Gilles Marckmann

Comparison of Hyperelastic Models for Rubber-Like Materials

The present paper proposes a thorough comparison of twenty hyperelastic models for rubber-like materials. The ability of these models to reproduce different types of loading conditions is analyzed thanks to two classical sets of experimental data. Both material parameters and the stretch range of validity of each model are determined by an efficient fitting procedure. Then, a ranking of these twenty models is established, highlighting new efficient constitutive equations that could advantageously replace well-known models, which are widely used by engineers for finite element simulation of rubber parts.

A theory of network alteration for the Mullins effect

This 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.

Dynamic inflation of non‐linear elastic and viscoelastic rubber‐like membranes

The present paper deals with the dynamic inflation of rubber-like membranes. The material is assumed to obey the hyperelastic Mooneys model or the non-linear viscoelastic Christensens 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.

A comparison of the hart-smith model with Arruda-Boyce and Gent formulations for rubber elasticity

The 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.

Numerical analysis of rubber balloons

The present paper deals with the inflation of two connected rubber balloons. This problem is known to exhibit instabilities and complex equilibrium paths. In some cases, the balloons inflate asymmetrically and equilibrium states with unequal radii take place. In this work, balloons are considered axisymmetric and discretized using an efficient B-spline discretization. The non-linear finite element procedure is associated with a stability and post-bifurcation analysis in order to determine singular points and to switch onto secondary equilibrium branches. The case of Mooney-Rivlin membranes is thoroughly investigated and the branching diagrams obtained are discussed in regards with the material parameters.

Modeling of Nomex honeycomb cores, linear and nonlinear behaviours

The purpose of this study is to develop tools dedicated to the design of sandwich panels involving Nomex® honeycomb cores. Special attention is paid to the ability to perform full three dimensional calculations up to failure of such structures. In the first part, the determination of effective elastic properties of Nomex® honeycomb cores is carried out thanks to strain based periodic homogenization technique. Using an equivalence in energy between a real honeycomb and a fictitious continuous medium, it becomes possible to evaluate the elastic behavior of Nomex® cores, starting from the knowledge of the behavior of the constitutive paper. Next, relying on experimental observations, the strengths of Nomex® honeycomb cores are evaluated with a linear Eulers buckling analysis. Results are compared with data coming from manufacturers, and give satisfaction. In order to carry out these two first studies, the NidaCore software has been developed using the finite element code Cast3M from CEA. The last part deals with the modeling of the nonlinear compressive response of Nomex® cores. A model based on the thermodynamics of irreversible process is proposed and the identification technique detailed. Good agreement between experimental data and computed values is obtained.

An axisymmetric B-spline model for the non-linear inflation of rubberlike membranes

A new B-spline interpolation model for the free inflation of axisymmetric rubberlike membranes is presented in this paper. The membrane coordinates are interpolated by cubic B-splines and the treatment of the spline boundary conditions is highlighted. Both circular and cylindrical cases are considered. The formulation of the element is detailed and formulas for the tangent operator are presented. In order to solve the non-linear system of equations, the Newton-Raphson algorithm is sucessfully associated with the arc-length method. Some numerical examples are presented to validate our approach and to exhibit convergence properties of the method.

Inflation of elastomeric circular membranes using network constitutive equations

The 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.

Numerical modelling of Nomex® honeycomb cores : Failure and effective elastic properties

The aim of the present study is to propose and develop the numerical determination of the effective stress-strain behaviour of Nomex® honeycomb cores made from aramid paper material. This study highlights the determination of the hexagonal and rectangular over-expanded core materials. These honeycombs are extensively used in the manufacturing of aeronautic structures and of oceanic multihull sailing race boats. These sandwich structures are made of carbon-fiber epoxy-matrix composite laminate skins and Nomex® cores. The understanding of the behaviour and eventually failure of honeycombs are extremely important for the design of these engineering composite sandwich structures. Honeycomb cores predictions are directly related to the structural integrity and safety requirements of the entire composite structure. Since the pioneering work numerous studies on the effective properties of cellular sandwich cores have been published [1]–[2]. In the past, core behaviours were studied under strength of material assumptions. In this context a software dedicated to Nomex® honeycombs was developed at the Laboratory in order to predict the failure conditions of these cores [2]. Our software NidaCore has been developed to determine the three dimensional mechanical core properties. The elastic mechanical properties have been determined by a three-dimensional Finite Element model that involves periodic homogenization techniques. For the homogenisation of the honeycomb microstructure, a strain energy-based concept is used which assumes macroscopic mechanical equivalence of a Representative Volume Element for the given microstructure with a similar homogeneous volume element. The software has been developed using the Finite Element structure analysis program Cast3M-CEA. Numerical predictions are compared with the mechanical properties given by the Euro-Composites company. The present study confirms that for honeycombs under consideration the Representative Volume Element symmetries lead to orthotropic homogenized mechanical properties. The key point of the modeling is that the RVE buckling modes conduct to determine the ultimate stresses of the homogenized core. Based on buckling modes, numerical analysis reproduces the ultimate stresses experimentally observed on standard test methods. This approach strengthens by experimental results leads to a failure criteria based on the mechanical understanding of local damage effect. In order to go further, the skin effect on the core properties is discussed for T700/M10 carbon-fiber epoxymatrix cross-ply and angle-ply laminates skins. The honeycomb mechanical properties and ultimate stresses are used to model three dimensional reinforcements that we used for the study of the Oceanic sailboat structures.

Dynamic analysis of nonlinear elastic materials

The paper is connected with the programmation of the constitutive law of hyperelastic materials so as to compute their response to impact loading. The law is obtained from a Hart-Smith model for given strain rate. A mixed variational principal is used to develop a finite element program for 3D dynamic behavior of nearly incompressible materials.