Multi-layered bird beaks: a finite-element approach towards the role of keratin in stress dissipation

Bird beaks are layered structures, which contain a bony core and an outer keratin layer. The elastic moduli of this bone and keratin were obtained in a previous study. However, the mechanical role and interaction of both materials in stress dissipation during seed crushing remain unknown. In this paper, a multi-layered finite-element (FE) model of the Java finch''s upper beak (Padda oryzivora) is established. Validation measurements are conducted using in vivo bite forces and by comparing the displacements with those obtained by digital speckle pattern interferometry. Next, the Young modulus of bone and keratin in this FE model was optimized in order to obtain the smallest peak von Mises stress in the upper beak. To do so, we created a surrogate model, which also allows us to study the impact of changing material properties of both tissues on the peak stresses. The theoretically best values for both moduli in the Java finch are retrieved and correspond well with previous experimentally obtained values, suggesting that material properties are tuned to the mechanical demands imposed during seed crushing.     

Hierarchical multiscale structure–property relationships of the red-bellied woodpecker (Melanerpes carolinus) beak

We experimentally studied beaks of the red-bellied woodpecker to elucidate the hierarchical multiscale structure–property relationships. At the macroscale, the beak comprises three structural layers: an outer rhamphotheca layer (keratin sheath), a middle foam layer and an inner bony layer. The area fraction of each layer changes along the length of the beak giving rise to a varying constitutive behaviour similar to functionally graded materials. At the microscale, the rhamphotheca comprises keratin scales that are placed in an overlapping pattern; the middle foam layer has a porous structure; and the bony layer has a big centre cavity. At the nanoscale, a wavy gap between the keratin scales similar to a suture line was evidenced in the rhamphotheca; the middle foam layer joins two dissimilar materials; and mineralized collagen fibres were revealed in the inner bony layer. The nano- and micro-indentation tests revealed that the hardness (associated with the strength, modulus and stiffness) of the rhamphotheca layer (approx. 470 MPa for nano and approx. 320 MPa for micro) was two to three times less than that of the bony layer (approx. 1200 MPa for nano and approx. 630 MPa for micro). When compared to other birds (chicken, finch and toucan), the woodpecker''s beak has more elongated keratin scales that can slide over each other thus admitting dissipation via shearing; has much less porosity in the bony layer thus strengthening the beak and focusing the stress wave; and has a wavy suture that admits local shearing at the nanoscale. The analysis of the woodpeckers'' beaks provides some understanding of biological structural materials'' mechanisms for energy absorption.     

In-situ X-ray computed tomography characterisation of 3D fracture evolution and image-based numerical homogenisation of concrete

In-situ micro X-ray Computed Tomography (XCT) tests of concrete cubes under progressive compressive loading were carried out to study 3D fracture evolution. Both direct segmentation of the tomography and digital volume correlation (DVC) mapping of the displacement field were used to characterise the fracture evolution. Realistic XCT-image based finite element (FE) models under periodic boundaries were built for asymptotic homogenisation of elastic properties of the concrete cube with Young's moduli of cement and aggregates measured by micro-indentation tests. It is found that the elastic moduli obtained from the DVC analysis and the FE homogenisation are comparable and both within the Reuss-Voigt theoretical bounds, and these advanced techniques (in-situ XCT, DVC, micro-indentation and image-based simulations) offer highly-accurate, complementary functionalities for both qualitative understanding of complex 3D damage and fracture evolution and quantitative evaluation of key material properties of concrete.     

Direct comparison between experiments and computations at the atomic length scale: a case study of graphene

This paper discusses a set of recent experimental results in which the mechanical properties of monolayer graphene molecules were determined. The results included the second-order elastic modulus which determines the linear elastic behavior and an estimate of the third-order elastic modulus which determines the non-linear elastic behavior. In addition, the distribution of the breaking force strongly suggested the graphene to be free of defects, so the measured breaking strength of the films represented the intrinsic breaking strength of the underlying carbon covalent bonds. The results of recent simulation efforts to predict the mechanical properties of graphene are discussed in light of the experiments. Finally, this paper contains a discussion of some of the extra challenges associated with experimental validation of multi-scale models.     

Adaptive vibration control of a cylindrical shell with laminated PVDF actuator

A generalized higher-order theory describing the mechanical behavior of multi-layered composite plates with arbitrary lamination scheme is proposed. Ritz’s method is employed to determine the kinematic unknowns expressed in a complete polynomial power series of the thickness-wise coordinate whereas the dependence on the in-plane coordinates is such that the functions satisfy all boundary conditions. The correct constitutive laws of a three-dimensional orthotropic elastic continuum are employed for each individual layer. The convergence and accuracy of the computational scheme are investigated by comparing elastic static and buckling results with analytical or finite element solutions for complex cross- and angle-ply laminates. For further validation of the theory, laminated plates under a transverse pressure are investigated for technically relevant lamination schemes and the associated deformation and stress results are compared with those obtained through FE calculations.     

Two solution strategies to improve the computational performance of sequentially linear analysis for quasi-brittle structures

Sequentially linear analysis (SLA), an event-by-event procedure for finite element (FE) simulation of quasi-brittle materials, is based on sequentially identifying a critical integration point in the FE model, to reduce its strength and stiffness, and the corresponding critical load multiplier (λ_crit), to scale the linear analysis results. In this article, two strategies are proposed to efficiently reuse previous stiffness matrix factorisations and their corresponding solutions in subsequent linear analyses, since the global system of linear equations representing the FE model changes only locally. The first is based on a direct solution method in combination with the Woodbury matrix identity, to compute the inverse of a low-rank corrected stiffness matrix relatively cheaply. The second is a variation of the traditional incomplete LU preconditioned conjugate gradient method, wherein the preconditioner is the complete factorisation of a previous analysis step's stiffness matrix. For both the approaches, optimal points at which the factorisation is recomputed are determined such that the total analysis time is minimised. Comparison and validation against a traditional parallel direct sparse solver, with regard to a two-dimensional (2D) and three-dimensional (3D) benchmark study, illustrates the improved performance of the Woodbury-based direct solver over its counterparts, especially for large 3D problems.     

Numerical prediction of damage in composite structures from soft body impacts

The paper summarises recent progress on materials modelling and numerical simulation of soft body impact damage in fibre reinforced composite aircraft structures. The work is based on the application of finite element (FE) analysis codes to simulate damage in composite shell structures under impact loads. Composites ply damage models and interply delamination models have been developed and implemented in commercial explicit FE codes. Models are discussed for predicting impact loads on aircraft structures arising from deformable soft bodies such as gelatine (synthetic bird) and ice (hailstone). The composites failure models and code developments are briefly summarised and applied in the paper to numerical simulation of synthetic bird impact on idealised composite aircraft structures.     

Progressive damage and nonlinear analysis of pultruded composite structures

This study combines a simple damage modeling approach with micromechanical models for the progressive damage analysis of pultruded composite materials and structures. Two micromodels are used to generate the nonlinear effective response of a pultruded composite system made up from two alternating layers reinforced with roving and continuous filaments mat (CFM). The layers have E-glass fiber and vinylester matrix constituents. The proposed constitutive and damage framework is integrated within a finite element (FE) code for a general nonlinear analysis of pultruded composite structures using layered shell or plate elements. The micromechanical models are implemented at the through-thickness Gaussian integration points of the pultruded cross-section. A layer-wise damage analysis approach is proposed. The Tsai–Wu failure criterion is calibrated separately for the CFM and roving layers using ultimate stress values from off-axis pultruded coupons under uniaxial loading. Once a failure is detected in one of the layers, the micromodel of that layer is no longer used. Instead, an elastic degrading material model is activated for the failed layer to simulate the post-ultimate response. Damage variables for in-plane modes of failure are considered in the effective anisotropic strain energy density of the layer. The degraded secant stiffness is used in the FE analysis. Examples of progressive damage analysis are carried out for notched plates under compression and tension, and a single-bolted connection under tension. Good agreement is shown when comparing the experimental results and the FE models that incorporate the combined micromechanical and damage models.     

Elastic constants of metal/ceramic composites with lamellar microstructures: Finite element modelling and ultrasonic experiments

The elastic properties of single domains of lamellar AlSi12/Al₂O₃ composites produced by metal infiltration of freeze cast preforms have been examined. The anisotropic elastic constants determined from ultrasonic phase spectroscopy (UPS) experiments have been compared to microstructure based FE-models created with the program OOF2, micromechanical models (Mori–Tanaka and inverse Mori–Tanaka) and an analytical model for an ideal laminate. The influences of lamellae orientations and ceramic contents on the elastic constants have been investigated. Along the lamellae directions the microstructure based FE model and the inverse Mori–Tanaka model are in good agreement with experimental results. Perpendicular to the lamellae the experiment shows a stiffer than expected elastic behaviour.     

Experimental and computational characterization of designed and fabricated 50:50 PLGA porous scaffolds for human trabecular bone applications

The present study utilizes image-based computational methods and indirect solid freeform fabrication (SFF) technique to design and fabricate porous scaffolds, and then computationally estimates their elastic modulus and yield stress with experimental validation. 50:50 Poly (lactide-co-glycolide acid) (50:50 PLGA) porous scaffolds were designed using an image-based design technique, fabricated using indirect SFF technique, and characterized using micro-computed tomography (μ-CT) and mechanical testing. μ-CT data was further used to non-destructively predict the scaffold elastic moduli and yield stress using a voxel-based finite element (FE) method, a technique that could find application in eventual scaffold quality control. μ-CT data analysis confirmed that the fabricated scaffolds had controlled pore sizes, orthogonally interconnected pores and porosities which were identical to those of the designed files. Mechanical tests revealed that the compressive modulus and yield stresses were in the range of human trabecular bone. The results of FE analysis showed potential stress concentrations inside of the fabricated scaffold due to fabrication defects. Furthermore, the predicted moduli and yield stresses of the FE analysis showed strong correlations with those of the experiments. In the present study, we successfully fabricated scaffolds with designed architectures as well as predicted their mechanical properties in a nondestructive manner.     

基于有限元和神经网络的杂交建模

针对复杂非线性结构动力学系统提出了一种基于有限元与神经网络相结合的杂交建模方法。依据该方法,首先将系统中的线性结构部分采用有限元建模,非线性或难以机理建模的结构部件采用神经网络描述。其次,再通过力和位移边界联接条件将有限元模型部分和神经网络模型部分结合从而得到整个系统的杂交模型,且杂交模型的物理结构明确,精度较高,网络规模较小。在一非线性隔振系统的杂交建模算例仿真中,用所建杂交模型对正弦及宽带随机激励进行了预测检验分析,结果良好,该杂交建模方法为主体结构为线弹性结构而又包含有强非线性器件的非线性动力学系统提供了一种有效的建模途径。     

A progressive damage simulation algorithm for GFRP composites under cyclic loading. Part II: FE implementation and model validation

The FE implementation of FADAS, a material constitutive model capable of simulating the mechanical behaviour of GFRP composites under variable amplitude multiaxial cyclic loading, was presented. The discretization of the problem domain by means of FE is necessary for predicting the damage progression in real structures, as failure initiates at the vicinity of a stress concentrator, causing stress redistribution and the gradual spread of damage until the global failure of the structure. The implementation of the stiffness and strength degradation models in the principal material directions of the unidirectional ply was thoroughly discussed. Details were also presented on the FE models developed, the computational effort needed and the definition of final failure considered. Numerical predictions were corroborated satisfactorily by experimental data from constant amplitude uniaxial fatigue of multidirectional glass/epoxy laminates under various stress ratios. The validation of predictions included fatigue strength, stiffness degradation and residual static strength after cyclic loading.     

Experimental and numerical investigations of the mechanical behavior of half sandwich laminate in the context of blanking

In this study, the complex mechanical behavior of an aluminum/low-density polyethylene (LDPE) half sandwich structure was investigated during the blanking process. Mechanical tests were conducted for the polymer and metal layer and the delamination behavior of the adhesive between the two layers. A new testing device was designed for detecting the delamination under tensile mode. Corresponding finite element models were established for the mechanical tests of the metal layer and the delamination of both layers for inverse parameter identification. Material parameters for Lemaitre-type damage, Drucker-Prager, and cohesive zone models were identified for the metal, polymer, and adhesive, respectively. A finiteelement (FE) model was established for the blanking process of the sandwich structures. The experimental forcedisplacement curves, obtained in the blanking process of the half sandwich sheet, were compared with the predicted results of the FE model. The results showed that the predicted force-displacement curves and the experimental results were in good agreement. Additionally, the correlation between cutting clearance and changes in the forcedisplacement curves was obtained. Three feature values quantitatively described the imperfection of the experimental cutting edge. The effect of punch clearance on these values was studied numerically and experimentally. The results indicated that a smaller clearance generated a better cutting-edge quality. The stress state of the half sandwich structure during blanking was analyzed using the established FE model.The full text can be downloaded at https://link.springer.com/article/10.1007/s40436-020-00308-z     

Characterisation by Inverse Techniques of Elastic,Viscoelastic and Piezoelectric Properties of Anisotropic Sandwich Adaptive Structures

In this article we present recent developments regarding parameter estimation in sandwich structures with viscoelastic frequency dependent core and elastic laminated skin layers, with piezoelectric patch sensors and actuators bonded to the exterior surfaces of the sandwich. The frequency dependent viscoelastic properties of the core material are modelled using fractional derivative models, with unknown parameters that are to be estimated by an inverse technique, using experimentally measured natural frequencies and associated modal loss factors. The inverse problem is formulated as a constrained minimisation problem, and gradient based optimization techniques are employed. Applications are presented and discussed, focused on the identification of viscoelastic frequency dependent core material properties.     

A linear-encoding model explains the variability of the target morphology in regeneration

A fundamental assumption of today''s molecular genetics paradigm is that complex morphology emerges from the combined activity of low-level processes involving proteins and nucleic acids. An inherent characteristic of such nonlinear encodings is the difficulty of creating the genetic and epigenetic information that will produce a given self-assembling complex morphology. This ‘inverse problem’ is vital not only for understanding the evolution, development and regeneration of bodyplans, but also for synthetic biology efforts that seek to engineer biological shapes. Importantly, the regenerative mechanisms in deer antlers, planarian worms and fiddler crabs can solve an inverse problem: their target morphology can be altered specifically and stably by injuries in particular locations. Here, we discuss the class of models that use pre-specified morphological goal states and propose the existence of a linear encoding of the target morphology, making the inverse problem easy for these organisms to solve. Indeed, many model organisms such as Drosophila, hydra and Xenopus also develop according to nonlinear encodings producing linear encodings of their final morphologies. We propose the development of testable models of regeneration regulation that combine emergence with a top-down specification of shape by linear encodings of target morphology, driving transformative applications in biomedicine and synthetic bioengineering.     

A review of some damage tolerance design approaches for aircraft structures

Damage tolerance design is becoming a necessity in the design of modern aircraft although its importance was recognized as long as four centuries ago by Leonardo da Vinci. Two decades ago structural design engineers and research workers felt the need of incorporating damage tolerance in the design of aircraft structure. Due to a lack of comprehensive damage tolerance methodology large scale component test results were used to develop empirical damage tolerance methods. Recently, linear elastic fracture mechanics has been used in predicting residual strength and crack growth rates in damaged structure. As a result of these efforts significant developments in cracked structure analytical methodology have been achieved. The recent Air Force requirement to apply linear elastic fracture mechanics approach in damage tolerance design of aircraft structures, warrants and critical review of various approaches. In this paper an attempt has been made to critically review some damage tolerance design approaches and their application to aircraft structures.

The paper consists of three main sections: The first section reviews the residual strength analysis methodology, assumptions and limitations of each method are discussed through a simple example. The second part surveys the various crack propagation laws, including linear and non-linear ranges and spectrum loading effects. In the third and last section, fracture mechanics methodology is applied to several types of built-up structural components under spectrum loading conditions. The comparison of test results and analysis of complex structures indicate that simple methods of fracture mechanics can be applied to find the damage tolerant strength and rate of crack growth.

The review presented in this paper indicates that the majority of work done in development of fracture mechanics analytical methodology has been based on data obtained from small scale laboratory specimens tested under closely controlled conditions of damage and environment. The validity of the methodology for complex structure under complex loading conditions has not been established. Before the results of a fracture mechanics analytical methodology can be accepted with a high degree of confidence many realism factors must be properly accounted for in the analysis.     

A scalable multi‐level preconditioner for matrix‐free µ‐finite element analysis of human bone structures

The recent advances in microarchitectural bone imaging disclose the possibility to assess both the apparent density and the trabecular microstructure of intact bones in a single measurement. Coupling these imaging possibilities with microstructural finite element (µFE) analysis offers a powerful tool to improve bone stiffness and strength assessment for individual fracture risk prediction. Many elements are needed to accurately represent the intricate microarchitectural structure of bone; hence, the resulting µFE models possess a very large number of degrees of freedom. In order to be solved quickly and reliably on state‐of‐the‐art parallel computers, the µFE analyses require advanced solution techniques. In this paper, we investigate the solution of the resulting systems of linear equations by the conjugate gradient algorithm, preconditioned by aggregation‐based multigrid methods. We introduce a variant of the preconditioner that does not need assembling the system matrix but uses element‐by‐element techniques to build the multilevel hierarchy. The preconditioner exploits the voxel approach that is common in bone structure analysis, and it has modest memory requirements, at the same time robust and scalable. Using the proposed methods, we have solved in 12min a model of trabecular bone composed of 247 734 272 elements, yielding a matrix with 1 178 736 360 rows, using 1024 CRAY XT3 processors. The ability to solve, for the first time, large biomedical problems with over 1 billion degrees of freedom on a routine basis will help us improve our understanding of the influence of densitometric, morphological, and loading factors in the etiology of osteoporotic fractures such as commonly experienced at the hip, spine, and wrist. Copyright © 2007 John Wiley & Sons, Ltd.     

羊毛角蛋白作为生物医用材料的研究进展

羊毛是一种天然角蛋白纤维,人们很早就开始用化学方法降解羊毛以研究其蛋白质组成和结构,并尝试研究它的各种再生应用.随着生物技术,特别是组织工程的发展,人们开始关注羊毛角蛋白在生物及医用上的研究,并取得一定研究结果.由此对经典的羊毛角蛋白结构、提取方法、相应生物材料及其应用的研究与进展进行了总结回顾,并对发展前景作了评述.     

Patient‐Specific Finite Element Modelling and Validation of Porcine Femora in Torsion

The accuracy of biomechanical simulation has been improved by using high‐resolution computed tomography (CT) to define the geometry and material parameters. This technique has been used to assess numerous systems, including the mechanical properties of bone, fixation techniques post‐fracture and the performance of bone microarchitecture. In this study, a semi‐automated process for converting CT data into finite element (FE) models was used to model the mid‐shaft (diaphysis) of porcine femoral samples under sub‐maximal torsional and compressive load. Physical validation was undertaken to investigate if the all‐important geometry and material property mapping functioned correctly. Porcine femoral specimens were imaged using contiguous helical CT, which was converted to FE models using ScanIP from Simpleware, Exeter, UK. The heterogeneous material properties were estimated using density–elasticity relationships proposed in literature for human bone samples. Laboratory testing performed favourably, with a linear strain response validating the use of the array of linear material models used in simulation. The simulation procedure also performed well. Linear regression and mean error calculation demonstrated accurate correlation between predicted (from simulation) and observed (measured within the laboratory) results that offered improvement over the accuracy within comparative testing for human samples. Using FE modelling on a patient‐specific basis offers potential in a number of scenarios, including the determination of injury risk and design of protective equipment. The increased accessibility of animal samples allows large‐scale fracture testing of complex loading mechanisms and the potential to consider younger animal samples (to investigate the behaviour of developing bone). Spiral fractures of long bones have been demonstrated to be an indicator of non‐accidental injury in children. Combining the increased accuracy in torsional simulation in this study with younger sample testing may be employed to attempt to determine the causes of fracture from post fracture scans, aiding in the diagnosis of non‐accidental injury.     

Free vibration analysis of reinforced thin-walled plates and shells through various finite element models

Abstract

This article deals with free vibration analysis of thin-walled structures reinforced by longitudinal stiffeners using refined one-dimensional (1D) models.The 1D theory, which is used in the present article, has hierarchical features and it is based on the Carrera Unified Formulation (CUF). The displacement field over the cross section is obtained by means of Taylor (TE) or Lagrange (LE) expansions. Finite element (FE) method is applied along the beam axis to obtain weak form solutions of the related governing equations. The obtained results are compared with those from classical finite element formulations based on plate and shell (2D), beam (1D), and solid (3D) elements that are available in commercial software. When solid formulation is used to build the FE solutions, stringers and skin are modeled with only 3D elements while, in the 2D-1D FE models, shell and beam elements are used for skin and stringers, respectively. Three benchmark problems are analyzed: a flat plate, a curved panel, and a thin-walled cylinder. When TE models are used, different orders of expansion, N, are considered, where N is a free parameter of the formulation. As far as Lagrange expansions are concerned, four-node (LE 4) and nine-node (LE 9) elements are used to build different meshes on the cross section. The results show that the present 1D models are able to analyze the dynamic behavior of complex structures and can detect 3D effects as well as very complex shell-like modes typical of thin-walled structures. Moreover, the 1D-CUF elements yield accurate results with a low number of degrees of freedom.