Abdessalem Jarraya

Fractional Derivative and Hereditary Combined Model of Flexible Polyurethane foam Viscoelastic Response under Quasi-Static Compressive Tests

The flexible polyurethane foam exhibits a highly nonlinear and viscoelastic behavior under quasi-static and uni-axial compressive tests. The dependence of the displacement rate during the loading phase is significantly higher than that of the unloading phase. A new identification of the Force-Displacement curve based on experimental observations is proposed. The total foam response is modeled as a sum of a nonlinear elastic component and a viscoelastic component. The elastic force is modeled as a sum of orthogonal polynomials in displacement, while the viscoelastic force is modeled according to the hereditary approach in the loading half-cycle and the fractional derivative approach in the unloading half-cycle. The objective of this paper is to develop a model able to make predictions of the total foam force as well as simulations of its components. A parameter calibration procedure is established according to the difference force method between two unloading responses corresponding to two different displacement rates of the same foam sample. The validity of the model results is discussed by addressing three efficiency requirements: the accuracy of simulations to experimental measurements, the repeatability of results for both tests, and the accordance of predicted components of the total response with the phenomenological identification of the Force-Displacement curve. The proposed optimization methodology is found to simulate reasonably well the responses of three different types of soft foam. Some morphologic characteristics of these foams have clear influence on viscoelastic damping and residual effects.

Modeling of Viscoelastic Behavior of Flexible Polyurethane Foams Under Quasi-Static and Cyclic Regimes

This paper discusses the reliability of two approaches in modeling the Flexible Polyurethane Foam (FPF) behavior. FPFs are cellular polymers characterized by highly complex mechanical behavior including nonlinearity, viscoelasticity, hysteresis, and residual deformations. The review of this topic reveals that several studies have developed models based either on hereditary or on fractional derivation formulations. However, the viscoelastic behavior of the material integrates both short and long memory effects, which needs the combination of the two mathematical approaches to cover the full behavior of such a material. This work compares the two methodologies in identifying the parameters of foam behavior using the combined model. The approaches are based on experimental observations of the FPF behavior on compression (short memory effects) and cyclic (long memory effects) loadings. The relative inefficiency of the force difference method widely addressed in modeling processes was specially discussed.

Sensitivity of GFRP Composite Integrity to Machining-Induced Heat: A Numerical Approach

This paper aims at investigating the temperature effects during abrasive milling of glass fiber reinforced plastic composites (GFRP). A 3D thermal model using volumetric heat source with Gaussian distributed cylindrical flux was developed as DFLUX subroutine and implemented into Abaqus/Standard code. The model employs linear power law for simulating the temperature variation during tool advance. The composite plate is made of glass fibers oriented perpendicular to the tool trajectory. The tool feed was simulated by the source constant motion while speed was taken variable. Four equidistant thermocouples were simulated within the medium plan of the specimen in order to record the temperature evolution. The predictions highlighted the sensitivity of temperature histories to cutting speed. The conductivity and heat capacity played for controlling heating and cooling phases of the curves. The peak temperature exhibited maximum value at TC3 irrespective to speed value. The pure thermal analysis showed sufficient ability to predict the heat affected zone in the GFRP, which is, in turn, a function of tool spindle speed.

FGM Shell Structures Analysis Using an Enhanced Discrete Double Directors Shell Element

In order to examine the accuracy of the enhanced double directors shell model for the functionally graded material (FGM) shell structures, a series of benchmark static tests are tackled using finite elements method. For implementing the discrete double directors shell model (DDDSM) within the Enhanced Strain Technique (EST), four parameters are used for enhancing the membrane strain. The vanishing of transverse shear strains on top and bottom faces is considered in a discrete form. The mechanical properties of the shell structure are assumed to vary continuously in the thickness direction by a simple power-law distribution in terms of the volume fractions of the constituents. A comparison with the exact solutions presented by several authors for shell structures indicates that the present model accurately estimates the stress-strain responses.