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Effects of internal pore pressure on closed-cell elastomeric foams
Abstract
A micromechanics framework for porous elastomers with internal pore pressure (Idiart and Lopez-Pamies, 2012) is used together with an earlier homogenization estimate for elastomers containing vacuous pores (Lopez-Pamies and Ponte Castañeda, 2007a) to investigate the mechanical response and stability of closed-cell foams. Motivated by applications of technological interest, the focus is on isotropic foams made up of a random isotropic distribution of pores embedded in an isotropic matrix material, wherein the initial internal pore pressure is identical to the external pressure exerted by the environment (e.g. atmospheric pressure). It is found that the presence of internal pore pressure significantly stiffens and stabilizes the response of elastomeric foams, and hence that it must be taken into account when modeling this type of materials.
... The analysis of the known technological solutions has shown that the thermodynamic parameters of the porous structures production require clarification. The analysis of publications has shown that in full are described various constructive scheme insulation, in particular, the thermophysical properties of new heat insulating materials [1][2][3][4] and methods of their production [5][6][7]. The questions of effective insulation of fencing structures were considered in works [8][9][10]. ...
... According to the scheme for the consistent removal of moisture from the material marked singular points (1)(2)(3)(4)(5), corresponding to a specific species of connection of moisture with the body. Accordingly, the heating process can be divided into five stages: -the first stage (0-1) passes with the constant moisture content and ends when the temperature of the wet thermometer is reached on the surface of the material t t п м ; -the second stage (1-2) removes capillary moisture contained in macropores, whose binding energy is insignificant; at the end of the stage, the temperature in the center is equal to the temperature of the wet thermometer t t ц м , and the drying rate increases to the maximum; -the third stage (2-3) the material the duct moist macropores are removed; the average volume moisture content is reduced to the end of the stage to the value of the maximum hygroscopic . ...
... U мг , corresponding to the first critical point of К 1 , on the drying curve; the drying rate practically does not change; -the fourth stage (3)(4) is to remove of the capillary moisture of the micropore; the medium volume moisture content of the material is reduced to the maximum adsorption . U ма corresponding to the second critical point of К 2 on the drying curve; the drying rate falls; -the fifth (4-5) stage removes the most firmly bound moisture of the multimolecular and monomolecular adsorption, respectively; the average moisture content of the material varies from . ...
The work is devoted to theoretical and experimental research of thermophysical features of the creation of new porous heat insulating materials, precisely: research of thermodynamic parameters of the heating processes, swelling and drying of materials; substantiation of the choice of the raw mixture method formation and determination of the optimal energy parameters of the swelling process; development of mathematical models of material heat treatment process and methods of basic technological parameters determination; development of advanced technologies for thermal protection of buildings and power equipment. Experimentally determined dependencies of technological parameters of heat treatment of the raw material mixture in the discharge, its composition, which allows obtaining material with minimal thermal conductivity. Also, the resulting dependencies ensure to find the required mode of heat treatment for the given thermophysical properties. The experimental setup has been developed, which provided to determine the basic laws of heat transfer of porous material, on the basis of which data were obtained, which allow to carry out an estimation of heat transfer and exchange characteristics of the new dispersed porous material necessary for technological calculations. A complex mathematical model of the heat energy mode of the building was created, as well as a program for solving the equations of this model, which makes it possible to determine the basic energy characteristics.
... The second generalization involves accounting for the presence of both an internal pressure within the bubbles and of surface tension at the bubbles/rubber interfaces. By now it is also well established that even an internal bubble pressure as low as atmospheric pressure can have a significant effect on the response of suspensions of bubbles in soft rubbers [41,42]. Equally well established is the fact that the presence of surface tension can become dominant for very small bubbles [43,44]. ...
This paper presents an analytical and numerical study of the homogenization problem of suspen-sions of vacuous bubbles in viscoelastic rubber subject to finite quasistatic deformations. The focus is on the elementary case of bubbles that are initially equiaxed in shape and isotropically distributed in space and on isotropic incompressible rubber with Gaussian elasticity and constant viscosity. From an analytical point of view, asymptotic solutions are worked out in the limits: i) of small deformations, ii) of finite deformations that are applied either infinitesimally slowly or infinitely fast, and iii) when the rubber loses its ability to store elastic energy and reduces to a Newtonian fluid. From a numerical point of view, making use of a recently developed scheme based on a conforming Crouzeix-Raviart finite-element discretization of space and a high-order accurate explicit Runge-Kutta discretization of time, sample solutions are worked out for sus-pensions of initially spherical bubbles of the same (monodisperse) size under a variety of loading conditions. Consistent with a recent conjecture of Ghosh et al. (J. Mech. Phys. Solids 155:104544, 2021), the various asymptotic and numerical solutions indicate that the viscoelastic response of the suspensions features the same type of short-range-memory behavior-in contrast with the generally expected long-range-memory behavior-as that of the underlying rubber, with the distinctive differences that their effective elasticity is compressible and their effective viscosity is compressible and nonlinear. By the same token, the various solutions reveal a simple yet accurate analytical approximation for the macroscopic viscoelastic response of the suspensions under arbitrary finite quasistatic deformations.
... The first of these is that the boundary conditions between the spheres and the matrix may not be ideal, i.e., the outer shell walls and the matrix may not be in ideal contact as is assumed in any theoretical analysis. The second is that the (potentially) entrained gas has an impact [48]. A third reason is that there could be a persistent gradient in the microsphere (positional) distribution in samples due to manufacturing, despite efforts to control gradients with thixotropic additives. ...
Due to their highly favourable thermal, mechanical, and acoustic properties in extreme environments, syntactic foams have emerged as a popular material choice for a broad variety of applications. They are made by infiltrating a polymeric matrix, in either a glassy or polymeric state, with hollow microspheres made from a wide range of materials. In particular, hollow plastic microspheres, such as Expancel made by Nouryon have recently emerged as an important filler medium, with the resulting all-polymer composites taking on excellent damage tolerance properties, strong recoverability under large strains, and very favourable energy dissipation characteristics. There is however, a near-complete absence of statistical information on the diameter and shell-thickness distributions of these microspheres. In this work, using X-Ray computed tomography, focused ion beam, and scanning electron microscopy, we report on these quantities and observe the spatial distribution of microspheres within a syntactic foam. We then employ this data to predict the effective stress-strain response of the foams at small strains, using both analytical micromechanical methods and computational finite element methods, where the latter involves the construction of appropriate representative volume elements. We find excellent agreement between the predictions of the effective Young's modulus and Poisson ratio from the computational and theoretical methods and good agreement between these predictions and experimental results for the macroscopic response.
... Due to the fabrication process and/or environment of operation, the pores in closed-cell porous elastomers typically contain a gaseous substance that may exert a significant internal pressure on the surrounding elastomeric matrix. The formulation introduced in Lopez-Pamies et al., 2012) allows one to directly transcribe the proposed macroscopic constitutive response (20) of a given porous elastomer with vacuous pores to the macroscopic constitutive response of the same porous elastomer when the underlying pores are pressurized internally. ...
An approximate homogenization solution is put forth for the effective stored-energy function describing the macroscopic elastic response of isotropic porous elastomers comprised of incompressible non-Gaussian elastomers embedding equiaxed closed-cell vacuous pores. In spite of its generality, the solution — which is constructed in two successive steps by making use first of an iterative technique and then of a nonlinear comparison medium method — is fully explicit and remarkably simple. Its key theoretical and practical features are discussed in detail and its accuracy is demonstrated by means of direct comparisons with novel computational solutions for porous elastomers with four classes of physically relevant isotropic microstructures wherein the underlying pores are: (i) infinitely polydisperse in size and of abstract shape, (ii) finitely polydisperse in size and spherical in shape, (iii) monodisperse in size and spherical in shape, and (iv) monodisperse in size and of oblate spheroidal shape.
... We take the matrix phase in the electret to be an ideal elastic dielectric with constant permittivity ε m and elasticity modulus µ m . To account for their internal pressure [17,27], we also take the airfilled pores to be ideal elastic dielectrics with constant permittivity ε p and elasticity modulus µ p and, accordingly, write the sole component (recall that in this example N = 1) of the local permittivity, elasticity, and electrostriction tensors (1) as the scalar functions ...
This paper presents the derivation of the homogenized equations for the macroscopic response of elastic dielectric composites containing space charges (i.e., electric source terms) that oscillate rapidly at the length scale of the microstructure. The derivation is carried out in the setting of small deformations and moderate electric fields by means of a two-scale asymptotic analysis. Two types of rapidly oscillating space charges are considered: passive and active. The latter type corresponds to space charges that appear within the composite in response to externally applied electrical stimuli, while the former corresponds to space charges that are present within the composite from the outset. The obtained homogenized equations reveal that the presence of (passive or active) space charges within elastic dielectric composites can have a significant and even dominant effect on their macroscopic response, possibly leading to extreme behaviors ranging from unusually large permittivities and electrostriction coefficients to metamaterial-type properties featuring negative permittivities. These results suggest a promising strategy to design deformable dielectric composites|such as electrets and dielectric elastomer composites|with exceptional electromechanical properties.
... The chemical blowing agent influenced the structure and mechanical properties of ethylene propylene diene monomer (EPDM) foam by increasing the number of cell structures, increasing the porosity, lowering the thermal conductivity and increasing the concentration of the blowing agent for optimum interfacial adhesion (Yamsaengsung and Sombatsompop, 2009). An investigation of the mechanical response and stability of closed-cell foams found that the presence of internal pore pressure significantly stiffens and stabilizes the response of elastomeric foams (Oscar et al., 2012). Nabil et al. (2014) reported the effect of the accelerators and vulcanizing system on the thermal stability of natural rubber/ recycled EPDM blends with four types of accelerators: n-tert-butyl-2-benzothiazylsulphonamide (TBBS), n-cyclohexylbenzothiazylsulphenamide (CBS), disulphide tetramethylthiuram (TMTD) and mercaptobenzothiazol (MBT). ...
An experiment was carried out to obtain the optimum natural rubber thermal insulation for a refrigeration and air conditioning system. Thermal insulation not only adds value to the rubber, but also develops an improved new product from natural rubber. Concentrations of benzenesulfonyl hydrazide (BSH) blowing agent at 2, 4, 6, 8 and 10 parts per hundred of rubber (phr) were used to study the effect of the BSH concentration on the mechanical properties, swelling and thermal conductivity of thermal insulation which were evaluated using the American Society for Testing and Materials (ASTM) standards (ASTM D412, ASTM D471 and ASTM C518, respectively). The rubber compound was prepared using a two-roll mill and expanding in a hot mould at 150°C. The results showed that both the average values of the tensile modulus and tensile strength were reduced by 25%. The average value of elongation at break not only increased by 33% before thermal aging, but also reduced by 33% after thermal aging. The maximum value of swelling was 324%. Moreover, the lowest value of thermal conductivity was 0.040 W/m/K. Therefore, the optimum concentration of the BSH was 6 phr which had optimum properties for thermal insulation.
... In [11], research is described on the influence of pressure in pores on elastomers of closed porosity. Pressure changes in pores are considered under different hydrostatic loads, with a conclusion that pressure can significantly change the macroscopic reaction and stability of closed porosity elastomers. ...
The study considers the Gibbs energy change at the time of pore nucleation. An equation is suggested for describing the critical radius of a pore nucleus. Since it is directly proportional to the surface tension, pores are formed in places with density irregularities or fluctuations. An analysis has revealed conditions for a pore to exist, the minimum work for a pore to nucleate, the time necessary for a pore to appear, and the likelihood of a pore nucleation. The undertaken laboratory tests concern the pore formation rate and the pore growth rate in aluminous materials. The study has determined the general dependencies of wetness changes in the material under its heat treatment and the dynamics of porosity changes in an intumescent material. It allows distinguishing between three stages of change in the number of pores in an intumescent alumina-based material: a stage of a declining number of generated pores, a stage of equable reduction of the number of pores, and a stage of pores overgrowth. The obtained results are applicable to such thermal insulation materials as expanded clay and refractory materials as well as other aluminous materials that are produced by swelling. The conducted experiments have identified the main patterns of changes in the number of pores and the total porosity in aluminous materials when they are heat-treated. It has consequently helped develop a system of equations that describe changes in the porosity of an alumina-based material. The devised equations suggest that the number of pores is directly proportional to the heat treatment temperature as well as to the difference between the surrounding pressure and the critical pressure of a pore. Besides, this system of equations can help predict the number of pores in an intumescent material, which facilitates control over thermophysical properties of the material. The research findings are very important for developing new high-intensity technologies in various industries, in particular for improving the existing production technology of thermal insulation materials based on alumina. Besides, the obtained results can help create new insulating materials.
... For this reason, closed-cell foams such as the one described in this paper are used in the construction sector. Though closed-cell foams have strut structures similar to open-cell foams, the cell membrane and the presence of enclosed gas inhibits the buckling of struts under compression (Gong and Kyriakides, 2005;Lopez-Pamies, Castañeda, and Idiart, 2012). ...
Modern foam-filled composite products have the advantage of low weight while
providing improved shock absorption and thermal-acoustic properties. Recent
investigations of foam-filled thin metal open sections have shown that these
composites also have excellent structural properties. However, when optimizing
new foam-filled products for structural applications, the material behaviour of
each constituent material has to be known before simulations can be performed
and potential failure predicted. This paper presents the results of mechanical
characterization tests of a low density polyurethane (PU) foam that is used in
foam-metal composite structural applications. Uniaxial tension and compression,
triaxial compression, simple shear, and fracture toughness tests on the PU foam
are described. These tests indicate that the foam is strongly anisotropic and
exhibits a significant amount of variation between samples.
... While it is evident that the fluid phase plays a non negligible role in the behavior of liquid filled closed-cell systems, it has recently been shown through micro-mechanical analyzes that the internal pore pressure exerted by air on the internal wall cavities can also significantly alter the macroscopic response of closed-cell elastomeric foams, see Lopez-Pamies et al., 2012). It becomes then evident that this fact must be taken into account within modeling tools. ...
The main purpose of this paper is the formulation of a modeling framework for closed-cell porous materials by means of the nowadays classical approach of poromechanics. The cavities being saturated with a single fluid phase, Biot's theory drastically simplifies since no fluid diffusion is present in this case. Nevertheless, the fluid contribution to the macroscopic behavior is still present and the fluid mass conservation controls the pore pressure that contributes to the total stress at the macro-scale. A constitutive law for the saturating fluid is introduced that encompasses both ideal gas and incompressible fluids as particular cases. The approach is built around the unified framework of continuum thermodynamics which is crucial in setting the convenient form for the state laws. As the finite strain range is of concern, the modeling strongly depends on the Eulerian porosity law adopted in the spatial configuration. Two model examples are discussed with parametric studies to show the effectiveness of the proposed approach.
The present work is a thorough study on the elastic instabilities of flexible polymeric foams under compression. Tessellation-based topologies are employed to generate micromechanical models of open-cell random foams with controlled morphologies. Solid distribution on the resulting topologies is assigned based on a closed-form expression for the relative density that accounts for material overlap at the nodes. Simulations of foams with different microstructures are used to first reproduce experimentally obtained results, and subsequently to elucidate the connection between microstructure and the corresponding buckling mode. Compression of an anisotropic foam along the rise and transverse directions displays two distinct buckling modes that have previously been reported experimentally: a long-wavelength instability corresponding to a limit-load type response, and a microscopic instability that produces a monotonically increasing nonlinear response. The presence of large cell size distributions, i.e. polydispersity, is shown to also lead to a monotonic response, which is associated with the increased compaction of the largest cells that are present within the domain. The agreement between experimental and numerical responses is very favorable. The critical stresses are subsequently calculated as a function of key microstructural characteristics including foam density, anisotropy, cell-size distributions and ligament uniformity. The results indicate that a strong amount of anisotropy is needed for the transition from a microscopic instability to the macroscopic one while polydisperse foams produce a stable monotonic response, even in the presence of cell anisotropy.
Even without the aid of muscle, plant tissue drives large, forceful motion via osmosis-driven fluid flow. Hydrogels are well-known synthetic materials that mimic this osmotic mechanism to achieve large swelling deformations. However, hydrogels can be limited by a loss of stiffness as their swelling increases. Here we demonstrate that a synthetic plant tissue analog (PTA) can mimic the closed-cell structure and osmotic actuation of non-vascular plant tissue, enabling the emergence of turgor-pressure-induced stiffness and leading to more forceful swelling deformations. PTAs consist of micrometer-sized saltwater droplets embedded within thin, highly stretchable, selectively permeable polydimethylsiloxane (PDMS) walls. When immersed in water, PTAs reach a state of equilibrium governed by the initial osmolyte concentration (higher produces more swelling) and cell wall mechanical response (stiffer and less stretchable yields less swelling). Given these behaviors, PTAs represent an alternate class of aqueous, autonomous synthetic materials that, like hydrogels, may benefit biomedical applications.
Determination of the porosity, structural characteristics of pores, and gas pressure in closed pores is the most important part of assessing physical and mechanical properties of materials. The internal pressure inside the pore can be used in estimating the level of strength reliability of the porous volume of the product to optimize the technological processes of product manufacturing, control their structure and properties, and avoid the formation of cracks at the boundaries of the particles consisting the material. We present a method for calculating the internal pressure in a spherical pore that has arisen in the material of a product obtained using powder metallurgy or additive technologies. The proposed procedure for measuring internal pressure in a pore consists in application of an external pressure to the product, measurements of the displacements of the points on the pore surface, and calculation of the internal pressure from the difference between the displacements. In this case, the known solutions of the problem of the theory of elasticity regarding the deformation of a spherical cavity located in the center of a spherical hollow ball are used. The results obtained can be used to assess the properties and structure of the products obtained by additive technology and methods of powder metallurgy, as well as to improve the technology of their manufacture.
This review focuses on the novel features of nonlinear elasticity for a range of gels and elastomers that were recently revealed through experiments using various types of strain such as uniaxial and biaxial stretching. Particular emphasis is placed on the magnitude of the cross-effect of strains in different directions which can be characterized by unequal biaxial stretching. The studied materials include (1) markedly swollen hydrogels with a water content of 98%, (2) tetra-arm poly(ethylene glycol) (Tetra-PEG) gels with nearly uniform network structures without entanglement couplings of network strands, (3) slide-ring gels with movable crosslinks along network strands and (4) elastomer foams with low densities of polymer solids. The magnitude of the cross-effect of strains reflects the structural features of networks and crosslinks as well as bulk compressibility for each material. We also summarize recent results on strain-driven swelling and the accompanying force reduction phenomena under various types of stretching. Remaining issues to be investigated are presented on the basis of existing results.
Nonlinear stress-strain behavior of the elastomer foams of high porosity is investigated in several types of biaxial tension, and uniaxial tension and compression. The values of Poisson's ratio for the open- and closed-cell foams are estimated to be about 0.24 almost independently of the imposed tensile strain, indicating that the foams undergo finite volume increase under tension. Unequal biaxial tensile experiments reveal no explicit cross-effect of strains between different axes in the elastomer foams: The deduced strain energy density function (W) has no appreciable contribution from the term of I2 which is the second invariant of deformation gradient tensor representing the explicit cross-effect of strains, while in general W for conventional non-cellular elastomers involves finite contributions from I2-term. No explicit cross-effect of strains result in a unique feature in biaxial tensile behavior that the effect of the strain in one direction on the stress in the other direction is considerably small. These features in tensile behavior are commonly observed for the open- and closed-cell foams. In contrast, the cell type has a pronounced effect on the compression behavior accompanying the buckling and collapsing processes of the cells, as observed in earlier studies. The stress-strain relations in compression accompanying the cell buckling are markedly different from the expectation of W obtained from the data of biaxial and uniaxial tension where the cell bucking is not possible.
Three dimensional (3D) cubic models with spherical pores ranged as Face-Centered Cubic (FCC) lattices are constructed to simulate the microstructures of rubber foams with various relative densities. The Mooney-Rivlin strain energy potential model is adopted to characterize the hyperelasticity of the constituent solid from which the foams are made. Large compressive deformations of closed-celled rubber foams are calculated by the iterative algorithm. Numerical results show that with the decreasing of foam relative densities, the effects of air pressures in cells on foam compressive stresses increase. When the ratio of initial Yangs modulus of cell material to the initial air pressure in cells reaches 2 order of magnitude, the influence of air pressures in cells can neglect.
In this Note, we propose a new hyperelastic model for rubber elastic solids applicable over the entire range of deformations. The underlying stored-energy function is a linear combination of the I1-based strain invariants φ(I1;α)=(I1α−3α)/(α3α−1), where α is a real number. The predictive capabilities of the model are illustrated via comparisons with experimental data available from the literature for a variety of rubbery solids. In addition, the key theoretical and practical strengths of the proposed stored-energy function are discussed.
Making use of the particulate microgeometries of Idiart (J.Mech. Phys. Solids 56:2599–2617, 2008), we derive an exact and closed-form result for the macroscopic response of porous Neo-Hookean solids with random microstructures. The stored-energy function is a solution to a Hamilton-Jacobi equation with initial porosity and macroscopic
deformation gradient playing the roles of time and space. The main theoretical and practical aspects of the result are discussed.
The finite deformation of porous elastomers was studied by means of the numerical simulation of a representative volume element of the microstructure. The size and the discretization of the volume element were selected to obtain an exact response (to a few percent) of the plane-strain deformation of a material made up of a random and isotropic dispersion of circular cylindrical voids embedded in an incompressible neo-Hookean matrix. Three different loading modes (in-plane isotropic deformation, uniaxial elongation, and uniaxial traction) were simulated, and the corresponding stress - strain curves as well as the evolution of the microstructure with deformation were presented for materials with an initial porosity of 5, 10 and 20%. The numerical results were compared with the available homogenization models for the finite deformation of porous elastomers. It was found that the second-order estimate with field fluctuations of Lopez-Pamies and Ponte Castaneda led to very good approximations to the numerical results in most cases, and significant differences were only found under conditions of highly constrained deformation. The sources of these differences were discussed in the light of the changes in the microstructure provided by the numerical simulations.
Peer Reviewed http://deepblue.lib.umich.edu/bitstream/2027.42/46162/1/205_2004_Article_BF00380256.pdf
This work provides a means of accounting for the presence of pressurized cavities on the overall response of elastomeric solids undergoing large deformations. The main idea is to refer the kinematics to a stress-free configuration and to express the overall response of the elastomer with pressurized cavities in terms of its overall response when the cavities are vacuous. This is achieved via a change of variables valid whenever the common assumption of incompressibility is used for the elastomeric matrix. The result permits then to incorporate straightforwardly the effect of internal pressure on any micromechanical model already available for elastomeric solids with vacuous cavities. The resulting models account for constitutive and geometric nonlinearities as well as for deformation-dependent internal pressure concomitant with large deformations. Sample results for isotropic porous rubbers under plane-strain conditions are provided and discussed.
Ethylene–propylene rubber (EPDM) and nitrile–butadiene rubber (NBR) composites having carbon black, silica, and no fillers were exposed to hydrogen gas at a maximum pressure of 10MPa; then, blister tests and the measurement of hydrogen content were conducted. The hydrogen contents of the composites were proportional to the hydrogen pressure, i.e., the behavior of their hydrogen contents follows Henry's law. This implies that hydrogen penetrates into the composite as a hydrogen molecule. The addition of carbon black raised the hydrogen content of the composite, while the addition of silica did not. Based on observations, the blister damages of composites with silica were less pronounced, irrespective of the hydrogen pressures. This may be attributed to their lower hydrogen content and relatively better tensile properties than the others.
In Part I of this paper, we developed a homogenization-based constitutive model for the effective behavior of isotropic porous elastomers subjected to finite deformations. In this part, we make use of the proposed model to predict the overall response of porous elastomers with (compressible and incompressible) Gent matrix phases under a wide variety of loading conditions and initial values of porosity. The results indicate that the evolution of the underlying microstructure—which results from the finite changes in geometry that are induced by the applied loading—has a significant effect on the overall behavior of porous elastomers. Further, the model is in very good agreement with the exact and numerical results available from the literature for special loading conditions and generally improves on existing models for more general conditions. More specifically, we find that, in spite of the fact that Gent elastomers are strongly elliptic materials, the constitutive models for the porous elastomers are found to lose strong ellipticity at sufficiently large compressive deformations, corresponding to the possible onset of “macroscopic” (shear band-type) instabilities. This capability of the proposed model appears to be unique among theoretical models to date and is in agreement with numerical simulations and physical experience. The resulting elliptic and non-elliptic domains, which serve to define the macroscopic “failure surfaces” of these materials, are presented and discussed in both strain and stress space.
In theories of the overall mechanical behaviour of polycrystals, composites, or other heterogeneous media, the transition from microscopic to macroscopic levels depends on finding connexions between suitably defined macro-variables and volume averages of microfields over a representative sample. Some connexions are established here for unrestricted deformation and internal rotations, without regard to constitutive properties. General measures of stress and finite strain are considered, together with objective fluxes of stress. The comparative advantages of such variables are assessed, more especially in relation to the averaging of tensor products. A bilinear differential form, akin to Poincare's integral invariant in Hamiltonian dynamics, plays an important role in the analysis.
A micromechanics framework for the development of continuum-level constitutive models for the large-strain deformation of porous hyperelastic materials is presented. A kinematically admissible deformation field is assumed which enables the derivation of a strain energy density function for the porous material. The strain energy density function depends on the properties of the incompressible hyperelastic matrix material, the initial level of porosity, and the macroscopic deformation. Differentiation of the strain energy density function, with respect to deformation, provides an expression for the stress–strain behavior of the porous hyperelastic material. Example calculations are carried out for porous hyperelastic materials with a Neo–Hookean matrix. The constitutive model is used to predict the stress–strain behavior of the pore-containing matrix as a function of initial porosity and macroscopic loading conditions. Predictions of the dependence of the small-strain elastic response on porosity are compared to various estimates of effective elastic moduli for porous materials found in the literature. Constitutive model predictions of the small to large-strain deformation behavior compare well with results from numerical three-dimensional micromechanical multi-void cell models.
An acoustic emission (AE) method was used to detect internal fracture of sealing rubber material by high pressure hydrogen decompression. According to preliminary results, AE signals were hardly detected during the tensile test in air, but many signals were detected during the static crack growth test in air. AE measurement of hydrogen exposed specimens was also conducted. With the increase in number and size of internal cracks generated due to high pressure hydrogen decompression, the AE event count and amplitude also increased. In addition, AE signals were generated from the specimen exposed to hydrogen gas at 0.7 MPa, although no cracks were initiated. It is inferred that these AE signals were generated due to bubbles, which are mechanically reversible cavities formed by dissolved hydrogen molecules after decompression.
In this paper, the mechanical behaviour of an unfilled silicone rubber is analysed. Firstly, silicone samples were subjected to five homogeneous tests: tensile, pure shear, compression, plane strain compression and bulge tests. During the tests, full-field measurements of the strain on the surface of deformed samples were obtained using a Digital Image Correlation technique. Results show that the Mullins effects and hysteresis, as well as strain rate sensitivity, can be considered as negligible. Results also emphasise the influence of the loading path. Then, five well-known hyperelastic models (neo-hookean, Mooney, Gent, Haines and Wilson and Ogden models) were fitted to the experimental data. Finally, a heterogeneous test was realised by stretching a silicone plate sample containing holes. Finite element simulations of this experiment have been performed with the hyperelastic models. The comparison of experimental and numerical results emphasises the importance of the choice of the hyperelastic modelling in the simulation of strain fields.
An experimental study is described of the formation and growth of gas bubbles in crosslinked elastomers. A critical condition for bubble formation is found to hold in most cases: The gas supersaturation pressure must exceed 5G/2, where G is the shear modulus of the elastomer. The kinetics of bubble growth are shown to be in good accord with a simple diffusion‐controlled growth relation for a variety of gases, elastomers, temperatures, and pressures. The number of bubbles depends strongly upon the degree of supersaturation above the critical level. This effect is attributed partly to kinetic factors and partly to the presence initially of internal holes of a range of sizes.
The purpose of this paper is to provide homogenization-based constitutive models for the overall, finite-deformation response of isotropic porous rubbers with random microstructures. The proposed model is generated by means of the “second-order” homogenization method, which makes use of suitably designed variational principles utilizing the idea of a “linear comparison composite.” The constitutive model takes into account the evolution of the size, shape, orientation, and distribution of the underlying pores in the material, resulting from the finite changes in geometry that are induced by the applied loading. This point is key, as the evolution of the microstructure provides geometric softening/stiffening mechanisms that can have a very significant effect on the overall behavior and stability of porous rubbers. In this work, explicit results are generated for porous elastomers with isotropic, (in)compressible, strongly elliptic matrix phases. In spite of the strong ellipticity of the matrix phases, the derived constitutive model may lose strong ellipticity, indicating the possible development of shear/compaction band-type instabilities. The general model developed in this paper will be applied in Part II of this work to a special, but representative, class of isotropic porous elastomers with the objective of exploring the complex interplay between geometric and constitutive softening/stiffening in these materials.
The present work is an in-depth study of the connections between microstructural instabilities and their macroscopic manifestations—as captured through the effective properties—in finitely strained porous elastomers. The powerful second-order homogenization (SOH) technique initially developed for random media, is used for the first time here to study the onset of failure in periodic porous elastomers and the results are compared to more accurate finite element method (FEM) calculations. The influence of different microgeometries (random and periodic), initial porosity, matrix constitutive law and macroscopic load orientation on the microscopic buckling (for periodic microgeometries) and macroscopic loss of ellipticity (for all microgeometries) is investigated in detail. In addition to the above-described stability-based onset-of-failure mechanisms, constraints on the principal solution are also addressed, thus giving a complete picture of the different possible failure mechanisms present in finitely strained porous elastomers.
On the overall response of elastomeric solids with pressurized cavities. Special issue on ''Recent Advances in Micromechanics of Materials A new I 1 -based hyperelastic model for rubber elastic materials
- M I Idiart
- O Lopez-Pamies
Idiart, M.I., Lopez-Pamies, O., 2012. On the overall response of elastomeric solids with pressurized cavities. Special issue on ''Recent Advances in Micromechanics of Materials''. C.R. Mec. doi:10.1016/j.crme.2012.02.018. Lopez-Pamies, O., 2010. A new I 1 -based hyperelastic model for rubber elastic materials. C.R. Mec. 338, 3–11.