Acoustic behavior prediction of monodisperse foams using polynomial surrogates

Acoustic properties of foams, such as macroscopic transports and sound absorption, are significantly influenced by their local morphology. The present paper develops a polynomial chaos expansion (PCE)-based surrogate model for characterizing the microstructure-properties relationships of acoustic monodisperse foams. First, the acoustic properties of the considered structures are estimated numerically by homogenization techniques using an idealized periodic unit cell and the Johnson-Champoux-Allard-Pride-Lafarge (JCAPL) model. The reference maps of transport parameters are then used to construct the PCE–based surrogates in the design space involving a set of foamy microstructural parameters such as membrane content, cell size, and porosity. Finally, after a validation phase and assessing convergence characteristics, the generated surrogates are employed to design some foam-based absorbers to illustrate the accuracy and computational efficiency of the proposed method.

LOCALIZATION ANALYSIS OF DAMAGE FOR ONE-DIMENSIONAL PERIDYNAMIC MODEL

Peridynamics is a recently developed extension of continuum mechanics, which replaces the traditional concept of stress by force interactions between material points at a finite distance. The peridynamic continuum is thus intrinsically nonlocal. In this contribution, a bond-based peridynamic model with elastic-brittle interactions is considered and the critical strain is defined for each bond as a function of its length. Various forms of length functions are employed to achieve a variety of macroscopic responses. A detailed study of three different localization mechanisms is performed for a one-dimensional periodic unit cell. Furthermore, a convergence study of the adopted finite element discretization of the peridynamic model is provided and an effective event-driven numerical algorithm is described.

The Emergence of Sequential Buckling in Reconfigurable Hexagonal Networks Embedded into Soft Matrix

The extreme and unconventional properties of mechanical metamaterials originate in their sophisticated internal architectures. Traditionally, the architecture of mechanical metamaterials is decided on in the design stage and cannot be altered after fabrication. However, the phenomenon of elastic instability, usually accompanied by a reconfiguration in periodic lattices, can be harnessed to alter their mechanical properties. Here, we study the behavior of mechanical metamaterials consisting of hexagonal networks embedded into a soft matrix. Using finite element analysis, we reveal that under specific conditions, such metamaterials can undergo sequential buckling at two different strain levels. While the first reconfiguration keeps the periodicity of the metamaterial intact, the secondary buckling is accompanied by the change in the global periodicity and formation of a new periodic unit cell. We reveal that the critical strains for the first and the second buckling depend on the metamaterial geometry and the ratio between elastic moduli. Moreover, we demonstrate that the buckling behavior can be further controlled by the placement of the rigid circular inclusions in the rotation centers of order 6. The observed sequential buckling in bulk metamaterials can provide additional routes to program their mechanical behavior and control the propagation of elastic waves.

HOMOGENIZATION OF UNREINFORCED OLD MASONRY WALL COMPARISON OF SCALAR ISOTROPIC AND ORTHOTROPIC DAMAGE MODELS

Masonry is a heterogeneous composite material made of bricks bonded by a mortar matrix. Modeling such a material on macroscale typically calls for homogenization adopting a suitable constitutive model capable of capturing its quasi-brittle behavior. The present contribution concentrates on comparison and potential application of classical isotropic and orthotropic damage models in the framework of strain based first order numerical homogenization. As an illustrative example, a representative volume element in terms of a periodic unit cell is constructed to address the response of an unreinforced masonry (URM) structure typical of “Placa” buildings (mixed masonry-reinforced concrete buildings) built in Portugal. The performance of the two models is examined on the basis of macroscopic stress-strain curves constructed for both tensile and compressive loading. The selected geometrical constraints clearly identify the differences in the predictive capabilities of the two models.

STRENGTH OF COMPOSITE YARN UNDER BIAXIAL LOADING

The present paper is concerned with two types of periodic unit cell of composite yarn with different geometry but the same material properties. Their macroscopic response under tensile and compressive loading in the transverse direction and their combination are plotted in the graphs. Based on stress-strain curves the failure envelopes are constructed. A simple maximum stress criterion and linear softening law is used in the adopted progressive damage analysis to outline the softening part of stress-strain diagrams. Finally the impact of selected representative volume element is observed through the comparison of results gained for both designed periodic unit cells in the microlevel, meaning the level of yarn.

WANG TILES LOCAL TILINGS CREATED BY MERGING EDGE-COMPATIBLE FINITE ELEMENT MESHES

In this contribution, we present the concept of Wang Tiles as a surrogate of the periodic unit cell method (PUC) for modelling of materials with heterogeneous microstructures and for synthesis of micro-mechanical fields. The concept is based on a set of specifically designed cells that compresses the stochastic microstructure into a small set of statistical volume elements – tiles. Tiles are placed side by side according to matching edges like in a game of domino. Opposite to the repeating pattern of PUC the Wang Tiles method with the stochastic tiling algorithm preserves the randomness for reconstructed microstructures. The same process is applied to obtain the micro-mechanical response of domains where the evaluation as one piece would be time consuming. Therefore the micro-mechanical quantities are evaluated only on tiles (with surrounding layers of tiles of each addressed tile included into the evaluation) and then synthesized to the micro-mechanical field of whole domain.

Adaptive Boundaries of Wang Tiles for Heterogeneous Material Modelling

This contribution deals with algorithms for the generation of modified Wang tiles as a tool for the heterogeneous materials modelling. The proposed approach considers material domains only with 2D hard discs of both equal and different radii distributed within a matrix. Previous works showed potential of the Wang tile principles for reconstruction of heterogeneous materials. The main advantage of the tiling theory for material modelling is to stack large/infinite areas with relative small set of tiles with emphasis on a periodicity reduction in comparison with the traditional Periodic Unit Cell (PUC) concept. The basic units of the Wang Tiling are tiles with codes (colors) on edges. The algorithm for distribution of hard discs is based on the molecular dynamics to avoid particles overlapping. Unfortunately the nature of the Wang tiling together with molecular dynamics algorithms cause periodicity artefacts especially in tile corners of a composed material domain. In this paper a new algorithm with adaptive tile boundaries is presented in order to avoid edge and corner periodicity.