Ewc Erica Coenen

Multi-scale computational homogenization of structured thin sheets

Structured and layered thin sheets are used in a variety of innovative applications, e.g. flexible displays, rollable solar cells or flexible electronics. Stacks of different materials, with often highly complex interconnects between layers, are thereby used, which are typically loaded in bending combined with intrinsic thermo-mechanical mismatches. As a result, different failure mechanisms at the level of the layered substructure occur, which constitutes a serious reliability concern.This paper deals with the two-scale homogenization of structured thin sheets, whereby a higher-order through-thickness representative volume element (RVE) is used. The methodology relies on the computational homogenization of the mechanics of microstructures, for which first-order and second-order solution strategies have been developed in the past decade. The upscaling of the deformation of structured thin sheets towards a shell-type continuum is second-order in nature. The higher-order kinematics is defined on the basis of a microstructural RVE, which represents the full thickness of the macroscopic structure and a periodic in-plane cell (e.g. a single pixel in a flexible display). The elaboration of the boundary conditions and the solution of the micro-scale boundary value problem are discussed. The obtained micro-scale stress state is homogenized towards a 3D macroscopic shell structure, for which detailed aspects will be emphasized. The coupled numerical solution strategy is briefly outlined. Finally, an example is given and the application to a number of practical problems is highlighted, where the solution provides direct information on each scale. The incorporation of failure events at the substructure level is thereby naturally at hand.

A multi-scale approach to bridge microscale damage and macroscale failure : a nested computational homogenization-localization framework

This paper presents a multi-scale modelling approach for bridging the microscale damage and macroscale failure. The proposed scheme evolves from a classical computational homogenization scheme (FE2) towards a discontinuity enriched framework. The classical homogenization approaches typically rely on the separation of scales principle, which is violated as soon as a strain localization band develops within a microstructural volume element (MVE). The newly developed scheme resolves this limitation by considering the bifurcation of the microscale deformation into a continuum ‘bulk’ part and a localization related part. The most distinct feature of the proposed framework is that both, the local macroscale traction-opening response of the cohesive crack and the stress-strain response of the surrounding ‘bulk’, are obtained from a single MVE analysis. The discontinuity enriched macroscale description is formulated to accommodate for the micro-macro coupling. The macroscale boundary value problem and the corresponding implementation are detailed for the use within the embedded discontinuities approach. The presented multi-scale method is demonstrated on a numerical example of a cohesive crack propagation in a macroscopic double notch specimen, with underlying voided microstructure.

Enabling microstructure-based damage and localization analyses and upscaling

This paper presents a framework that enables microstructural modelling of complex microstructures involving damage, localization and fracture. Classical computational homogenization schemes hinge on the separation of scales and the existence of representative volume elements. Due to the accumulation of micro-damage, the microstructural volume elements gradually loose their representative character and evolve towards a unique volume with a developing strain localization band, rendering classical homogenization approaches inapplicable.The assumption that the representative nature of the microstructure along the strain localization band is preserved enables the definition of advance scale transition relations for both imposing the overall macroscale load and coarse graining the cohesive behaviour of the strain localization band. Newly developed strain percolation path aligned boundary conditions have been used for this purpose. It is shown that this enables the development and progressive evolution of a strain localization band with minimal interference of the imposed boundary conditions. In addition to classical homogenization of the stress–strain response, a coarse graining scheme for the effective cohesive behaviour of the strain localization band is proposed. This enables the assessment of the microstructural evolution within the strain localization band and simultaneously provides the effective cohesive response useful for macroscale failure models.