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This book gathers contributions addressing issues related to the analysis of composite structures, whose most relevant common thread is augmented numerical efficiency, which is more accurate for given computational costs than existing methods and methodologies. It first presents structural theories to deal with the anisotropy of composites and to embed multifield and nonlinear effects to extend design capabilities and provide methods of augmenting the fidelity of structural theories and lowering computational costs, including the finite element method. The second part of the book focuses on damage analysis; the multiscale and multicomponent nature of composites leads to extremely complex failure mechanisms, and predictive tools require physics-based models to reduce the need for fitting and tuning based on costly and lengthy experiments, and to lower computational costs; furthermore the correct monitoring of in-service damage is decisive in the context of damage tolerance. The third part then presents recent advances in embedding characterization and manufacturing effects in virtual testing. The book summarizes the outcomes of the FULLCOMP (FULLy integrated analysis, design, manufacturing, and health-monitoring of COMPosite structures) research project.



Chapter 1. Introduction

This chapter provides an overview of the book contents and the most significant works from the literature on related topics. Each section of this chapter deals with one of the main parts of the book, namely, advanced structural theories, failure and damage analyses, virtual characterization and manufacturing. The first part of this volume presents structural theories to deal with the anisotropy of composites and to embed multifield and nonlinear effects to widen design capabilities. The aim is to provide methods to augment the fidelity of structural theories and lower computational costs with attention paid to the finite element method. The second part handles the damage analysis. The multiscale and multicomponent nature of composites leads to extremely complex failure mechanisms and predictive tools require physics-based models to lower the need for fitting and tuning from costly and lengthy experimental campaigns, and lower computational costs. Furthermore, the proper monitoring of in-service damage is decisive in a damage tolerant perspective. The third part presents recent advances to embed characterization and manufacturing effects in virtual testing. Higher cost-effectiveness claims the reduction of physical characterization campaigns as well as higher fidelity for multiscale identification. Variations of properties due to defects stemming from manufacturing can propagate through scales and dramatically alter performances. The characterization of the material requires proper uncertainty quantification tools based on stochastic models and should embed metadata handling for informed virtual testing.
M. Petrolo

High-Fidelity and Computationally Efficient Models for Multiphysics and Design


Chapter 2. Variable Kinematic Shell Formulations Accounting for Multi-field Effects for the Analysis of Multi-layered Structures

This chapter presents refined shell finite element models with variable kinematics for the analysis of multi-layered structures involved in four physical fields: mechanical, electric, thermal, and hygroscopic. Variable kinematic models in the framework of Carrera Unified Formulation (CUF) with various kinematic assumptions are discussed. An efficient tool to realize adaptable refinement in finite element models, Node-Dependent Kinematics approach, is introduced. Refined doubly curved shell finite element formulations derived from the principle of virtual displacements accounting for multi-field coupling effects are presented.
G. Li, E. Carrera, M. Cinefra, E. Zappino, E. Jansen

Chapter 3. Bistable Buckled Beam-Like Structures by One-Dimensional Hierarchical Modeling

In the last few years, great interest has been shown in harnessing bistability, or more generally multistability, as a source of energy and motion in engineering applications, both at micro-scale (such as switches, relays, valves or pumps) and macro-scale (shape-changing aerodynamic panels, variable geometry engine exhausts and reconfigurable airplane wings). Bistability is a highly non-linear phenomenon relying on the snap-through buckling, an elastic instability in which a structure passes from one equilibrium configuration to another nonadjacent equilibrium state by means of a sudden displacement jump. The theoretical understanding of such phenomenon plays a key role in the structural design optimization for practical applications. To this aim, the development of accurate yet efficient computational models for the analysis of bistable composite structures represents an important and up-to-date research topic. This chapter addresses the development of a hierarchical framework based on the Carrera Unified Formulation that allows the derivation of several kinematic models by arbitrarily setting the polynomial order approximation of the displacement field. The proposed approach is assessed towards reference and commercial software finite elements solutions for the analysis of bistable buckled beam-like structures, showing the capability of accurately yet efficiently predicting stable configurations, snap-through load, force-displacement curves and stress evolution in the geometrically non-linear regime.
G. De Pietro, G. Giunta, S. Belouettar, E. Carrera

Chapter 4. Multiscale Nonlinear Analysis of Beam Structures by Means of the Carrera Unified Formulation

This chapter addresses a multi-scale analysis of beam structures using the Carrera Unified Formulation (CUF). Under the framework of the \(\text {FE}^{2}\) method, the analysis is divided into a macroscopic/structural problem and a microscopic/material problem. At the macroscopic level, several higher-order refined beam elements can be easily implemented via CUF by deriving a fundamental nucleus that is independent of the approximation order over the thickness and the number of nodes per element (they are free parameters of the formulation). The unknown macroscopic constitutive law is obtained by numerical homogenization of a Representative Volume Element (RVE) at the microscopic level. Vice versa, the microscopic deformation gradient is calculated from the macroscopic model. Information is passed between the two scales in a \(\text {FE}^{2}\) sense. The resulting nonlinear problem is solved through the Asymptotic Numerical Method (ANM) that is more reliable and less time consuming when compared to classical iterative methods. The developed models are used as a first attempt to investigate the microstructure effect on the macrostructure geometrically nonlinear response. Results are compared regarding accuracy and computational costs towards full FEM solutions demonstrating the robustness and efficiency of the proposed approach.
Y. Hui, G. Giunta, S. Belouettar, H. Hu, E. Carrera

Failure Analysis, Impact and Health-Monitoring


Chapter 5. On the Effectiveness of Higher-Order One-Dimensional Models for Physically Nonlinear Problems

The chapter presents numerical assessments of physically nonlinear problems through a class of refined one-dimensional theories based on the Carrera Unified Formulation (CUF). CUF is a hierarchical formulation to generate refined structural theories through a variable kinematic approach. Physical nonlinearities include von Mises plasticity and cohesive interface modeling for delamination of composites. This work aims to provide insights into the effect of kinematic enrichment on the overall nonlinear behavior of the structure. Guidelines stem from the evaluation of the accuracy and numerical efficiency of the proposed models against analytical and numerical approaches from the literature.
I. Kaleel, M. Petrolo, E. Carrera, A. M. Waas

Chapter 6. Post-buckling Progressive Failure Analysis of Composite Panels Using a Two-Way Global-Local Coupling Approach Including Intralaminar Failure and Debonding

A novel two-way global-local coupling approach to model progressive separation of skin and stringer in combination with intralaminar damage in stiffened CFRP panels under compression is presented. The methodology makes it possible to examine the damage at two levels of accuracy, taking advantage of fast calculations at the global level and assessing in detail the damage propagation at the local level. The required appropriate information exchange between the global and local level in both directions has been attained. This chapter presents an overview of this efficient approach for progressive failure analysis of composite panels and illustrates the approach on the basis of a one-stringer panel, in particular for the case of skin-stringer debonding.
M. Akterskaia, E. Jansen, S. R. Hallet, P. M. Weaver, R. Rolfes

Chapter 7. Mesoscale Hyperelastic Model of a Single Yarn Under High Velocity Transverse Impact

In this chapter the modellisation of a single dry yarn under impact load as an homogeneous hyperelastic continuous body will be treated. In the first part, a preliminary introduction to dry fabrics mesoscopic models in impact applications will be performed. In the second part, an hyperelastic constitutive law for yarn structures continuous modeling will be presented. The proposed constitutive behaviour aims to the modellisation of the yarn transverse cross section evolution during an impact which is actually obliged in the classical linear elastic formulation. A theoretical introduction to the hyperelastic law is followed by its validation using the numerical model of transversely impacted yarn as benchmark test. The obtained results are compared with those from microscopic and classic linear elastic mesoscopic studies. A good agreement is obtained from the comparison with the different approaches. Moreover, the ability of the proposed model in representing yarn transverse behavior and formulate multiaxial failure criteria compared to the linear elastic approach universally adopted is remarked.
P. Del Sorbo, J. Girardot, F. Dau, I. Iordanoff

Chapter 8. Structural Health Monitoring: Numerical Simulation of Lamb Waves Via Higher-Order Models

This chapter proposes a numerically efficient method to simulate Lamb waves in laminated structures in the framework of structural health monitoring (SHM). Due to the high frequencies involved in Lamb wave problems, time-domain analyses call for very fine spatial and temporal discretizations of the numerical model. As a consequence, standard models based on the finite element method (FEM) might become extremely large, and new efficient simulation tools must be introduced. A series of multi-layered plate elements for the wave propagation problem are proposed. Equivalent single layer (ESL) and layer wise (LW) kinematics based on hierarchical assumptions are tested. Exploiting their superior convergence rates, higher-order polynomials are used as shape functions of the finite elements. Numerical examples of composite plates are included to show the advantages of each model proposed.
A. G. de Miguel, A. Pagani, E. Carrera

Virtual Characterization, Manufacturing Effects and Uncertainty Quantification


Chapter 9. Improving the Static Structural Performance of Panels with Spatially Varying Material Properties Using Correlations

This chapter introduces an approach to systematically analyze stochastic distributions of spatially varying material properties in structures. The approach gives insight into how spatial variations of material properties affect the mechanical response of a structure. If sufficient knowledge of the production processes is available, this allows designers to analyze the probability that a certain design criterion (e.g. a certain buckling load level) is met. Stochastic structural analyses can be used to analyze how variations are correlated to a structural measure. This gives information on the sensitivity of the structure with respect to variations. In the present work, this is used to improve the structural performance by distributing a material pattern according to a pattern based on the sensitivity topology. This approach is illustrated by redistributing the material properties of an axially loaded panel on the basis of the correlation of the spatially varying Young’s modulus with the linear buckling load of the panel.
S. van den Broek, S. Minera, E. Jansen, A. Pirrera, P. M. Weaver, R. Rolfes

Chapter 10. Multiscale Identification of Material Properties for Anisotropic Media: A General Inverse Approach

This work deals with the problem of characterizing the material properties of a composite plate, made of unidirectional fiber-reinforced laminae, at each pertinent scale (microscopic and mesoscopic ones). The characterization is achieved through a single non-destructive harmonic test performed at the macroscopic scale of the specimen. A general multi-scale identification strategy (MSIS) is proposed to accomplish this goal. The multi-scale identification problem is split into two interdependent sub-problems which are stated, at both levels, as constrained minimization problems. At the first level the lamina properties are retrieved by minimizing the distance between the numerical and the reference harmonic responses of the multilayer plate. Conversely, the second-level problem aims at characterizing fiber and matrix elastic properties by exploiting the results of the first step. The whole procedure is based on a special global hybrid optimization algorithm and on the strain energy homogenization method of periodic media as well. The effectiveness of the approach is illustrated through a meaningful numerical benchmark.
L. Cappelli, M. Montemurro, F. Dau, L. Guillaumat

Chapter 11. Metamodel-Based Uncertainty Quantification for the Mechanical Behavior of Braided Composites

This chapter presents an uncertainty quantification framework for triaxially braided composites simulation, dealing with the stochastic stiffness prediction via numerical multiscale analysis. Efficiency is achieved by using various metamodeling techniques, such as neural networks, polynomial chaos expansion and Kriging modeling. Uncertainties accounting for material and geometric randomness are propagating through the scales to the final scatter of the mechanical properties of the macroscale. Information about the stochastic input and the dominating uncertain parameters is offered via application of a variance-based global sensitivity analysis. All methods employed in this work are non-intrusive, hence the framework can be used for all sorts of composite materials and numerical models. The need for realistic uncertainty quantification is highlighted.
G. Balokas, B. Kriegesmann, S. Czichon, A. Böttcher, R. Rolfes
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