Departments, Schools, Centers & InstitutesResearch, creative, and scholarly works created by the university community organized by department.https://digital.library.txstate.edu/handle/10877/12022-09-29T12:16:14Z2022-09-29T12:16:14ZAnalysis of stagnation point flow of an upper-convected Maxwell fluidPaullet, Josephhttps://digital.library.txstate.edu/handle/10877/161742022-09-26T20:45:43Z2017-12-06T00:00:00ZAnalysis of stagnation point flow of an upper-convected Maxwell fluid
Paullet, Joseph
Several recent papers have investigated the two-dimensional stagnation point flow of an upper-convected Maxwell fluid by employing a similarity change of variable to reduce the governing PDEs to a nonlinear third order ODE boundary value problem (BVP). In these previous works, the BVP was studied numerically and several conjectures regarding the existence and behavior of the solutions were made. The purpose of this article is to mathematically verify these conjectures. We prove the existence of a solution to the BVP for all relevant values of the elasticity parameter. We also prove that this solution has monotonically increasing first derivative, thus verifying the conjecture that no ``overshoot'' of the boundary condition occurs. Uniqueness results are presented for a large range of parameter space and bounds on the skin friction coefficient are calculated.
2017-12-06T00:00:00ZModeling, analysis and simulations of debonding of bonded rod-beam system caused by humidity and thermal effectsKuttler, KennethKruk, SergeMarcinek, PawelShillor, Meirhttps://digital.library.txstate.edu/handle/10877/161732022-09-26T20:39:40Z2017-12-06T00:00:00ZModeling, analysis and simulations of debonding of bonded rod-beam system caused by humidity and thermal effects
Kuttler, Kenneth; Kruk, Serge; Marcinek, Pawel; Shillor, Meir
This work models, analyses and simulates a one-dimensional process of debonding of a structure made of two viscoelastic bonded slabs that is described by a rod-beam system. It is motivated, primarily, by the degradation of adhesively bonded plates in automotive applications and studies the effects of the humidity, horizontal and vertical vibrations and temperature on the debonding process. The existence of a weak solution to the model is established by using approximate problems, existence theorems for differential inclusions, and a fixed point theorem. An implicit finite differences algorithm for the problem is developed and used to simulate the system dynamics. It is found that the qualitative behavior of the system correlates well with experimental results. Moreover, it indicates that using the shifts in the spectrum, as described by the FFT of one component of the solution, may be used to measure nondestructively the integrity of the bonds and their deterioration.
2017-12-06T00:00:00ZGrowing sandpile problem with Dirichlet and Fourier boundary conditionsNassouri, EstelleOuaro, StanislasTraore, Urbainhttps://digital.library.txstate.edu/handle/10877/161722022-09-26T19:59:24Z2017-12-06T00:00:00ZGrowing sandpile problem with Dirichlet and Fourier boundary conditions
Nassouri, Estelle; Ouaro, Stanislas; Traore, Urbain
In this work, we study the Prigozhin model for growing sandpile with mixed boundary conditions and an arbitrary time dependent angle of repose. On one part of the boundary the homogeneous Dirichlet boundary condition is provided, on the other one the Robin condition is used. Using the implicit Euler discretization in time, we prove the existence and uniqueness of variational solution of the model and for the numerical analysis we use a duality approach.
2017-12-06T00:00:00ZAnalysis of a rate-and-state friction problem with viscoelastic materialsPatrulescu, FlaviusSofonea, Mirceahttps://digital.library.txstate.edu/handle/10877/161712022-09-26T19:32:35Z2017-12-05T00:00:00ZAnalysis of a rate-and-state friction problem with viscoelastic materials
Patrulescu, Flavius; Sofonea, Mircea
We consider a mathematical model which describes the frictional contact between a viscoelastic body and a foundation. The contact is modelled with normal compliance associated to a rate-and-state version of Coulomb's law of dry friction. We start by presenting a description of the friction law, together with some examples used in geophysics. Then we state the classical formulation of the problem, list the assumptions on the data and derive a variational formulation of the model. It is in a form of a differential variational inequality in which the unknowns are the displacement field and the surface state variable. Next, we prove the unique weak solvability of the problem. The proof is based on arguments of history-dependent variational inequalities and nonlinear implicit integral equations in Banach spaces.
2017-12-05T00:00:00Z