FellowDr.-Ing Michael W√ľnsche
Project NameMultiscale modeling of layered, fibre reinforced and porous magnetoelectric materials
Host organisationInstitute of Construction and Architecture
Duration of the project01.09.2015 - 31.08.2017

Abstract
Smart multifield materials offer certain important performance advantages over conventionally used metals. Due to the capability of converting electric/magnetic energy into mechanical energy and vice versa, piezoelectric/piezomagnetic materials play an important role in smart structures. Piezoelectric/piezomagnetic ceramics are very brittle and therefore micro-cracks and cavities exist in them. Beside cracks inside a homogenous material, one of the most dominant failure mechanisms in layered or fiber reinforced composites is interface failure. The numerical simulation of smart multifield composites is especially important for the design, optimization and safety of structure. The multiscale modelling provides a powerful tool to investigate the interaction between the micro structure and the real macro structure. Due to the high mathematical complexity the solution of general boundary value problems for coupled field problems on the microstructural as well as on the macrostructural levels requires efficient numerical methods. On the microstructural level the computation of the effective material properties is performed for a representative volume element (RVE) while on the macroscopic level the whole structure with the prescribed boundary conditions is considered. To solve the boundary value problems in both levels of the multiscale modelling a Galerkin boundary element method (GBEM) will be developed. The GBEM will be general without any restrictions on the geometry and the boundary conditions. Layered, fiber reinforced and porous composites with micro- and macro-cracks of arbitrary shape will be investigated. Mechanical, electric and magnetic loadings are considered to determine the effective material properties. In intensive studies the influence of the layer combination, the fibers, the pores and the micro-cracks on the effective material properties and the whole structure will be investigated.

Project Summary with Interim Results

Due to the capability of converting electric/magnetic energy into mechanical energy and vice versa, piezoelectric/piezomagnetic materials play an important role in smart structures. The investigation of effective piezoelectric/piezomagnetic properties of fiber reinforced and porous materials containing micro cracks is of special scientific significance and engineering importance. The multiscale modeling provides a powerful possibility to investigate the interaction between the micro structure and the real macroscopic structure. Due to the high mathematical complexity the solution of general boundary value problems for coupled field problems on the micro-structural as well as on the macro-structural levels requires efficient advanced numerical methods.

In the first year of the project a Galerkin BEM has been successfully developed to model two-dimensional piezoelectric and magnetoelectroelastic representative volume elements (RVEs) with pores and fibers of arbitrary shape as micro-structure. The macro-structure is also computed by a Galerkin BEM. The already implemented time-domain symmetric Galerkin BEM has been extended to time-harmonic problems. For this purpose, an efficient frequency-domain symmetric Galerkin boundary element method has been developed. The whole solution algorithm is general without any restrictions on the geometry, fiber and matrix configuration, distribution of the pores and the boundary conditions.

For the numerical simulations a modular BEM program system has been developed in Fortran2008. It allows systematic extensions to further research activities. Special interfaces are included to use external pre- and postprocessors to achieve a high level of applicability.

Intensive numerical parametric studies have been performed to analyze smart composites with passive elastic materials as matrix and piezoelectric ceramics or polymers as active fibers. Further, the influences of voids in magnetoelectroelastic materials on the effective material properties have been studied. Since smart composite materials are often applied under time-harmonic and transient dynamic loading conditions the effects of fibers, voids and micro-cracks on the intensity factors and the scattered wave fields have been considered.

The obtained results indicate a significant influence of the fibers, the material combination and possible voids on the effective material properties and the transient dynamic behavior of real structures. It is concluded that the controlled variation of fibers can increase the piezoelectric/piezomagnetic coupling effects significantly. This can be applied to design and optimize advanced material behavior to satisfy the high-performance requirements according the special in-service conditions. Voids in generally decrease the coupling parameters but special material constants can be positive influenced by a proper selection of the number and the size of the voids. As well expected pores and fibers have a major influence on the scattered wave fields. Although fibers increase the stiffness of the material micro-cracks may lead to higher intensity factors and to a more complicated failure behavior in contrast to homogeneous materials which is mainly induced by transient dynamic effects.

The obtained results are a very good base for the planed developments in the second year of the project.