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• W565839206 abstract "Elastomersare viscoelastic polymers with low Young's modulus and high failure strainthat are used in manycivilengineering applications, including bridge bearings, seismic isolators forbuildings and resilient rail wheels.Their constitutive behaviouris characterized by a nonlinear stress-strain relation withanextensibility limit. This contrastswith materials that haveinsteada limit on the tensile stresses, suchas mild steel.ThisMScthesisis concerned with thenumerical modelingof elastomers.This involvesdealing with a mediumwith two phases:a constrained region, wherethe particles have reached theirmaximum allowable deformation, and afree region, where theinextensibility constraintis stillinactive.Moreover, one can think of an interface splitting the two phases of the medium. If the focus isput in obtaining methods tolocate and evolve such interface, then a two phase medium with amoving interfaceis considered.From the mathematical point of view, this is a constrained minimizationproblem. One of thestrategies to solve it is to turn the minimization problem into a shape equilibrium one. Thisapproach has been successfully employed for aninterface location problemin small strainsandserves as the starting point of this work.Thus, the main purpose of this thesis is to extend this formulation to alarge strainsinterfacelocating and evolving scenario. A first analysis of the problem reveals two sources ofnonlinearity:the inextensibility constraint and the kinematics in large strains.A simplebutthoroughone-dimensionalstudy of the problem isthendevelopedto find methodsto sort outbothnonlinearities.Following this,explicit iterative schemes to locate and evolve one ormultiple interfacesare straightforwardly obtained in 1D linear elasticity.However, the same ideas applied to a simpleSt.Venant-Kirchhoffhyperelasticitymodel,evidences that even very simple 1D problems become rather complex and cannot be solved asdirectly and explicit as before.Numerical examples areprovided throughout this analysis and they are also useful to concludethat both locating and evolving the interface can beessentiallyseen as the same problem, but withdifferent driving effects.After that,an extension of the one-dimensional schemes to two or more dimensionsis explored.Although the same ideas can be applied, more sophisticated modeling tools are required, namely,theX-FEM and Level setmethods, theshape sensitivityanalysis and theArbitrary Lagrangian-Eulerian methods.Acomplementarynumerical implementation of the proposed strategy is to show itscomputational benefits. In particular, a combination of the three previous techniques shall makeunnecessary a stepwise update of the Level set.The work presented heremay not be limited to this particular case andbe relevant tootherengineering problems involvingmoving interfacesand boundaries, such as plasticity analysis orthe saturation of a porous medium." @default.
• W565839206 created "2016-06-24" @default.
• W565839206 creator A5083441306 @default.
• W565839206 date "2014-06-20" @default.
• W565839206 modified "2023-09-26" @default.
• W565839206 title "Treating inextensibility constraints in hyperelastic materials with inequality level sets" @default.
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