Multi-scale modelling of localization and damage

No abstract

Novel boundary conditions for strain localization analyses in microstructural volume elements

Multi-scale modeling frequently relies on microstructural representative volume elements (RVEs) on which macroscopic deformation is imposed through kinematical boundary conditions. A particular choice of these boundary conditions may influence the obtained effective properties. For strain localization and damage analyses, the RVE is pushed beyond the limits of its representative character, and the applied boundary conditions have a significant impact on the onset and the type of macroscopic material instability to be predicted. In this article, we propose a new type of boundary conditions for microstructural volume elements, called percolation-path-aligned boundary conditions. Intrinsically, these boundary conditions capture the constraining effect of the material surrounding the RVE upon developing localization bands. The alignment with evolving localization bands allows the highly strained band to cross the RVE and fully develop with minimal interference of the applied boundary conditions. For an illustration of the performance of the newly proposed boundary conditions, macroscopic deformation has been imposed on a voided elasto-plastic RVE using different types of boundary conditions. It is observed that the new RVE boundary conditions provide a good estimate for the effective stiffness, are not susceptible to spurious localization, and permit the development of a full strain localization band up to failure

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

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 combinedwith intrinsic thermo-mechanical mismatches. As a result, different failure mechanisms at the level of the layered substructure occur, which constitutes aserious reliability concern. This paper deals with the two-scale homogenization of structured thinsheets, whereby a higher-order through-thickness representative volume element (RVE) is used. The methodology relies on the computationalhomogenization of the mechanics of microstructures, for which first-order and second-order solution strategies have been developed in the past decade. Theupscaling of the deformation of structured thin sheets towards a shell-type continuum is second-order in nature. The higher-order kinematics is definedon 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 microscale stress state is homogenized towards a 3D macroscopic shell structure, forwhich detailed aspects will be emphasized. The coupled numerical solution strategy is briefly outlined. Finally, an example is given and the applicationto a number of practical problems is highlighted, where the solution provides direct information on each scale. The incorporation of failure events at thesubstructure level is thereby naturally at hand