Master Thesis Projects - Dr. Hammoud

Potential master thesis students who are interested in one of the following projects presented by Dr. Mohammad Hammoud ( for Fall semester 2014-2015 are kindly requested to meet him as soon as possible in the School of Engineering (Saida Campus – Block A – First floor) before they do their registration in the offered MENG695 “Master Thesis – Part I” section of Saida campus.

Four subjects classified under the Proper Generalized Decomposition method (PGD):

We here present the development of the Proper Generalized Decomposition (PGD) method for solving coupled multiphysics problems with different characteristic times. This method consists in approximating solutions of Partial Differential Equations with separated representations.

To deal with the viscoelasticity of polymers, we have to consider a continuous distribution of relaxation times. Cunat [1] has demonstrated that a minimal number of relaxation times and consequently internal variables are needed to correctly describe the viscoelastic behavior with a discrete point of view. Usually, 50 relaxation times are used to approximate a discrete spectrum with six decades [2]. The evolution law associated to each internal variable consists in a differential equation with respect to time. To simulate this behavior, we have to solve simultaneously the mechanical equilibrium equation and fifty evolution laws.

From a numerical point of view, the use of classical finite element method leads to a large computation time linked to the incremental scheme especially in the case of non linear differential equations. Namely, at each time step, we have to solve 50 equations for each Gauss point in the case of viscoelastic polymer. In the case of linear differential equations, analytical solutions allow a quick estimation of the evolution of the internal variables at each time step. Otherwise, if the differential equations are strongly non linear, their solving necessitates to consider another temporal scheme for example an adaptive Runge Kutta [3]. Let us note that these numerical issues are particularly adapted for long relaxation times. To predict viscoelasticity of polymers under cyclic loading, we have to consider another time linked to the loading. The time steps of the integration scheme will be more constraints.

Moreover, polymers material  don’t reach a stabilized cycle after few  fatigue cycles like metals but cycle evolves slowly under the effect of creep at average stress mainly due to the strong coupling with temperature. It has been shown that 200 cycles are not enough to reach the stabilized cycle for polypropylene under multiaxial fatigue. Therefore, the temporal domain becomes very large which induces a very high computation time with a classical finite element method.

These projects are in collaboration with Dr. Marianne Beringhier, ENSMA France. A deep follow up is scheduled during the two parts via Skype. Hereafter the projects:
  1. Viscoelasticity of polymer with the PGD:

    The resolution of a global model coupled to local models with the PGD may be realized in different ways: a) resolution of local models at each Gauss point (as in the finite element); b) resolution of global model (already done in the training of Mohamad Hammoud [5] (LIU student) 2 years ago); c) resolution of a parametric PGD where the parameter is the number of internal variable. These different resolutions will be discussed and compared at the level of prediction of the internal variables and the displacement, computational time and also the possibility of the extension of the PGD to the 3D or the nonlinear equations.


    • Required Skills: Matlab – Finite Element Analysis.

    • Deliverables: MATLAB Routine – Master Thesis Report.

    • Co-supervisor: Dr. Marianne Beringhier, ENSMA, France.


  2. PGD for a non-linear viscoelastic polymer:  

    The resolution of a viscoelastic problem with the PGD was realized in the thesis of Mohamad [5]. We propose to expend its implementation to a non-linear viscoelastic material. There are different strategies to deal with this non-linearity such as PGD, Newton, MAN.


    • Required Skills: Matlab – Finite Element Analysis.

    • Deliverables: MATLAB Routine – Master Thesis Report.

    • Co-supervisor: Dr. Marianne Beringhier, ENSMA, France.


  3. PGD of the thermo-viscoelastic behavior of polymer:

    In this project the extension of the PGD to a thermoviscoelastic problem is considered. The coupling between the thermal and mechanical behaviors will be treated in different manners: weak coupling (starting by effect of the thermal behavior on the mechanical one and later the mechanical on the thermal). In this case, weak coupling means that the coupling is solved incrementally. Another way to solve the problem is the strong coupling where all equations are solved at the same time. These different approaches will be discussed in terms of number of PGD modes, computational time etc.


    • Required Skills: Matlab – Finite Element Analysis.

    • Deliverables: MATLAB Routine – Master Thesis Report.

    • Co-supervisor: Dr. Marianne Beringhier, ENSMA, France.


  4. 3D Viscoelasticity of polymer for industrial applications:

    In this project, we week to expend the viscoelasticity problem to the 3 dimensional case (3D) for industrial applications. Different strategies can be discussed; the incremental PGD (only on the space variables). It allows a coupling with the Finite Element Method in the case of complex geometry.


    • Required Skills: Matlab – Finite Element Analysis.

    • Deliverables: MATLAB Routine – Master Thesis Report.

    • Co-supervisor: Dr. Marianne Beringhier, ENSMA, France.


  5. Evaluation of adult to child scaling procedure of thoracic mechanical response to pendulum impact:  

    The determination of mechanical impact response of humans is vital in automotive safety research.   Historically, data was collected from tests involving adult human cadavers.  Crash test dummies were built as surrogates representing adult human males and females of various sizes. Studies dealing with the impact biomechanics of children are very scarce. To circumvent this scarcity, scaling techniques have been used almost exclusively. For frontal impact child dummies, General Motors conducted a comprehensive scaling study [6].  Another study by TNO, dealt specifically with the 3 year-old child dummy designed for both frontal and side impacts [7].  For side impact dummies of various ages and sizes, general guidelines were introduced in 2002 and have been recently proposed for rulemaking by the Department of Transportation in the USA [8].   The recently published document proposes to amend the previous child side impact regulations to add specification and qualification requirements for an anthropomorphic test device (ATD) representing a 3-year old child side impact dummy.  Thoracic impact response has been historically obtained using a pendulum test.  The scaling procedure assumed a spring mass model of the thorax.  The mass at the front of thorax i.e. the chest is assumed negligible.  This study investigates the effect of this assumption on the obtained scaled response. 


    • Required Skills: Mechanics of Materials – Vibrations – MATLAB.

    • Deliverables: MATLAB Routine Master Thesis Report.

    • Co-supervisor: Dr. Ali Hage Diab.


  6. Tuned Vibration Absorber (TVA) for suppression of rest tremor in Parkinson’s disease:

    Parkinson's disease is a degenerative disorder of the central nervous system that often impairs the sufferer's motor skills, speech, and other functions. This disease is well known around the entire world. Patients that suffer from this disease especially the youth are disabled to live normally. The objective of this project is to develop a tuned vibration absorber (TVA) for suppression of rest tremor in Parkinson’s disease that occurs when voluntary muscle activity is absent. This device will be helpful for people in need to have a kind of normal life.


    • Required Skills: Vibrations – Dynamics–MATLAB.

    • Deliverables: Device – Master Thesis Report.

    • Co-supervisors: Dr. Hassan Shreim and Dr.  Mohamad Hajj Hassan.


  7. Using of phase change materials in PV panel’s cooling:

    Solar energy is one of the most important sources of renewable energy available today. One of the main types of solar energy systems, in use nowadays, is based on the use of photovoltaic cells which tends to convert solar radiation into electricity using PV panels. Whereas under the effect of high operating temperatures, a loss of efficiency in solar photovoltaic and thermal panels is detected. In order to maintain the temperature of the panels to be close to the ambient temperature, there are several methods including natural or forced convection of the air or the wind and using the phase change materials. The first method of cooling is inherently limited due to the poor heat transfer properties of air in natural ventilation therefore the heat dissipation effect is not satisfied [9]. As a novel method, to regulate the rise in PV temperature, phase change materials (PCM), which absorb energy as latent heat at a constant phase transition temperature, are employed.


    • Required Skills: Heat transfer – Thermodynamics–MATLAB.

    • Deliverables: Matlab Routine– Master Thesis Report.

    • Co-supervisors: Dr. Wassim Salameh and Dr. Ali Assi.


  8. Modeling of the impact loading subjected to 2D and 3D woven and braided composites tubes:

    This study aims to investigate the energy absorption of tubes made from different kinds of composites. Different architectures studied consist of 2D and 3D woven and braided composites. Moreover, different fibers are used, as glass fibers, carbon fibers and aramid fibers. Also, hybrid aluminum/composite tubes should be studied. In order, to perform the study, a modeling of the impact loading at a defined velocity ranging from 70km/h to 200 km/h is done using Finite Element method. The absorption for different architectures and fibers configurations, as well as the effect of hybridization is compared to each other. This project aims to enhance the energy absorption for car chassis tubular parts subjected to impact, and in the same time to reduce its weights.


    • Required Skills: Stress Analysis – Material Sciences–Finite Element–MATLAB.

    • Deliverables: Matlab Routine– Master Thesis Report.

    • Co-supervisor: Dr. Ali Hallal.


[1]    Cunat Ch (1991). A thermodynamic theory of relaxation based on a distribution of non-linear processes, Journal of Non-Crystalline Solids, Volumes 131-133, Part 1, p. 196-199.

[2]    Cunat Ch (2001). The DNLR Approach and Relaxation Phenomena. Part I – Historical Account and DNLR Formalism, Mechanics of Time-Dependent Materials, 5, p.39-65. 

[3]    Press W.H, Flannery B.P, Teukolsky S.A and Vetterling W.T (1989). Numerical Recipes in Pascal by, Cambridge U. Press, Cambridge.

[4]    Beringhier M, Gueguen M , Grandidier J.C (2010) Solution of strongly coupled multiphysics problems using space-time separated representations – Application to thermoviscoelasticity, Archives of Computational Methods in Engineering, Volume 17, Number 4, p. 393-401

[5]  Hammoud Mohamad (2013) Proper Generalized Decomposition method applied to fatigue of polymer under different loading, Master thesis, School of Engineering of the Lebanese International University, Beirut, Lebanon. 

[6]    Irwin A., and Mertz H. J., “Biomechanical Basis for the CRABI and Hybrid III Child Dummies”, SAE 973317, Proceedings of the Forty-first Stapp Car Crash Conference, Society of Automotive Engineers, Warrendale, PA. 

[7]    Van Ratingen M. R., Twisk D., Schrooten M., Beusenberg C., Barnes A., and Platten G., “Biomechanically Based Design and Performance Targets for a 3-Year Old Child Crash Dummy for Frontal and Side Impact”, SAE 973316, Proceedings of the Forty first Stapp Car Crash Conference, Society of Automotive Engineers, Warrendale, PA. 

[8]    Irwin A.L., Mertz H.J., Elhagediab A.M., Moss S.: Guidelines for Assessing the Biofidelity of Side Impact Dummies of Various Sizes and Ages. Stapp Car Crash Journal, Vol. 46, Nov. 2002, p. 297-319. Report No. SAE 2002-22-0016 

[9]    P. Biwole, P. Eclache, F. Kuznik, Improving the performance of solar panels by the use of phase-change materials, World Renewable Energy 2011, Sweden, May 8-13, 2011