Denis Anders

Application of operator-scaling anisotropic random fields to binary mixtures

In modern technical applications various multiphase mixtures are used to meet demanding mechanical, chemical and electrical requirements. To understand their structural properties as continuous macroscopic materials, it is important to capture the microstructure of these mixtures. Due to their vast range of applications multicomponent systems are subjected to microstructural changes such as phase separation and coarsening. Therefore the ultimate microstructural arrangement depends on the systems configuration and on exterior driving forces. In addition to this, random physical imperfections within the material and random noise in the exterior thermodynamic fields influence in essence the microstructural evolution. Since all physical processes are subjected to a certain degree of random inhomogeneity under realistic conditions, the influence of random phenomena cannot be neglected in modern physical models. An advanced mathematical description and an implementation of these stochastic processes are required to adapt simulation results based on deterministic mathematical models to experimental observations. In our contribution we will present an operator-scaling anisotropic random field embedded in the Cahn–Hilliard phase-field model to describe the phase evolution in a binary mixture. The arising nonlinear diffusion equation will be solved numerically in the innovative framework of the isogeometric finite element method. To illustrate the flexibility and versatility of our approach, numerical and experimental results for a eutectic Sn-Pb alloy are contraposed. This is the first time that the microstructural evolution in a multicomponent system has been associated with operator-scaling anisotropic random fields. Due to its enormous potential as an essential ingredient in stochastic mathematical and physical modeling it is only a matter of time until these processes will become prevalent in engineering applications.

Numerical investigation of diffusion induced coarsening processes in binary alloys

Microscopic small solder joints are part of most microelectronic packages. They show a variety of micro-morphological changes such as decomposition into phases and phase coarsening. In order to analyze the evolution of the alloy by means of a diffusion theory of heterogeneous solid mixtures we apply an extended Cahn-Hilliard phase-field model. The Cahn-Hilliard equation involves a bipotential operator and, accordingly, fourth-order spatial derivatives. In our contribution we discretize the diffusion equation spatially by means of rational B-spline finite element basis functions. To illustrate the versatility of this approach numerical simulations of phase decomposition and coarsening controlled by diffusion and by mechanical loading are discussed and compared with experimental results.

A Chemo-Mechanical Model of Diffusion in Reactive Systems

The functional properties of multi-component materials are often determined by a rearrangement of their different phases and by chemical reactions of their components. In this contribution, a material model is presented which enables computational simulations and structural optimization of solid multi-component systems. Typical Systems of this kind are anodes in batteries, reactive polymer blends and propellants. The physical processes which are assumed to contribute to the microstructural evolution are: (i) particle exchange and mechanical deformation; (ii) spinodal decomposition and phase coarsening; (iii) chemical reactions between the components; and (iv) energetic forces associated with the elastic field of the solid. To illustrate the capability of the deduced coupled field model, three-dimensional Non-Uniform Rational Basis Spline (NURBS) based finite element simulations of such multi-component structures are presented.

A Thermodynamically Consistent Approach to Phase-Separating Viscous Fluids

Abstract The de-mixing properties of heterogeneous viscous fluids are determined by an interplay of diffusion, surface tension and a superposed velocity field. In this contribution a variational model of the decomposition, based on the Navier–Stokes equations for incompressible laminar flow and the extended Korteweg–Cahn–Hilliard equations, is formulated. An exemplary numerical simulation using C 1 {C}^{1}-continuous finite elements demonstrates the capability of this model to compute phase decomposition and coarsening of the moving fluid.

Thermal Diffusion in a Polymer Blend

This contribution presents a thermodynamically sound approach to model temperature sensitive diffusion in multi-phase solids. In order to describe the phenomena of thermal diffusion (thermophoresis) and to simulate the effect numerically, an extended version of the Cahn-Hilliard phase-field model is combined with the heat-diffusion equation. The derived model is formulated consistently with the basic laws of thermodynamics. Its discretized version is embedded in a NURBS-based finite element framework. Numerical simulations and a comparison to experimental results show the effect of thermal diffusion, induced by non-uniform and non-steady temperature fields, on the microstructural evolution of a binary polymer blend consisting of polydimethylsiloxane and polyethylmethylsiloxane.

Investigating a flexible wind turbine using consistent time‐stepping schemes

Purpose – Wind turbines are of growing importance for the production of renewable energy. The kinetic energy of the blowing air induces a rotary motion and is thus converted into electricity. From the mechanical point of view the complex dynamics of wind turbines become a matter of interest for structural optimization and optimal control in order to improve stability and energy efficiency. The purpose of this paper therefore is to present a mechanical model of a three‐blade wind turbine with a momentum and energy conserving time integration of the system.Design/methodology/approach – The authors present a mechanical model based upon a rotationless formulation of rigid body dynamics coupled with flexible components. The resulting set of differential‐algebraic equations will be solved by using energy‐consistent time‐stepping schemes. Rigid and orthotropic‐elastic body models of a wind turbine show the robustness and accuracy of these schemes for the relevant problem.Findings – Numerical studies prove that p...