Julie Diani

• PhD
• Characterizing and modeling the mechanical behavior of polymers at French National Centre for Scientific Research

The constitutive equations of several finite strain viscoelastic models, based on the multiplicative decomposition of the deformation gradient tensor and formulated in a thermodynamically consistent framework, are reviewed to demonstrate their similarities and differences. The proposed analysis shows that dissipation formulations, which may appear...

Brittle material Mode I fracture may be characterized by the double cleavage drilled compression test. For linear elastic materials, the critical energy release rate, or fracture toughness, can be estimated simply using the linear elastic fracture mechanics. For other types of constitutive behavior, the material parameter has to be determined with...

We investigate numerically via finite element (FE) simulations and analytically the nonlinear behavior of a soft matrix comprising a large volume fraction (up to 55%) of monodisperse spherical inclusions, which can be either rigid particles or voids. To address the issue of severe mesh distortion at large strains, we employ a successive remeshing a...

In this work, damping properties of bending viscoelastic thin structures are enhanced by topology optimization. Homogeneous linear viscoelastic plates are optimized and compared when modeled by either the Kirchhoff–Love or Reissner–Mindlin plate theories as well as by the bulk 3D viscoelastic constitutive equations. Mechanical equations are numeric...

The goal of this work is to significantly enhance the damping of linear viscoelastic structures under free vibration by relying on optimal design. Homogeneous cantilever slender beams and plates satisfying, respectively, the Euler-Bernoulli and Kirchhoff-Love assumptions are considered. A sizing optimization of the beam or plate thickness is propos...

Two hot melt pressure sensitive adhesives have been submitted to bonded joint creep tests. An amorphous and a semicrystalline adhesives have been considered for their different microstructures leading to different mechanical behaviors. The adhesives are referred as soft since their glass transition temperatures stand well below the temperatures of...

An amorphous acrylate interpenetrated polymer network (IPN) was made in the laboratory and tested by dynamic mechanical analysis. Using frequency sweep tests, it was shown that the time-temperature superposition principle applies to the double network. Moreover, a generalized Maxwell model with forty Maxwell branches successfully reproduced the mat...

The mechanical behaviors of five polyether block amide foams, obtained by mold‐opening foam injection process, were investigated with regard to their microstructures. The materials vary in mass ratios of hard versus soft segments, and/or in process packing time. The resulting microstructures have been characterized in terms of cavity size and shape...

The purpose of this paper is to present a general upscaling strategy for deriving macroscopic constitutive laws for rubber-like materials from the knowledge of the network distribution and a mechanical description of the individual chains and of their free energy. The microscopic configuration is described by the position of the cross-links and is...

The development of new generations of propellants with better energetic properties may be hampered by unsatisfactory mechanical behaviors in terms of strength and toughness. A micromechanical approach is adopted to provide a better understanding of the existing links between the constitutive phase behaviors and the local damage, and the macroscopic...

The free vibrations of cantilever slender beams of polymers, which are viscoelastic materials, are theoretically described using the simple Euler-Bernoulli assumption. The comparison between the theory and the experimental data collected for a thermoplastic elastomer, polyether block amide, shows very satisfactory results. Consequently, the theory...

The impact of the loading history on the resistance to break of a carbon-black filled styrene butadiene rubber is explored experimentally. Carbon-black filled rubberlike materials soften significantly upon the first loading due to the well known Mullins effect. The impact of this effect on the critical energy release rate at break, Gc, of the consi...

Motivated by the different uniaxial responses of two actual materials filled with either sifted glass beads or sifted glass grits, the influence of the fillers shape on the finite strain behavior of highly filled composites (>50%) is examined through micromechanical finite element simulations accounting for matrix/filler debonding with a cohesive-z...

A rubberlike matrix highly filled with spherical micrometric glass beads is submitted to uniaxial tension tests until break. X-ray tomography imaging performed on the material while submitted to uniaxial tension reveals early debonding at the matrix/filler interfaces at the poles of the particles followed by void coalescence creating damage localiz...

A rubberlike matrix highly filled with spherical micrometric glass beads is submitted to uniaxial tension tests until break. X-ray tomography imaging performed on the material while submitted to uniaxial tension reveals early debonding at the matrix/filler interfaces at the poles of the particles followed by void coalescence creating damage localiz...

The effect of strain-softening due to Mullins effect on the propagation of a crack is experimen- tally investigated by applying various pre-stretches to a non-crystallizing carbon-black filled elastomer, followed by crack propagation tests. Pure shear tests carried at constant crosshead speed on notched samples, are chosen to characterize crack gro...

In order to estimate mode I fracture strain energy release rate of a rubber upon monotonic loadings, the material is submitted to pure shear and single edge notch tension tests. Catastrophic failure happens suddenly for both tests, revealing mirror-like crack surfaces, assessing the fragile fracture. Nonetheless, Griffith failure analysis could be...

A non-affine microsphere model for rubberlike materials is proposed, based on a local minimization of the network free energy under a maximal advance path constraint. It accounts for any chain weight distribution and for damage such as Mullins softening observed in filled rubber materials. The non-affine equal-force model is compared to the common...

A method is proposed for generating reliable representative volume elements (RVEs) that allows reducing the statistical analysis required for the simulation of the mechanical behavior of isotropic composites highly filled with monosized spheres. The method combines (i) an algorithm inspired from molecular dynamics and associated with an analytical...

The resistance to mode I failure of rubbers is studied by submitting single edge notch samples to uniaxial tension. Reproducing the seminal work of Rivlin and Thomas (J Polym Sci 10:291–318, 1953), single edge notch tension specimens, presenting notches of various lengths, are stretched until break. A styrene butadiene rubber, unfilled and filled w...

Solid polymer linear viscoelasticity in shear is often characterized by applying torsion and using the Saint-Venant solution when rectangular prismatic specimens are considered. It is shown that experimental dynamic torsion tests can show a dependency of the storage modulus and damping factor on the dimensions of the rectangular prismatic specimen...

The integrity of propellant/liner structures in rocket motors is critical to ensure controlled combustion of the engine. In an effort to improve the bonding between the liner and the propellant, it is necessary to characterize it well. Therefore, a propellant-liner structure, bounded thanks to co-curing, has been submitted to a peel test while reco...

The stress-strain response of a rubbery polymer network highly filled with micrometric glass beads was measured at low strain rate in uniaxial tension. The volume change of the glass bead filled material upon stretching was recorded by video extensometry and X-ray tomography scans were used to identify the type of damage within the composite materi...

A three-dimensional cubic Monte Carlo lattice model is considered to test the impact of volume on the molecularmobility of amorphous polymers. Assuming classic polymer chain dynamics, the concept of locked volume limiting the accessible volume around the polymer chains is introduced. The polymer mobility is assessed by its ability to explore the en...

A loading/unloading/reloading process is applied to a cohesive zone where the model proposed by Park, Paulino and Roesler in 2009 is combined with a linear unloading/reloading relationship. The applied loading and unloading use the same mixed mode and reloading is in mode I. When the amplitude of preloading is varied, several features are evidenced...

The mechanical behavior and damage of highly filled elastomers such as propellants are studied experimentally. A model material made of a polyacrylate matrix filled with glass beads and energetic binders filled with ammonium perchlorate and HMX have been formulated. The focus is on materials containing micrometric size particles. The size of filler...

Atomic force microscopy has provided access to local moduli for propellants prepared with bonding agents, which create a stiffness gradient in the matrix producing a stiffer interphase surrounding the fillers. The reinforcing impact of the bonding agent appears up to some distance and interphase percolation is observed. In order to better understan...

The nonlinear behavior and failure of highly filled elastomers are significantly impacted by the volume fraction, the size and nature of fillers and the matrix stiffness. Original experimental data obtained on glass beads reinforced acrylates and on propellants allow illustrating and discussing the main effects generally observed. In order to bette...

This study shows how the results given by a cohesive-zone model at finite strain may depend strongly on its numerical implementation. A two-dimensional four-node cohesive element is considered, which includes several variants depending on a part of the strain-displacement matrix, on the quadrature rule applied, and on the configuration chosen to pe...

Directional laws, also called micro-sphere laws, are based on the rubber elasticity theory and are designed to fit rubber mechanical stress strain responses at large strain. Because they depend on material directions, directional changes may be introduced accounting for anisotropic damage or residual stretch such as resulting from Mullins softening...

The effect of the Mullins softening on mode I fracture of carbon-black filled rubbers was investigated experimentally. Large specimen of NR and SBR filled with the same amount and nature of carbon-black were submitted to uniaxial tension. Then, single edge notch tension samples were cut along various directions with respect to the direction of prec...

Solid propellants manufacturers commonly monitor the granulometries of the explosive fllers they introduce in the material to pack high fller volume fraction and thus obtain satisfactory energetic performance. However, to our knowledge, the effect of a mix of small and large particles in the micrometric size range in flled elastomers has not yet be...

The time-temperature superposition property of an amorphous polymer acrylate network is characterized at infinitesimal strain by standard dynamic mechanical analysis tests. Comparison of the shift factors determined in uniaxial tension and in torsion shows that both tests provide equivalent time-temperature superposition properties. More interestin...

A 40 phr carbon-black filled styrene butadiene rubber has been submitted to several experiments in order to identify the physical damage responsible for the mechanical softening recorded upon first stretch. Damage in the rubber matrix was determined by swelling. The filler structure alteration was monitored by electrical conductivity measurements....

Shape memory polymer composites (SMPCs) have become an important way to leverage improvements in the development of applications featuring shape memory polymers (SMPs). In this study, an amorphous SMP matrix has been filled with different types of reinforcements. An experimental set of results is presented and then compared to three-dimensional (3D...

The dependence to temperature of the rebound of a solid polymer ball on a rigid slab is investigated. An acrylate polymer ball is brought to a wide range of temperatures, covering its glass to rubbery transition, and let fall on a granite slab while the coefficient of restitution, duration of contact, and force history are measured experimentally....

The self-consistent model based on morphological representative patterns is applied to the realistic case of the linear viscoelasticity of polymers reinforced by elastic nano-particles coated with a viscoelastic interphase. This approach allows to study the effect of such microstructure parameters as particle dispersion, particle size distribution...

An acrylate polymer network was submitted to thermomechanical shape memory cycles. The set of experiments characterized the material stress-free strain recovery and the strain-constrained stress recovery in uniaxial tension. Experimental parameters like temperature of strain fixation, amount of strain and heating rate, were varied in order to provi...

A chemically crosslinked acrylate network was submitted to various thermomechanical strain and stress recoveries while changing the experimental parameters in order to better define the benefits and the limits of using chemically crosslinked polymers for multicycle applications or applications under external constraints. The results showed that the...

The authors compared the mechanical behavior and, more precisely, the Mullins and the cyclic (post-Mullins) softenings of two filled rubbers. A crystallizing natural rubber and a noncrystallizing styrene-butadiene rubber of similar compositions resulting in similar cross-link densities and filled with 40 phr of N347 carbon-black fillers were tested...

Le comportement sous sollicitations cycliques des matériaux élastomères induit un adoucissement, une déformation rémanente et une anisotropie. Le travail présenté portera sur la caractérisation de ces phénomènes d'endommagements afin d'établir des liens avec les propriétés matériaux. The behavior of rubber-like materials under cyclic loading induce...

Several carbon-black filled styrene-butadiene rubbers are subjected to monotonic uniaxial tension tests in order to investigate the effects of the amount of fillers and of the crosslink density on their mechanical properties. The Young modulus, the volume changes associated with material damage and the stretch to failure are extracted and discussed...

Several carbon-black filled styrene butadiene rubbers were submitted to dynamic mechanical analysis tests in order to investigate the effect of nano-size filler reinforcement on rubber linear viscoelasticity. Experimental data are in favor of the existence of a rubber interphase at the filler-rubber interface with enhanced properties compared to th...

This work aims at proving that the shape memory property of amorphous polymer networks is a mere expression of the intrinsic time-temperature equivalence and viscoelasticity properties of the materials. For this purpose, an acrylate network was synthesized in the laboratory. The time-temperature superposition property and the material viscoelastici...

Micromechanics modeling of the linear viscoelasticity of carbon-black filled styrene butadiene rubbers (SBR) shows that a simple representation of a spherical rigid-phase surrounded by rubber gum and embedded in an homogeneous equivalent medium provides access to the effective volume fraction of fillers. This simple representation is successful for...

Original constitutive modeling is proposed for filled rubber materials in order to capture the anisotropic softened behavior induced by general non-proportional pre-loading histories. The hyperelastic framework is grounded on a thorough analysis of cyclic experimental data. The strain energy density is based on a directional approach. The model lea...

Volumetric strains in a filled SBR specimen subjected to cyclic uniaxial tension with increasing extensions are studied. Digital image correlation is used to follow the kinematics of two orthogonal free faces. A volume expansion is observed past a critical elongation, which can be interpreted as the onset of cavitation. Under unloading, the volume...

Etliche rußgefüllte Styrol-Butadien-Kautschukmischungen reagieren bei zyklischen, uniaxialen Spannungstests hinsichtlich der Mullins-Erweichung unterschiedlich empfindlich. Um diesen Effekt zu quantifizieren, wurde ein Schädigungsparameter eingeführt. Er lässt sich mittels eines klassischen Schädigungsansatzes bestimmen. Seine Abschätzung kann entw...

Samples of carbon-black filled styrene butadiene rubbers (SBR) were submitted to successive non proportional loadings in order to define a general criterion for the Mullins softening. For this purpose, each sample was initially submitted to uniaxial or biaxial preloadings followed by a cyclic uniaxial tension test. An original experimental analysis...

A model has been proposed recently, which describes the experimentally observed mechanical behavior of some shape memory polymers. It considers a purely thermoelastic behavior, without strain rate effects, and assumes essentially that the polymer can be considered as a two-phase composite, with glassy and rubbery phases having volume fractions that...

The viscoelastic behavior of an amorphous shape memory polymer network and its dependence on time and temperature were measured by dynamic mechanical analysis. The resulting thermo-mechanical behavior was modeled and implemented in a commercial finite element code. The ability of the resulting thermomechanical model to simulate and, eventually, pre...

A quantitative estimate of the Mullins softening is proposed and tested on various carbon-black filled styrene-butadiene rubbers. In order to model the behaviour of elastomeric materials, some constitutive equations reported in the literature are based on the account of a strain amplification factor, which evolves with the maximum strain history. T...

The study of the stress-strain responses of a carbon-black filled rubber submitted to cyclic uniaxial tension loadings evidenced two specific features common to filled rubbers. First, as originally shown by (Mullins and Tobin 1965), the Mullins softened stress-strain responses collapse into a single master curve by introducing strain amplification...

Several carbon-black filled Styrene Butadiene Rubbers (SBR) were tested in cyclic uniaxial tension in order to investigate their cyclic stress-softening. A classic representation using the maximum stress with respect to the number of cycles is first applied to present the experimental data. Nonetheless, the limiting interest of such a representatio...

Several carbon-black filled styrene-butadiene rubbers (SBRs) were submitted to uniaxial tension cyclic tests at large strain for investigating filled rubbers cyclic softening. In order to study the effect of the material composition (amount of fillers and crosslink density) and of the stretch intensity, an original method for cyclic softening chara...

Several carbon-black filled styrene-butadiene rubbers showed different sensibilities to the Mullins softening when submitted to cyclic uniaxial tension. In order to quantify this softening, a damage parameter was introduced. It is defined by using a classic damage approach and can be estimated by using either the strain amplification factor method...

A torsion device was designed and built for testing the shape fixity and shape recovery of shape memory polymers at large deformations. A simple thermal chamber was used to regulate the thermal environment during testing and a CCD camera was used for recording the deformation. Such a torsion testing system provided a quantitative estimate of the ki...

A formulation of a constitutive behaviour law is proposed for hyperelastic materials, such that damage induced anisotropy can be accounted for continuously. The full-network approach with directional damage is adopted as a starting point. The full-network law with elementary strain energy density based on the inverse Langevin is chosen as a referen...

A carbon-black filled SBR was submitted to various uniaxial tension cyclic tests in order to study its cyclic softening. Stress-softening and stretch creep were monitored during stretch-control tests and ratcheting tests, respectively. The material softening induced by cyclic loadings appeared to depend on the maximum loading applied. The cyclic am...

Two carbon black filled SBRs were submitted to various uniaxial tension cyclic tests, including stretch-control tests and stress-control tests. Stress relaxation and stretch creep were measured according to the number of cycles. Results show a strong dependence of the material softening to the maximum loading applied and the number of cycles. After...

A study of direction-based models for the representation of isotropic and anisotropic hyperelastic behaviour of rubber-like materials is proposed. The interest in such models is sustained by their ability to account for the Mullins effect induced anisotropy. For such a purpose, the directional models should be initially isotropic and representative...

Polyurethane networks have been prepared from a mix of tri- and quadriisocyanate and from two types of diols, polyether-based (with molar masses of 1,000, 2,000, and 4,000g/mol) and polyester-based (1,035g/mol). The weight fraction of sol has been measured, as well as the elastic shear modulus of the gels. It has been found that the statistical the...

Homogenization micromechanical models are applied to predict the linear viscoelastic properties of an amorphous poly(ethylene)terephthalate (PET) composite in the range of glass transition by using the elastic-viscoelastic superposition principle defined by Hashin [1]. An amorphous PET is reinforced by glass beads and is submitted to dynamic mechan...

The Mullins effect remains a major challenge in order to provide good mechanical modeling of the complex behavior of industrial rubber materials. It has been forty years since Mullins [Mullins L. Softening of rubber by deformation. Rubber Chem Technol 1969;42:339–62.] wrote his review on the phenomenon and still no general agreement has been found...

The temperature dependence of the bulk modulus of polyisoprene has been studied using molecular dynamics simulations. Virtual polyisoprenes have been submitted to volume contractions above and below the glass transition. Bulk modulus has been observed to be linearly dependent on temperature both above and below the glass transition respectively, an...

Photoinitiated polymer networks were formed by copolymerization of tert-butyl acrylate with di(ethylene glycol) dimethacrylate (DEGDMA) or poly(ethylene glycol) dimethacrylate (PEGDMA). The degree of crosslinking was systematically varied by modifying the weight fraction and molecular weight of the dimethacrylate crosslinking agent. An increase in...

Crosslinked networks were synthesized by copolymerization of mono-functional tert-butyl acrylate (tBA) with diethyleneglycol dimethacrylate (DEGDMA) or polyethylene glycol dimethacrylates (PEGDMA). By varying the chain length and concentration of the difunctional PEGDMA, we obtained tBA-PEGDMA copolymer networks while by varying the concentration o...

The temperature dependence of the Young's modulus of amorphous polymers has been explained well in the literature, however, the moderate drop of the bulk modulus of a factor 2 or 3 is still not fully understood and the question of a possible entropic contribution to the bulk deformation is still open. In this work, we propose to address the questio...

While the theory of elasticity has been well verified for the non ideal structures accounting for contribution of entanglements, some effort is needed to investigate the contribution of dangling chains. In order to establish a quantitative contribution of dangling chains, networks with a controlled architecture, i.e. where architecture is determine...

The relevance of micromechanics modeling to the linear viscoelastic behavior of semi-crystalline polymers is studied. For this purpose, the linear viscoelastic behaviors of amorphous and semi-crystalline PETs are characterized. Then, two micromechanics modeling methods, which have been proven in a previous work to apply to the PET elastic behavior,...

Full-atomistic molecular dynamics simulations are used to study the shape-memory behaviour of a representative amorphous polymer. A virtual polyisoprene was constructed and subjected to uniaxial stretch and hydrostatic compression thermomechanical cycles. Uniaxial stretch loading results demonstrate that a temporary shape can be stored at low tempe...

A new mechanism for a biaxial tension test is developed for loading an in-plane specimen simultaneously in two principal directions. This mechanism can be adapted to any uniaxial tension test machine and thereby it reduces the cost of conducting tests on expensive machines. It provides a uniform state of equibiaxial tension necessary for procedure...

A stress softening, commonly known as the Mullins effect, is observed usually in filled rubberlike materials after the first load. Experimental observations have shown that the Mullins effect induces a permanent set and some anisotropy. In order to account for these two features, a strain energy density is proposed, which is based on material direc...

The visco-hyperelastic behavior of a filled rubberlike material has been studied experimentally by large deformation cyclic uniaxial loadings, and an anisotropy induced by the Mullins effect has been demonstrated. By applying a generalized Maxwell model to a set of material directions, damage could be included in order to reproduce the stress softe...

Considering semicrystalline polymers as heterogeneous materials consisting of an amorphous phase and crystallites, several micromechanical models have been tested to predict their elastic behavior. Two representations have been considered: crystallites embedded in a matrix and a layered-composite aggregate. Several homogenization schemes have been...

A 3D thermoviscoelastic model is proposed to represent the thermomechanical behavior of shape memory polymers. The model is based on a physical understanding of the material behavior and a mechanical interpretation of the stress–strain–temperature changes observed during thermomechanical loading. The model is thermodynamically motivated and is form...

Shape memory polymers (SMPs) can retain a temporary shape after pre-deformation at an elevated temperature and subsequent cooling to a lower temperature. When reheated, the original shape can be recovered. Relatively little work in the literature has addressed the constitutive modeling of the unique thermomechanical coupling in SMPs. Constitutive m...

Suitably defined invariants of the logarithmic strain are shown to be more adequate than the usual invariants of the left Cauchy–Green tensor to define the type and intensity of a strain applied to hyperelastic rubber-like materials. Coupling these invariants with the macromolecular full-network model clarifies some features of the state of strain...

Even though semi-crystalline polymers are closer to composite, even nano-composite material, little work has been done to predict their properties as in the case of composite or filled polymer. In their work Halpin and Kardos [1] proposed to determine the elastic modulus of semi-crystalline polymers. The lamellae are supposed to be like fibers. An...

A material direction-dependent constitutive model has been formulated for large deformations for isotropic and anisotropic rubber-like materials. Although such materials are usually isotropic, anisotropic behavior has been observed in calendered plates of filled rubbers. Strain energy density function characterizing rubber-like materials is usually...

The aim of this article is to try to explain why isotactic polypropylene (PP) is stiffer than high density polyethylene (HDPE) despite the fact that this latter is more crystalline and that its crystallites are stiffer than PP ones. Two micromechanical models were chosen for their ability to represent semi-crystalline polymers. The first one is a d...

A material direction-dependent constitutive model has been formulated for large deformation of anisotropic rubber-like materials. Anisotropic behavior has been observed in calendered plates of filled elastomers. Strain energy density functions characterizing rubber-like material behavior are usually dependent on the principal stretch ratios and are...

A fracture mechanics analysis is performed to get a criterion for irreversible growth of cavities in rubber-like materials. The limit of reversible growth of a hole is calculated using the Griffith fracture criterion for a hyperelastic incompressible material (neo-Hookean behavior law) submitted to a hydrostatic tension under the assumptions of lar...