Rabah Bouzidi

Finite elements for 2D problems of pressurized membranes

This paper presents theoretical and numerical developments of finite elements for axisymmetric and cylindrical bending problems of pressurized membranes. The external loading is mainly a normal pressure to the membrane and the developments are made under the assumptions of follower forces, large displacements and finite strains. The numerical computing is carried out in a different way that those used by the conventional finite element approach which consists in solving the non-linear system of equilibrium equations in which appears the stiffness matrix. The total potential energy is here directly minimized, and the numerical solution is obtained by using optimization algorithms. When the derivatives of the total energy with respect to the nodal displacements are calculated accurately, this approach presents a very good numerical stability in spite of the nil bending rigidity of the membrane. Our numerical models show a very good accuracy by comparisons to analytical solutions and experimental results.

Numerical wrinkling prediction of thin hyperelastic structures by direct energy minimization

This paper is concerned with an efficient algorithm for the wrinkling with finite strains of very thin structures made of hyperelastic material. In this work, the problem of wrinkling is solved by directly minimizing the total potential energy of the structure. The numerical solution is carried out by the means of an iterative method such as the conjugate gradient algorithm. Although the proposed approach is theoretically equivalent to the traditional finite element method, it proves to be an attractive alternative which is particularly efficient for thin wrinkled structures.

Identification of young modulus profile in PVC foam core thickness using speckle inteferometry and inverse method

The aim of this paper is to investigate the mechanical properties of a PVC foam core and especially the Young modulus profile along a commercialised 50 mm beam thickness. The identification of the Young modulus gradient is realized through the uniaxial compression test of a 50 mm cube sample. The in-plane strain fields of one cube face under loading in both directions (longitudinal and transversal) are achieved using a diffuse light interferometric technique, the speckle interferometry. Next to that, a numerical model is built using finite elements code CAST3M. We choose a multilayer model in order to introduce spatial variation of the mechanical properties. The boundaries conditions are very close to those prescribed in the experimental tests. Finally, the present work shows that the non uniform profile of the Young modulus can be estimated by using a simple inverse method and the finite elements analysis to reproduce the experimental strain field.

Behavior of unbound granular materials—part I: isotropic case

Abstract The paper discusses the modeling of the behavior of unbound granular materials. A representative approach that highlights some salient features of the behavior is proposed. This approach is essentially based on experimental results and the study is extended to the construction of the elastic potential from test results. to complete the analysis, two no-linear elastic models involving 3 parameters are proposed. In the construction of these models, two important aspects—the accuracy and the numerical stability—are analyzed.

Resolution of elastoplastic constitutive relations application to the fiber reinforced sand

Abstract The aim of this paper is to introduce a new formulation for the resolution of elastoplastic constitutive relations. A variant of the initial stress method is proposed to reduce the number of increments and iterations and avoid a drift of results. A validation of this new algorithm is performed in two homogeneous tests : unreinforced sand and fiber reinforced sand in triaxial compression. For the sand, the basic elements used in the study are a double yield surface with isotropic hardening and a non-associated flow rule. Then, in order to check our computer program and the mechanical principle of superposition of the two continua (sand and fibers), a finite element simulation of the construction of a wall under gravity forces is presented.