the Poynting effect of freely twisted thin-walled tubes made of highly elastic soft materials

Toward handling nonlinear coupling effects at large elastic deformations, a decoupled form of the multi-axial elastic potential for highly elastic soft materials is first constructed based on Hencky’s logarithmic strain, and this new potential is then used to obtain analytic results for the uniaxial extension and compression of a bar, the equi-biaxial extension of a plate, the plane-strain extension of a strip and, in particular, the large torsion of a thin-walled tube with free ends. Novelties are included in the following three respects: (a) Experimental data for responses of the uniaxial extension, equi-biaxial extension (uniaxial compression) and plane-strain extension (simple shear) may be accurately matched up to large strain with strain-stiffening effects; (b) exact responses for the Poynting effect of freely twisted thin-walled tubes may be derived for changes in the axial length and the wall thickness as well as the averaged radius; and (c) the coupling nonlinear complexities involved in all such responses may be worked out in a decoupled sense.

Stretch formulations and the Poynting effect in nonlinear elasticity

The second invariant of the left Cauchy–Green deformation tensor B (or right C) has been argued to play a fundamental role in nonlinear elasticity. Generalized neo-Hookean materials, which depend only on the first invariant, lead to universal relations that conflict with experimental data, fail to display important mechanical behaviors (such as the Poynting effect in simple shear), and may not provide a satisfactory link with the mesoscale. However, the second invariant term is not a higher order strain contribution to the energy, which lead us to reflect on what is incomplete about neo-Hookean materials. Instead of the usual Cauchy–Green elastic formulation, we investigate this matter from the perspective of left stretch V=B and Bell strain EBell=V−I formulations. Invariants of these tensors offer a different interpretation than those of B and are linked to different classes of materials. The main example we adopt is a general isotropic energy quadratic in Bell strains, the quadratic-Biot material. Despite being quadratic in stretch like neo-Hookean, this material presents both the classic and reverse Poynting effect in simple shear, whose direction switches as a function of the constant conjugate to the second invariant of EBell. Its second normal stress also presents a local maximum as a function of the amount of shear, a transition that is not observed in a Mooney–Rivlin solid. Moreover, even the Varga model, linear in Bell strains, presents Poynting in simple shear, which poses the question of why this is not true for a model linear in Green–Lagrange strains. Pure torsion of a solid cylinder is also discussed, particularly how the behavior of the resultant axial force contrasts between the different formulations.

A constitutive model for fibrous tissues with cross-linked collagen fibers including dispersion — With an analysis of the Poynting effect

The present work deals with cross-links in collagenous tissues and proposes a planar continuum model for large strains to mechanically characterize, for example, the well-known stiffening effect associated with the presence of these cross-links. A key novelty of the paper is the consideration of dispersed fibers connected by randomly distributed cross-links. The model is essentially based on two mechanisms: (i) a fiber dispersion-induced cross-link dispersion and (ii) a fiber-independent cross-link dispersion connecting two arbitrary parallel fibers of the sample space. Within the framework of the generalized structure tensors, we derive appropriate invariants that enter the stored-energy function, taking into account the stiffness and relative orientation of the cross-links and the cross-link-fiber interaction. To illustrate the power of the proposed model, we first consider uniaxial tension and simple shear. We investigate the influence of different cross-link configurations on the stress response. In particular, we are interested in simple shear and the sign of the normal stress perpendicular to the shear planes, which is referred to as the Poynting effect. We show that the cross-links have a significant impact on the normal stress considered. This may provide a deeper insight into the microstructural mechanisms in semi-flexible biopolymer gels that are responsible for the tendency, in simple shear, of the top and bottom faces to approach each other. Finally, we investigate the Poynting effect that occurs in a circular hollow cylinder under pure torsion, i.e. how the axial normal force correlates with the cross-linked fibrous microstructure of the specimen.

Torsion of hydrogel cylinder with a chemo-mechanical coupled nonlinear elastic theory

In this paper, a chemo-mechanically coupled elastic model is proposed for hydrogel based on the classical physical constitutive theory. This model includes a hydrostatic pressure dependent constant, two linear Lamé constants and three second-order elastic constants, where all the constants are coupled with the chemical field. The influences of key chemical and physical parameters are investigated on the elastic constants, and the deformation of a cylinder are then analytically studied subject to torsion in solvent through linear and nonlinear approaches. Both methods may reproduce the conventional relation between the torque and twist angle of classical mechanics, which incorporate the effect of the chemically coupled shear modulus. The results reveal that a negative Poynting effect is demonstrated that the cylinder tends to shorten on twisting, and that the chemical potential has significant effect on the elastic constants and subsequently on the deformation and mechanical behavior of hydrogels. Further studies show that the Flory parameter and the degree of crosslinking also have important impact on the torsion of hydrogels.