Computational modelling of some problems of elasticity and viscoelasticity with applications to thermoforming process

Copyright @ 2012 Northwestern Polytechnical University and ISCIThe reliability of computational models of physical processes has received much attention and involves issues such as the validity of the mathematical models being used, the error in any data that the models need, and the accuracy of the numerical schemes being used. These issues are considered in the context of elastic, viscoelastic and hyperelastic deformation, when finite element approximations are applied. Goal oriented techniques using specific quantities of interest (QoI) are described for estimating discretisation and modelling errors in the hyperelastic case. The computational modelling of the rapid large inflation of hyperelastic circular sheets modelled as axisymmetric membranes is then treated, with the aim of estimating engineering QoI and their errors. Fine (involving inertia terms) and coarse (quasi-static) models of the inflation are considered. The techniques are applied to thermoforming processes where sheets are inflated into moulds to form thin-walled structures

The determination of the poles of the mapping function and their use in numerical conformal mapping

Let f be the function which maps conformally a simply-connected domain Ω onto the unit disc. This paper is concerned with the problem of determining the dominant poles of f in comp1(Ω∩∂Ω), and of using this information in order to obtain accurate numerical approximations to f by means of the Bergman kernel method

The treatment of corner and pole-type singularities in numerical conformal mapping techniques

This paper is a report of recent developments concerning the nature and the treatment of singularities that affect certain numerical conformal mapping techniques. The paper also includes some new results on the nature of singularities that the mapping function may have in the complement of the closure of the domain under consideration

Numerical techniques for conformal mapping onto a rectangle

This paper is concerned with the problem of determining approximations to the function F which maps conformally a simply-connected domain onto a rectangle R, so that four specified points on are mapped Ω∂respectively onto the four vertices of R. In particular, we study the following two classes of methods for the mapping of domains of the form . (i) Methods which approximate where f is an approximation to the conformal map of Q onto the unit disc, and S is a simple Schwarz-Christoffel transformation. (ii) Methods based on approximating the conformal map of a certain symmetric doubly-connected domain onto a circular annulus. Keywords: Conforma

Modelling of thermoforming processes for bio-degradable thermoplastic materials

Thin walled container structures have for decades been manufactured from oil based polymeric materials using thermoforming processes. Since the 1980's computational modelling has been used to simulate and aid in the development of these processes. Oil based materials are not eco-friendly, as they do not degrade after use and cause problems of waste. We report here on the computational modelling, using solid mechanics and elasto-plastic deformation, of the thermoforming of food packaging structures made from starch based (bio-degradable) biomaterials. It is shown that, with limited data, it is possible to predict satisfactorily the wall thickness of thermoformed structures. This work was undertaken in BICOM in collaboration with engineering colleagues at Brunel University London, and in association with companies from the polymer industry to provide technical information for their customers

Discretization error and modelling error in the context of the rapid inflation of hyperelastic membranes

The computational modelling of the rapid large inflation of hyperelastic circular sheets modelled as axisymmetric membranes is treated, with the aim of estimating engineering quantities of interest and their errors. Fine (involving inertia terms) and coarse (quasi-static) models of the inflation are considered and, using goal oriented techniques, both modelling and discretization error are estimated. Numerical results involving only discretization errors for the quasi-static problem, and both modelling and discretization errors for the dynamic problem are presented

Modeling of the compressed-air flow impact for thermoforming simulations

Thermoforming is a process for the cheap mass-production of thin-walled plastic parts. A sheet of plastic is heated for increased deformability, and then deformed by overpressure into a mold with the end productâs shape. The main drawback is the inhomogeneous wall thickness distribution resulting from the common process. The authors believe that it is possible to improve these inhomogeneities by locally influencing the highly temperature-dependent material strength using directed jets of pressurized air for local cooling. As the high number of potentially influential parameters renders purely experimental parameter studies infeasible, a computational model that couples the flow of the pressurized air with the structural simulation of the deforming plastic is set up. With the combined results of experiments and simulations, a parameter study can be conducted, which allows for an optimization of air flow parameters for a more evenly distributed wall thickness