Abstract

This note is concerned with the application of Finite Element Methods (FEM) and Newton-Multigrid solvers for the simulation of thixotropic flow problems. The thixotropy phenomena are introduced into viscoplastic material by taking into account the internal material micro structure using a scalar structure parameter. Firstly, the viscoplastic stress is modified to include the thixotropic stress dependent on the structure parameter. Secondly, an evolution equation for the structure parameter is introduced to induce the time-dependent process of competition between the destruction (breakdown) and the construction (buildup) inhabited in the material. Substantially, this is done simply by introducing a structure-parameter-dependent viscosity into the rheological model for yield stress material. The modified thixotropic viscoplastic stress w.r.t. the structure parameter is integrated in quasi-Newtonian manner into the generalized Navier-Stokes equations and the evolution equation for the structure parameter constitutes the main core of full set of modeling equations, which are creditable as the privilege answer to incorporate thixotropy phenomena. A fully coupled monolithic finite element approach has been exercised which manages the material internal micro structure parameter, velocity, and pressure fields simultaneously. The nonlinearity of the corresponding problem, related to the dependency of the diffusive stress on the material parameters and the nonlinear structure parameter models on the other hand, is treated with generalized Newton's method w.r.t. the Jacobian's singularities having a global convergence property. The linearized systems inside the outer Newton loops form a typical saddle-point problem which is solved using a geometrical multigrid method with a Vanka-like smoother taking into account a stable FEM approximation pair for velocity and pressure with discontinuous linear pressure and biquadratic velocity spaces. We examine the accuracy, robustness and efficiency of the Newton-Multigrid FEM solver throughout the solution of thixotropic viscoplastic flow problems in Couette device and in 4:1 contraction.

Abstract

One of the main "drivers" in the development of aeronautical structures in composite material is the development of more integrated structures that are manufactured in a single step ("One-Shot") to optimize times. The adhesive materials in film format are one of the main variables to take into consideration to achieve the aforementioned integration. This need has promoted creativity at the level of use / parameterization of new adhesives in the form of a film.

Film adhesives are used in the integration of composite, sandwich or monolithic structures. Regarding sandwich structures, the adhesive film is used to ensure a good adhesion between the core and the prepreg, through the formation of a meniscus of adhesive material in the core cell. This function is fulfilled depending on the type of "carrier". For Monolithic structures, the adhesive film is used to ensure a good adhesion in co-bonding processes (bonding of cured laminate with fresh prepreg) and secondary bonding (bonding between 2 previously cured laminates), interleaved between materials to achieve optimum thickness, guaranteeing the best mechanical properties of the element at interlaminar level. This, without forgetting, the repair processes that are within the processes of co-bonding, with all its specificities and operational limitations, either in manufacturing or in service.

The market options, qualified by OEMs or not, are wide, having developed different support materials, or variants of the same material, with the aim of achieving the best mechanical properties of the elements where they are used.