Hyperelastic Multiphase Porous Media with Strain-Dependent Retention Laws

This article presents poroelastic laws accounting for a retention behavior dependent also on porosity, as suggested by experimental evidence. Motivated by the numerical formulation of the corresponding boundary-value problem presented in a companion article, these constitutive equations employ displacements and fluid pressures as primary variables. The thermodynamic admissibility of the proposed rate laws for stress and fluid contents is assessed by means of symmetry and Maxwell conditions obtained from the Biot theory. In the case of strain-dependent saturation, the two elasticity tensors describing the drained response in saturated and unsaturated conditions, respectively, are proven to be in general not coincident, with their difference depending on capillary pressure and porosity. Furthermore, it is shown that besides the stress decomposition proposed by Coussy, also the stress split proposed by Lewis and Schrefler is consistent with the Biot framework. The former decomposition is obtained for retention laws depending only on capillary pressure, as expected. The Lewis–Schrefler split is proven to be consistent with retention models depending also on porosity. In these developments, the compressibility of all the phases is taken into account, in order to assess the thermodynamic consistency of an extension of the Biot’s coefficient to partially saturated anisotropic porous media.     

Torsional Swelling of a Hyperelastic Tube with Helically Wound Reinforcement

This paper examines the combination of radial deformation with torsion for a circular cylindrical tube composed of a transversely isotropic hyperelastic material subject to finite deformation swelling. The stored energy function involves separate matrix and fiber contributions such that the fiber contribution is minimized when the fiber direction is at a natural length. This natural length is not affected by the swelling. Hence swelling preferentially expands directions that are orthogonal to the fiber. The swelling itself is described via a swelling field that prescribes the local free volume at each location in the body. Such a treatment is a relatively simple generalization of the conventional incompressible theory. The direction of transverse isotropy associated with the fiber reinforcement is described by a helical winding about the tube axis. The swelling induced preferential expansion orthogonal to this direction induces the torsional aspect of the deformation. For a specific class of strain energy functions we find that the twist increases with swelling and approaches a limiting asymptotic value as the swelling becomes large. The fibers reorient such that fibers at the inner portion of the tube assume a more circumferential orientation whereas, at least for small and moderate swelling, the fibers in the outer portion of the tube assume a more axial orientation. For large swelling the fibers in the outer portion of the tube reorient beyond the axial orientation, and so are described by helices with orientation in the opposite sense to that in the reference configuration.      

Constitutive Equations of an Isotropic Hyperelastic Body

Stress—strain equations for an isotropic hyperelastic body are formulated. It is shown that the strain energy density whose gradient determines stresses can be defined as a function of two rather than three arguments, namely, strain–tensor invariants. In the case of small strains, the equations become relations of Hooke's law with two material constants, namely, shear modulus and bulk modulus.     

Theory of Deformation of Isotropic Hyperelastic Bodies

Deformation of isotropic hyperelastic bodies is considered. The solution of the problem of gravitational compression of a sphere is given as an example of application of the theory.     

CAVITATION BIFURCATION FOR COMPRESSIBLE ANISOTROPIC HYPERELASTIC MATERIALS

I. INTRODUCTION The cavitation bifurcation problem, sudden formation and growth of voids in solid materials, haslong attracted much attention because of the fundamental role it plays in the local failure and fractureof materials. For hyperelastic materi…     

Modelling Slight Compressibility for Hyperelastic Anisotropic Materials

In order to avoid the numerical difficulties in locally enforcing the incompressibility constraint using the displacement formulation of the Finite Element Method, slight compressibility is typically assumed when simulating the mechanical response of nonlinearly elastic materials. The current standard method of accounting for slight compressibility of hyperelastic materials assumes an additive decomposition of the strain-energy function into a volumetric and an isochoric part. A new proof is given to show that this is equivalent to assuming that the hydrostatic stress is a function of the volume change only and that uniform dilatation is a possible solution to the hydrostatic stress boundary value problem, with therefore no anisotropic contribution to the mechanical response. An alternative formulation of slight compressibility is proposed, one that does not suffer from this defect. This new model generalises the standard model by including a mixed term in the volume change and isochoric response. Specific models of slight compressibility are given for isotropic, transversely isotropic and orthotropic materials.     

On thermoelastic dielectrics

Constitutive equations for a linear thermoelastic dielectric are derived from the energy balance equation assuming dependence of the stored energy function on the strain tensor, the polarization vector, the polarization gradient tensor and entropy. A method is indicated for constructing a hierarchy of constitutive equations for materials with arbitrary symmetry by introducing various thermodynamic potentials. Maxwell's relations are constructed for the thermodynamic potential W^L. The entropy inequality is used to obtain stability conditions for an elastic dielectric in equilibrium under prescribed boundary constraints. Frequencies are explicitly determined for a plane wave propagating along the x₁-axis in an infinite centro-symmetric isotropic thermoelastic dielectric.     

Modeling viscoelastic dielectrics

Dielectric elastomers, as an important category of electroactive polymers, are known to have viscoelastic properties that strongly affect their dynamic performance and limit their applications. Very few models accounting for the effects of both electrostatics and viscoelasticity exist in the literature, and even fewer are capable of making reliable predictions under general loads and constraints. Based on the principles of non-equilibrium thermodynamics, this paper develops a field theory that fully couples the large inelastic deformations and electric fields in deformable dielectrics. Our theory recovers existing models of elastic dielectrics in the equilibrium limit. The mechanism of instantaneous instability, which corresponds to the pull-in instability often observed on dielectric elastomers, is studied in a general non-equilibrium state. The current theoretical framework is able to adopt most finite-deformation constitutive relations and evolution laws of viscoelastic solids. As an example, a specific material model is selected and applied to the uniform deformation of a dielectric elastomer. This model predicts the stability criteria of viscoelastic dielectrics and its dependence on loading rate, pre-stress, and relaxation. The dynamic response, as well as the hysteresis behavior of a viscoelastic dielectric elastomer under cyclic electric fields, is also studied.     

Simple Torsion of Isotropic, Hyperelastic, Incompressible Materials with Limiting Chain Extensibility

The purpose of this research is to investigate the simple torsion problem for a solid circular cylinder composed of isotropic hyperelastic incompressible materials with limiting chain extensibility. Three popular models that account for hardening at large deformations are examined. These models involve a strain-energy density which depends only on the first invariant of the Cauchy–Green tensor. In the limit as a polymeric chain extensibility tends to infinity, all of these models reduce to the classical neo-Hookean form. The main mechanical quantities of interest in the torsion problem are obtained in closed form. In this way, it is shown that the torsional response of all three materials is similar. While the predictions of the models agree qualitatively with experimental data, the quantitative agreement is poor as is the case for the neo-Hookean material. In fact, by using a global universal relation, it is shown that the experimental data cannot be predicted quantitatively by any strain-energy density which depends solely on the first invariant. It is shown that a modification of the strain energies to include a term linear in the second invariant can be used to remedy this defect. Whether the modified strain-energies, which reflect material hardening, are a feasible alternative to the classic Mooney–Rivlin model remains an open question which can be resolved only by large strain experiments. This revised version was published online in August 2006 with corrections to the Cover Date.     

Electroconvection of liquid dielectrics

Ponderomotive forces, which are responsible for electroconvection, were investigated in relation to the properties of the liquid and the strength of the electric field of an infinite charged plate. The obtained solutions were used to obtain a parameter of the relative intensification of heat transfer in various dielectrics in an external electrostatic field.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 13–18, July–August, 1971.     

Finite Anticlastic Bending of Hyperelastic Solids and Beams

This paper deals with the equilibrium problem in nonlinear elasticity of hyperelastic solids under anticlastic bending. A three-dimensional kinematic model, where the longitudinal bending is accompanied by the transversal deformation of cross sections, is formulated. Following a semi-inverse approach, the displacement field prescribed by the above kinematic model contains three unknown parameters. A Lagrangian analysis is performed and the compressible Mooney-Rivlin law is assumed for the stored energy function. Once evaluated the Piola-Kirchhoff stresses, the free parameters of the kinematic model are determined by using the equilibrium equations and the boundary conditions. An Eulerian analysis is then accomplished to evaluating stretches and stresses in the deformed configuration. Cauchy stress distributions are investigated and it is shown how, for wide ranges of constitutive parameters, the obtained solution is quite accurate. The whole formulation proposed for the finite anticlastic bending of hyperelastic solids is linearized by introducing the hypothesis of smallness of the displacement and strain fields. With this linearization procedure, the classical solution for the infinitesimal bending of beams is fully recovered.     

Hyperelastic model for polyacrylamide-gelatin double network shape-memory hydrogels

A shape-memory double network hydrogel consists of two polymer networks: a chemically crosslinked primary network that is responsible for the permanent shape and a physically crosslinked secondary network that is used to fix the temporary shapes. The formation/melting transition of the secondary network serves as an effective mechanism for the double network hydrogel's shape-memory effect. When the crosslinks in the secondary network are dissociated by applying an external stimulus, only the primary network is left to support the load. When the secondary network is re-formed by removing the stimulus, both the primary and secondary networks support the load. In the past, models have been developed for the constitutive behaviors of double network hydrogels, but the model of shape-memory double network hydrogels is still lacking. This work aims to build a constitutive model for the polyacrylamide-gelatin double network shape-memory hydrogel developed in our previous work. The model is first calibrated by experimental data of the double network shape-memory hydrogel under uniaxial loading and then employed to predict the shape-fixing performance of the hydrogel. The model is also implemented into a three-dimension finite element code and utilized to simulate the shape-memory behavior of the double network hydrogel with inhomogeneous deformations related to applications.

Graphic abstract

A shape-memory double network hydrogel consists of a chemically crosslinked primary network and a physically crosslinked secondary network. The formation/melting transition of the secondary network serves as an effective mechanism for the shape-memory effect of the double network hydrogel. This work built a constitutive model for the polyacrylamide-and-gelatin double network shape-memory hydrogel. The model was first calibrated by experimental data and then employed to predict the shape-fixing performance of the hydrogel. The model was also implemented into a three-dimension finite element code and utilized to simulate the shape-memory behavior of double network hydrogel in complex geometries.

     

Radiation contamination of dielectrics irradiated with a fast-electron flux

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 11–17, May–June, 1991.     

Measuring Hyperelastic Properties of Hydrogels Using Cavity Expansion Method

Experimental Mechanics - Numerous methods have been proposed to measure the mechanical properties of hyperelastic materials such as hydrogels. Common techniques, such as tension, compression, and...     

An Invariant-Based Ogden-Type Model for Incompressible Isotropic Hyperelastic Materials

The Ogden model for an incompressible isotropic hyperelastic material is versatile enough to match complicated data for rubber-like materials at large deformations. However, the tensorial expression for the Cauchy stress in the Ogden model requires determination of the eigenvalues and eigenvectors of the left Cauchy-Green deformation tensor \(\mathbf{B}\). The objective of this paper is to propose an invariant-based Ogden-type model for isotropic incompressible hyperelastic materials. The strain energy function in this new model depends on classical invariants of \(\mathbf{B}\) and the Cauchy stress tensor can be expressed directly in terms of the tensor \(\mathbf{B}\) without need for its spectral form. Examples show that this new Ogden-type model retains the versatility of the original Ogden model in characterizing material response.