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Granular computational homogenisation of composite structures with imprecise parameters

Beluch W., Hatłas M., Ptaszny J.

Archives of Mechanics

2023

Vol. 75, nr 3

271--300

The paper presents the formulation of a granular computational homogenisation problem and the proposition of a method to solve it, which enables multiscale analysis of materials with uncertain microstructure parameters. The material parameters and the geometry, represented by the interval and fuzzy numbers, are assumed to be unprecise. An _-cut representation of fuzzy numbers allows the use of interval arithmetic for epistemic uncertainties. Directed interval arithmetic is used to reduce the effect of interval widening during arithmetic operations. Response surfaces of diverse types, including Artificial Neural Networks, are used as model reduction methods. The finite element method is employed to solve the boundary value problem on a micro scale. Numerical examples are provided to demonstrate the effectiveness of the proposed approach.

On the static nature of minimal kinematic boundary conditions for computational homogenisation

Wojciechowski M., Lefik M.

Engineering Transactions

2016

Vol. 64, iss. 4

581--587

In the paper, the concept of minimal kinematic boundary conditions (MKBC) for computational homogenisation is considered. In the presented approach, the strain averaging equation is applied to the microscopic representative volume element (RVE) via Lagrange multipliers, which are, in turn, interpreted as macroscopic stresses. It is shown that this formulation fulfil automatically Hill-Mandel macrohomogeneity condition. Also, it is demonstrated, that MKBCs are in fact static, Neumann kind boundary conditions. As a consequence the effective parameters computed with this approach are lower bounds of the true effective values. Numerical analysis illustrating these results is also provided.

Multi-scale modelling of heterogeneous shell structures

Massart T. J., Mercatoris B. C. N., Piezel B., Berke P., Laiarinandrasana L., Thionnet A.

Computer Assisted Mechanics and Engineering Sciences

2011

Vol. 18, no. 1-2

53-71

This paper reviews multi-scale computational homogenisation frameworks for the non-linear behaviour ofheterogeneous thin planar shells. Based on a review of some of the currently available methods, a computational homogenisation scheme for shells is applied on to representative volume elements for plain weave composites. The e?ect of ?exural loading on the potential failure modes of such materials is analysed, focusing on the reinforcement-matrix delamination mechanism. The attention is next shifted toward failure localisation in masonry unit cells. Subsequently, a recently developed computational FE2solution scheme accounting for damage localisation at structural scales based on RVE computations is applied.