Inflation of elastomeric circular membranes using network constitutive equations

International audienceThe present paper deals with the use of network-based hyperelastic constitutive equations in the context of thin membranes inflation. The study focus on the inflation of plane circular membranes and the materials are assumed to obey Gaussian and non-Gaussian statistical chains network models. The governing equations of the inflation of axisymmetric thin rubber-like membranes are briefly recalled. The material models are implemented in a numerical tool that incorporates an efficient B-spline interpolation method and a coupled Newton-Raphson/arc-length solving algorithm. Two numerical examples are studied: the homogeneous inflation of spherical balloons and the inflation of initially plane circular membranes. In the second example, the inflation profiles and the distributions of extension ratios along the membrane are extensively analysed during the inflation process. Both examples highlight the need of an accurate modelling of the strain-hardening phenomenon in elastomers

Efficiency of hyperelastic models for rubber-like materials

International audienceThis paper focuses on the modeling of rubber-like material behaviour under several modes of deformation using hyperelastic constitutive equations. A procedure based on genetic algorithms coupled to classical optimisation methods is proposed to identify the parameters of the models upon experimental data given in the literature. This leads to the classification of nineteen models with respect to criteria related to their capability to predict material behaviour

A comparison of the Hart-Smith model with the Arruda-Boyce and Gent formulations for rubber elasticity

International audienceThe present paper demonstrates that the Hart-Smith constitutive model and the more recent Arruda and Boyce eight chains and Gent constitutive models are closely related. The ability of these three models to predict both small and large strain responses of rubbers is highlighted and equations that relate their material parameters are established

Dynamic inflation of non-linear elastic and viscoelastic rubberlike membranes

International audienceThe present paper deals with the dynamic inflation of rubber-like membranes. The material is assumed to obey the hyperelastic Mooney's model or the non-linear viscoelastic Christensen's model. The governing equations of free inflation are solved by a total Lagrangian finite element method for the spatial discretization and an explicit finite-difference algorithm for the time-integration scheme. The numerical implementation of constitutive equations is highlighted and the special case of integral viscoelastic models is examined in detail. The external force consists in a gas flow rate, which is more realistic than a pressure time history. Then, an original method is used to calculate the pressure evolution inside the bubble depending on the deformation state. Our numerical procedure is illustrated through different examples and compared with both analytical and experimental results. These comparisons yield good agreement and show the ability of our approach to simulate both stable and unstable large strain inflations of rubber-like membranes

Unified model for Mullins effect and high cycle fatigue life prediction of rubber materials

Proceedings of the 8th European Conference on constitutive models for rubbers (ECCMR VIII), San Sebastian, Spain, 25-28 June 2013International audienceThe study describes the basic principles of a general damage model (GDMF) for Mullins effect and high cycle fatigue loadings of rubber materials and demonstrates its prediction possibilities for simulating the complete fatigue failure phenomenon. The present paper focuses on stiffness modelling of rubber materials for uniaxial and multiaxial static and fatigue loadings with a minimal number of material parameters in order to ensure robustness of the identification. The proposed hyperplastic model is expressed in terms of classical independent strain invariants. Mullins effect and high cycle fatigue loadings are both modelled according to a continuum damage mechanics approach

Experimental investigation and theoretical modelling of induced anisotropy during stress-softening of rubber

International audienceThe Mullins effect refers to a stress-softening phenomenon of rubber-like materials during cyclic loading. Anisotropy of the material behaviour is generally observed after stretching. In this paper, a large set of original suitable experiments are reported to characterise this effect under several deformation conditions. Then, a phenomenological model is derived to capture the anisotropic distribution. For that, the affine micro-sphere model (Miehe et al., 2004) is amended with a directional network alteration in order to describe anisotropy. The alteration process, involving the breakage and the slippage of the links embedded in the macromolecular network, is modeled by the evolution of the average number of monomer segments per chain during stretching. The average chain length and the chain density are incrementally described by functions to allow both softening and stiffening, depending to the maximum and the minimum stretch rates and levels endured in each direction. The good capacity of the model to reproduce experimental observations validates the above assumptions

Self Designing Structures: a new evolutionary rule for thickness distribution in 2D problems

International audienceThis paper deals with an evolutionary rule for material distribution in topology optimization problems. This rule is determined in order to satisfy the design constraints that can appear in an industrial design problem. Some other topology optimization techniques are presented before describing our scheme. The classical MBB problem is used to illustrate the capabilities of our approach. The influences of a design parameter and the mesh refinement are discussed

A theory of network alteration for the Mullins effect

International audienceThis paper reports on the development of a new network alteration theory to describe the Mullins effect. The stress-softening phenomenon that occurs in rubber-like materials during cyclic loading is analysed from a physical point of view. The Mullins effect is considered to be a consequence of the breakage of links inside the material. Both filler-matrix and chain interaction links are involved in the phenomenon. This new alteration theory is implemented by modifying the eight-chains constitutive equation of Arruda and Boyce (J. Mech. Phys. Solids 41 (2) (1993) 389). In the present method the parameters of the eight-chains model, denoted C-R and N in the bibliography, become functions of the maximum chain stretch ratio. The accuracy of the resulting constitutive equation is demonstrated on cyclic uniaxial experiments for both natural rubbers and synthetic elastomers

A new modelling of the Mullins'effect and viscoelasticity of elastomers based on physical approach

The mechanical behaviour of elastomers is known to be highly non-linear, time-dependent and to exhibit hysteresis and stress-softening known as the Mullins effect (Mullins, 1948) upon cyclic loading. These phenomena are classically studied and modelled independently. Some studies are based on physical approaches (Arruda and Boyce, 1993; Bergström and Boyce, 1998; Marckmann et al., 2002) in which macroscopic constitutive equations are build in regards with the physics of polymeric chains. In this context of physical considerations, the aim of the present paper is to study independently each phenomenon involved in rubber-like materials and to assemble them in a global constitutive equation. First, the hyperelastic behaviour of elastomers is modelled by the physical approach of Arruda and Boyce (1993), widely known as the eight-chains model. This model accurately reproduces the large strains elastic behaviour of elastomers under different types of deformation. Second, the hysteretic time dependent behaviour is approached by the model developed by Bergström and Boyce (1998) that considers the separation of the network in two phases: an elastic equilibrium network and a viscoelastic network that captures the nonlinear rate-dependent deviation from equilibrium. This model is quite simple and successfully reproduces the rate-dependent hysteretic properties of elastomers. Last, as shown in the bibliography, the Mullins stress-softening effect can be considered as a damage phenomenon which only depends on the maximum stretch attained during the deformation history (Govindgee and Simo, 1992). In the present approach, the physical theory of Marckmann et al. (2002) based on an alteration of the polymeric network is adopted. This theory was introduced in the eight-chains hyperelastic model and successfully simulates the decrease of the material stiffness between the first and the second loading curves under cyclic loading. As these three models are based on the physics of the polymeric network, they are gathered in a new efficient constitutive equation. This model is able to reproduces imultaneously the Mullins effect and the time-dependent hysteretic behaviour of elastomers. Finally, the constitutive parameters of this new model are identified by fitting experimental data

Theoretical and numerical limitations for the simulation of crack propagation in natural rubber components

International audienceIn this paper, two commercial software packages dedicated to the simulation of crack propaga-tion in elastomer components were tested: FLEXPAC and MSC-MARC. Firstly, the theoretical limitations ofclassical crack propagation laws were examined to demonstrate that actual numerical predictions are limitedto very simple loading conditions. Secondly, crack propagation approaches implemented in both softwareswere analysed. In order to compare their performances, fatigue experiments are performed. Different rubbercomponents with different pre-cracks were tested under several loading conditions. Crack propagation, i.e.size and direction of the crack, was measured as a function of the number of cycles. Then, these results werecompared with crack direction criteria proposed by the two models. It was demonstrated that loading ampli-tude highly influenced the crack direction and that the models must take this into account in their solver. Fi-nally, limitations of this type of numerical analysis to predict the duration life of rubber components werehighlighted