Topology Optimization using the UNsmooth VARiational Topology OPtimization (UNVARTOP) method: an educational implementation in Matlab (preprint)

This paper presents an efficient and comprehensive MATLAB code to solve two-dimensional structural topology optimization problems, including minimum mean compliance, compliant mechanism synthesis and multi-load compliance problems. The Unsmooth Variational Topology Optimization (UNVARTOP) method, developed by Oliver et al. [22], is used in the topology optimization code, based on the finite element method (FEM), to compute the sensitivity and update the topology. The paper also includes instructions to improve the bisection algorithm, modify the computation of the Lagrangian multiplier by using an Augmented Lagrangian to impose the constraint, implement heat conduction problems and extend the code to three-dimensional topology optimization problems. The code, intended for students and newcomers in topology optimization, is included as an appendix (AppendixA) and it can be downloaded fromhttps://github.com/DanielYagotogether with supplementary material

Multiresonant Layered Acoustic Metamaterial (MLAM) solution for broadband low-frequency noise attenuation through double-peak sound transmission loss response (preprint)

The problem of noise control and attenuation is of interest in a broad range of applications, especially in the low-frequency range, below 1000 Hz. Acoustic metamaterials allow us to tackle this problem with solutions that do not necessarily rely on high amounts of mass, however most of them still present two major challenges: they rely on complex structures making them difficult to manufacture, and their attenuating capabilities are limited to narrow frequency bandwidths. Here we propose the Multiresonant Layered Acoustic Metamaterial (MLAM) concept as a novel kind of acoustic metamaterial based on coupled resonances mechanisms. Their main advantages hinge on providing enhanced sound attenuation capabilities in terms of a double-peak sound transmission loss response by means of a layered configuration suitable for large scale manufacturing

A partitioned model order reduction approach to rationalise computational expenses in multiscale fracture mechanics

We propose in this paper an adaptive reduced order modelling technique based on domain partitioning for parametric problems of fracture. We show that coupling domain decomposition and projection-based model order reduction permits to focus the numerical effort where it is most needed: around the zones where damage propagates. No \textit{a priori} knowledge of the damage pattern is required, the extraction of the corresponding spatial regions being based solely on algebra. The efficiency of the proposed approach is demonstrated numerically with an example relevant to engineering fracture.Comment: Submitted for publication in CMAM

Implementation and assessment of a two-scale computational framework for softening materials

Structural EngineeringCivil Engineering and Geoscience

Multiscale domain decomposition analysis of quasi-brittle materials

Computational material design is progressively gaining momentum in the engineering world. Recent breakthroughs in high performance computing and emerging multiscale algorithms have facilitated the simulation of materials at different scales of observation. In particular, the multiscale study of failure phenomena becomes crucial to assess the performance of engineering materials and structures. In this thesis, a concurrent multiscale method is proposed for the failure analysis of quasi-brittle materials. Domain decomposition techniques, such as the Finite Element Tearing and Interconnecting (FETI) method, are used to partition the structure in a number of non-overlapping domains. A different treatment, from a numerical standpoint, is given to linear elastic and non-linear domains in the sense that most of the computational effort is spent in non-linear regions. Multiscale analysis is achieved by means of an adaptive refinement at those domains that are affected by damage processes. This refinement is done in terms of material scale and finite element size. It is verified that the framework is able to correctly capture the initiation and growth of non-linearity at a reduced computational cost when compared to full scale computations. The multiscale framework is found specially attractive for the study of failure in quasi-brittle materials.Structural EngineeringCivil Engineering and Geoscience

Multi-scale modeling of softening materials

This paper presents an assessment of a two-scale framework for the study of softening materials. The procedure is based on a hierarchical Finite Element (FE) scheme in which computations are performed both at macro and mesoscopic scale levels. The methodology is chosen specifically to remain valid when the scales are coupled which is frequently encountered in fracture processes of heterogeneous materials. The effect of the boundary conditions chosen to construct the meso-scale problem is studied in this contribution by comparing multiscale and monoscale analysis of an equivalent problem. It is shown in this study that macroscopic mesh size dependence is encountered when using linear interpolated boundary displacements at the interface between mesospecimens. An improvement to the linear interpolated boundary displacements is presented which proves to be more adequate when strain localisation phenomena is encountered at the interface of the meso-specimens. The specific upscaling procedure for the improved boundary conditions remains an issue of ongoing research.Structural EngineeringCivil Engineering and Geoscience

Model order reduction in computational multiscale fracture mechanics

Nowadays, the model order reduction techniques have become an intensive research field because of the increasing interest in the computational modeling of complex phenomena in multiphysic problems, and its consequent increment in high-computing demanding processes; it is well known that the availability of high-performance computing capacity is, in most of cases limited, therefore, the model order reduction becomes a novelty tool to overcome this paradigm, that represents an immediately challenge in our research community. In computational multiscale modeling for instance, in order to study the interaction between components, a different numerical model has to be solved in each scale, this feature increases radically the computational cost. We present a reduced model based on a multi-scale framework for numerical modeling of the structural failure of heterogeneous quasibrittle materials using the Strong Discontinuity Approach (CSD). The model is assessed by application to cementitious materials. The Proper Orthogonal Decomposition (POD) and the Reduced Order Integration Cubature are the proposed techniques to develop the reduced model, these two techniques work together to reduce both, the complexity and computational time of the high-fidelity model, in our case the FE2 standard model.Fil: Caicedo, M.. Universidad Politecnica de Catalunya; EspañaFil: Oliver, J.. Universidad Politecnica de Catalunya; EspañaFil: Huespe, Alfredo Edmundo. Universidad Nacional del Litoral; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Centro de Investigaciones En Metodos Computacionales. Universidad Nacional del Litoral. Centro de Investigaciones En Metodos Computacionales; ArgentinaFil: Lloberas Valls, O.. Universidad Politecnica de Catalunya; Españ

Multiscale domain decomposition analysis of quasi-brittle heterogeneous materials

A hybrid multiscale framework is presented, which processes the material scales in a concurrent manner, borrowing features from hierarchical multiscale methods. The framework is used for the analysis of non-linear heterogeneous materials and is capable of tackling strain localization and failure phenomena. Domain decomposition techniques, such as the finite element tearing and interconnecting method, are used to partition the material in a number of non-overlapping domains and adaptive refinement is performed at those domains that are affected by damage processes. This refinement is performed in terms of material scale and finite element size. It is verified that the results are independent of the chosen domain decomposition. Moreover, the multiscale analyses are validated with reference solutions obtained with a full fine-scale solution procedure

On micro-to-macro connections in domain decomposition multiscale methods

Micro-to-macro connection techniques constitute a key ingredient in the formulation of multiscale strategies. In this contribution several connection methods are explored for the concurrent multiscale analysis of brittle heterogeneous materials. Particularly, these techniques are investigated in a domain decomposition strong coupling multiscale framework. The structural component under analysis is partitioned into a number of non-overlapping domains and a fine scale resolution is assigned therein in an adaptive manner exploiting a zoom-in technique. Mesh refinement is employed in the domains where crack coalescence and growth take place. The original contribution presented in this manuscript consists in the study of different strong and weak locality constraints that connect coarse and fine resolution domains. Standard collocation and average compatibility are considered and serve as a basis for the development of two new interscale links. The influence of different locality constraints is studied in terms of the mechanical response and the error distribution is compared to a full fine scale analysis

Enhanced domain decomposition techniques for the modeling of softening materials

In this study a FETI: Finite Element Tearing and Interconnecting [1] technique is adopted and exploited for the efficient and accurate modeling of softening materials such as concrete and rock. A fie scale analysis in which concrete is modelled as a three-phase material is used. Special attention is given to the treatment of linear and non-linear domains during the analysis. Several optimization enhancements are introduced in order to identify the active non-linear domains and selectively use computational effort. The effect of different decomposition criteria is analyzed in this study. The brittle constitutive behaviour of the above mentioned material is simulated by means of a Gradient Enhanced Damage model.Structural EngineeringCivil Engineering and Geoscience