893 research outputs found
Microstructural enrichment functions based on stochastic Wang tilings
This paper presents an approach to constructing microstructural enrichment
functions to local fields in non-periodic heterogeneous materials with
applications in Partition of Unity and Hybrid Finite Element schemes. It is
based on a concept of aperiodic tilings by the Wang tiles, designed to produce
microstructures morphologically similar to original media and enrichment
functions that satisfy the underlying governing equations. An appealing feature
of this approach is that the enrichment functions are defined only on a small
set of square tiles and extended to larger domains by an inexpensive stochastic
tiling algorithm in a non-periodic manner. Feasibility of the proposed
methodology is demonstrated on constructions of stress enrichment functions for
two-dimensional mono-disperse particulate media.Comment: 27 pages, 12 figures; v2: completely re-written after the first
revie
A jigsaw puzzle framework for homogenization of high porosity foams
An approach to homogenization of high porosity metallic foams is explored.
The emphasis is on the \Alporas{} foam and its representation by means of
two-dimensional wire-frame models. The guaranteed upper and lower bounds on the
effective properties are derived by the first-order homogenization with the
uniform and minimal kinematic boundary conditions at heart. This is combined
with the method of Wang tilings to generate sufficiently large material samples
along with their finite element discretization. The obtained results are
compared to experimental and numerical data available in literature and the
suitability of the two-dimensional setting itself is discussed.Comment: 11 pages, 7 figures, 3 table
Modular-topology optimization of structures and mechanisms with free material design and clustering
Topology optimization of modular structures and mechanisms enables balancing
the performance of automatically-generated individualized designs, as required
by Industry 4.0, with enhanced sustainability by means of component reuse. For
optimal modular design, two key questions must be answered: (i) what should the
topology of individual modules be like and (ii) how should modules be arranged
at the product scale? We address these challenges by proposing a bi-level
sequential strategy that combines free material design, clustering techniques,
and topology optimization. First, using free material optimization enhanced
with post-processing for checkerboard suppression, we determine the
distribution of elasticity tensors at the product scale. To extract the
sought-after modular arrangement, we partition the obtained elasticity tensors
with a novel deterministic clustering algorithm and interpret its outputs
within Wang tiling formalism. Finally, we design interiors of individual
modules by solving a single-scale topology optimization problem with the design
space reduced by modular mapping, conveniently starting from an initial guess
provided by free material optimization. We illustrate these developments with
three benchmarks first, covering compliance minimization of modular structures,
and, for the first time, the design of non-periodic compliant modular
mechanisms. Furthermore, we design a set of modules reusable in an inverter and
in gripper mechanisms, which ultimately pave the way towards the rational
design of modular architectured (meta)materials.Comment: 30 page
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