Wajdi Zouari

Analysis of the mechanical behaviour of flax and glass fabrics-reinforced thermoplastic and thermoset resins

This paper aims at comparing the mechanical behaviour of different composite materials constituted of twill flax and glass fabrics-reinforced liquid thermoplastic and thermoset resins. The main objective is to study the possibility of thermoplastic to replace thermoset matrix, and flax fibre to replace glass fibre. For this purpose, the studied composites were fabricated using the vacuum infusion technique. Next, they were subjected to several monotonic and load-unload tensile tests in order to determine their mechanical properties and their evolution with damage. Two elastic damage and elastic-plastic damage models were also considered to predict their behaviour. The obtained results show that the used thermoplastic resin could constitute an interesting alternative to the thermoset resin for the vacuum infusion process. Furthermore, the flax fibre composites, in particular those based on the thermoplastic resin, present specific tensile moduli close to those of glass composites.

A FSDT–MITC Piezoelectric Shell Finite Element with Ferroelectric Non-linearity

A shell finite element based on the Reissner/Mindlin first-order shear deformation theory and integrating a bi-dimensional phenomenological ferroelectric constitutive law for domain switching effects is proposed. An electric switching function is considered to indicate the onset of domain switching. Only one internal variable (the remanent polarization) is used in the model. An implicit integration technique based on the return-mapping algorithm is adopted. The shell element is implemented into the commercial finite element code Abaqus ® via the subroutine user element. Some linear (piezoelectric) and non-linear (ferroelectric) tests are considered to validate first, the element formulation and second, the implementation of the bi-dimensional ferroelectric model. It is shown by studying a complex example (the spiral actuator) that the Reissner/Mindlin kinematic hypothesis (no variation of the displacement across the thickness or no thickness variation) is not sufficient for some electromechanical applications for which the d33 effect is of major importance.

Updated Lagrangian formulations of two hexahedral elements with rotational DOFs

ABSTRACT Updated Lagrangian formulations of two eight-node hexahedral solid elements with rotational degrees of freedom (DOFs) are developed to analyse geometrically nonlinear large deflection problems. These two elements are based on the so-called Space Fibre Rotation (SFR) concept that considers fictive small rotations of a nodal fibre within the element to enrich the displacement vector approximation of low-order finite elements. The validity and efficiency of the proposed formulations are demonstrated by solving several nonlinear large deflection benchmarks and the obtained results show a much better accuracy than those based on the total Lagrangian approach.

A Mindlin multilayered hybrid-mixed approach for shell structures without shear correction factors

In this paper, we present two four-node multilayered hybrid-mixed shell elements for the static and free vibration analyses of plate and shell composite structures. Their formulation is based on the first shear deformation theory of Reissner/Mindlin without transverse shear correction factors. Linear and quadratic variations of the local in-plane and transverse shear stresses across the thickness, respectively, are supposed. To reduce the total number of variables in these models, transverse shear stresses are directly related to bending stresses by using two equilibrium equations. The performances of the proposed elements are assessed by means of two known numerical benchmarks and their results are found to agree globally well with the reference solutions.

A multilayered 3D hexahedral finite element with rotational DOFs

The study presents a multilayer eight-node hexahedral finite element with rotational degree of freedom to model composite laminate structures. Its formulation is based on virtual rotations of a nodal fibre within the element that enriches the displacement vector approximation. A particular attention is made to the determination of transverse deflections as well as in-plane stresses. To assess the accuracy of the proposed element, several benchmarks are considered and the obtained results are compared with 3D elasticity solutions and other advanced finite elements from the literature.

Development of a Ferroelectric Shell Finite Element

Ferroelectricity is the non-linear behaviour exhibited by piezoelectric ceramics, especially in the application of high electric field. Actually, the demand for numerical tools taking into account this non linear phenomenon is increasing to reliably design applications using piezoelectric ceramics. In this context, a shell finite element based on the Reissner/Mindlins theory and integrating a bi-dimensional macroscopic constitutive law for domain switching effects (ferroelectricity) is developed. This element is implemented into the finite element code ABAQUS using the subroutine UEL (User ELement). The thermodynamical framework of the law is based on two scalar valued functions: the Helmoltz free energy and an electric switching function. One internal variable (the remanent polarization) is introduced and a non linear switching effect hardening is considered. An implicit integration of the constitutive equations based on the return-mapping algorithm is developed.