Fictitious Material Research Articles

Translaminar fracture toughness characterisation for a glass fibre/polyamide 6 laminated composite by a novel approach based on fictitious material concept

This paper proposes a novel approach for the characterisation of the material fracture toughness associated with translaminar tensile failure, consisting in the application of the Fictitious Material Concept (FMC) by using the testing configuration of the Modified Two Parameter Model (MTPM). The main advantage of such an approach is to avoid the use of nonlinear fracture mechanics for material fracture toughness characterisation. The novel approach is applied to compute the translaminar fracture toughness of a unidirectional glass fibre (GF)/polyamide 6 (PA6) laminated composite. Moreover, the experimental campaign carried out is numerically simulated by means of a micromechanical finite element model, and the fracture toughness is computed by employing two different approaches, that is, the novel one and the MTPM. The present study proves, for the first time, that the Fictitious Material Concept can be applied by considering both experimental and numerical structural responses since it provides, in both cases, quite satisfactory accuracy in term of laminated composite fracture toughness. Therefore, the great advantage is that, when a validated numerical model is available, experimental campaigns may be avoided, saving time and money. Moreover, it is proved that the FMC can be used to investigate specimen size effect on fracture toughness.

Does VIMC-FMC work well on highly ductile bimetal joints? An investigation on mixed mode I/II fracture of AA1050/Cu bimetal weakened by U-notches

In this study, it is attempted to check if the virtual isotropic material concept (VIMC), originally suggested for fiber-reinforced composite laminates, can be used as an appropriate simplifying tool in fracture estimation of notched bimetals. First, the aluminum alloy AA1050 and the copper are cladded together using the roll-bonding technique. Then, several U-notched bimetal specimens are manufactured to perform fracture tests under mixed mode I/II loading conditions. Due to the highly ductile behavior of the AA1050/Cu bimetal, the fictitious material concept (FMC) is adopted to equate the bimetal with a fictitious material having perfectly linear elastic behavior with the aim to avoid the elastoplastic fracture analysis. Finally, the VIMC and FMC are coupled with three famous brittle fracture models, i.e., the U-notch maximum tangential stress (UMTS), U-notch mean stress (UMS), and U-notch strain energy density (USED) criteria, for predicting the experimentally measured strength of the notched bimetal specimens. The results indicate that the maximum discrepancy between the theoretical predictions and the experimental results in all the combined failure criteria is less than 8%. Therefore, the VIMC-FMC combination is found to be quite effective as a converter to solve the complex problem of highly ductile fracture of notched inhomogeneous anisotropic bimetals under mixed mode I/II loading using only the linear elastic analysis of the fictitious homogeneous isotropic plates. Also, found in this research is that not only VIMC works well on fiber-reinforced composite laminates, but also on bimetal joints.

Notch strength evaluation for highly ductile Al/Cu bi-metal fabricated by the roll-bonding technique under pure mode I and pure mode II loading conditions

In this work, the aluminum alloy AA1050 and copper sheets are cladded together using the roll-bonding technique to make rectangular bi-metallic joints. To examine the notch strength of this bi-metal under quasi-static loading, central slits with two U-shaped ends are introduced into the bi-metal. The slit orientation angle is adopted such that for horizontal slit, the notched rectangular specimen experiences pure mode I loading. However, when the slit orientation angle changes to about 67 degrees, which is obtained by the finite element (FE) analysis, the U-ends of the slit are subjected to pure mode II loading. Considering three different notch tip radii, two loading conditions, and three replicates for each test configuration, totally 18 U-notched specimens are produced and tested with the goal to measure the notch strength of bi-metal experimentally. According to the experimental observations, the bi-metal joint is perfect such that crack initiates from the notch in the whole thickness, proposing that the whole bi-metal joint can be considered as a single bulk material. Based on these observations and thanks to the virtual isotropic material concept (VIMC), the AA1050/Cu bi-metal is firstly equated with a virtual bulk material having homogeneous and isotropic behavior. Secondly, due to highly ductile behavior of the bi-metal joint proven by the associated tensile stress–strain curve, the fictitious material concept (FMC) is used to equate the virtual isotropic material obtained from the previous step having elastoplastic behavior with a fictitious material having perfectly linear elastic behavior. Finally, the VIMC and FMC are linked to the U-notch maximum tangential stress (UMTS), U-notch mean stress (UMS), and U-notch strain energy density (USED) criteria to predict the notch strengths of the bi-metal joint experimentally measured. With always higher than 92% accuracy for all VIMC-FMC-UMTS, VIMC-FMC-UMS, and VIMC-FMC-USED combined criteria, it is shown that the two-level strategy of material simplification, i.e., VIMC-FMC, is quite successful to be combined with different brittle fracture criteria for predicting the notch strength of AA1050-Cu bimetals under both pure tensile and pure in-plane shear modes of loading.

A review on ductile fracture prediction of cracked/notched components: The distinct and simplifying roles of the equivalent material concept and fictitious material concept

Most of engineering structures and components are made of ductile materials, while fracture mechanics tools have been mostly developed for brittle materials. This article investigates the critical load estimation in fracture problems in presence of the elasto-plasticity from the standpoint of major approaches in fracture mechanics including theoretical, experimental, and computational. A review is comprehensively performed on literature with a main focus on two new concepts, namely the Equivalent Material Concept (EMC) and the Fictitious Material Concept (FMC), by which elastoplastic ductile materials can be simplified to linear elastic brittle materials. Therefore, by overcoming the nonlinear aspects, solving of the fracture problems in the linear elastic fracture mechanics (LEFM) framework becomes possible. It is understood from this comprehensive literature survey that while there are several approaches for estimating ductile fracture in cracked/notched members under various loading conditions, most of them need nonlinear analyses, which are typically time-consuming and complicated. It is shown that EMC can work simply and well on those nonlinear materials having small strain-hardening and small/moderate strain-to-failure, while FMC can be effectively and easily applied to nonlinear materials having moderate/great strain-hardening and/or large strain-to-failure, where failure means necking.

Fracture prediction in flat PMMA notched specimens under tension - effectiveness of the equivalent material concept and fictitious material concept

The fracture of notched elements under mode I loading (tension) remains an inexhaustible research topic, especially when it comes to the fracture of thermoplastic materials such as polymethylmethacrylate (PMMA), which experience considerable plastic strains under tension. The paper points out that traditional brittle fracture criteria such as mean stress (MS) or maximum tangential stress (MTS) criteria used to predict this phenomenon do not accurately indicate the value of the critical load. They work much better when combined with the equivalent material concept (EMC) and fictitious material concept (FMC). The effectiveness of both concepts depends on the size of the notch root radius, and thus on the yield zone size.

A 2D FEM Model for Impedance and Loss Calculation of Armored Three-Core Cables With Inclusion of 3D Pitching Effects

A method is introduced for impedance and loss calculation of three-core power cables with steel armoring, based on 2D finite element method (FEM) computations. The pitching effect of the cores and armor wires is taken into account by 1) enforcing identical net current on the wires, and by 2) introducing a fictitious non-conductive material between the wires having a complex-valued permeability. The permeability is obtained by considering the effect of the pitching on the total energy in a volume slab around each wire, which involves the solving of a small 2D FEM problem in an optimization loop. The method permits to calculate the positive-sequence and zero-sequence impedance on cables, induced sheath currents, and losses in cores, sheaths, and armor. The method is validated against published results using a full 3D FEM model. The calculations are fast, requiring only a few seconds of computation time. The procedure is simplified by use of pre-calculated look-up tables for the fictitious material permeability value.

An equivalent cohesive zone model for a wide range of ductile and brittle adhesives

AbstractThis paper aims to propose an equivalent trapezoidal traction–separation law (ET‐TSL) of the cohesive zone model applicable to a wide range of ductile and brittle adhesives using equivalent and fictitious material concepts. The ET‐TSL can reduce the analysis time and cost of complex problems without degrading the prediction accuracy. To experimentally validate the proposed ET‐TSL, double‐cantilever beam (DCB) samples were fabricated with glass fiber‐reinforced polymer substrates and a highly ductile adhesive and then tested. The fracture behavior of the specimens was modeled using the proposed ET‐TSL. Moreover, the accuracy and comprehensiveness of the proposed model were verified by employing the proposed ET‐TSL for different adhesive joints made of different adhesives ranging from brittle to ductile adhesives and different substrates found in the literature. It was found that the proposed ET‐TSL can provide reasonable accuracy in simulating the fracture response of different types of adhesive joints with brittle and ductile adhesives.

Mixed mode I-III fracture resistance of stainless steel 316L weakened by V-notches with end holes

Notch fracture resistance of stainless steel 316L is investigated under mixed-mode I/III loading. A previously proposed test fixture, utilized in the past for testing low/medium toughness polymeric and metallic materials, is first modified to make it appropriate for testing significantly tough materials like stainless steel 316L. Then, original fracture tests are carried out on a specific sample weakened by V-notches with end holes (VO-notches) and loaded under different combinations of tension and out-of-plane shear, from which the critical loads and the fracture behaviour are extracted. Due to great strain-hardening and significant strain-to-failure for stainless steel 316L, the Fictitious Material Concept (FMC) is first employed to avoid complexities associated with fracture prediction. Then, FMC is combined with the maximum tangential stress (MTS) and mean stress (MS) criteria to predict the notch fracture toughness values determined experimentally. With approximately 87 % and 86 % accuracy in estimation of the mean experimental results, both combined criteria, called FMC-MTS and FMC-MS, are revealed to be successful.

Coupling Soil–Fluid–Structure Domains by Localized Lagrange Multipliers Mixed Formulation (u, p) for Modeling Offshore Wind Turbine Vibration

Modeling is frequently used to design structures in a large range of engineering applications. Coupled models can be solved by several numerical procedures. This paper presents a soil–fluid–structure coupling analysis applied to offshore wind turbines design. The goal of this work is to develop a coupled structural finite element procedure using Localized Lagrange Multipliers (LLM) at idealized offshore wind turbines with poroelastic soil foundation. The poroelastic media theory of Biot is used to represent the soil domain as two-phase material which is considered to be fully saturated with water. The numerical model is validated through a fully coupled model at classical problems results. In this work, the mixed formulation (u,p) is used to model the interface frames between the domains. The interface domain behaves as fictitious porous material generating a nonsymmetrical coupling between elastic solid and potential fluid. The momentum equilibrium and mass continuity equations are solved by algebraic equation system imposed by Lagrange multipliers methodology. In order to fully model the coupled system, aerodynamic decoupling effects are implemented to separate the tower structure, the soil foundation and the rotor-nacelle assembly. This procedure is based on the blade aerodynamic characteristics. The force and moment vectors are assembled considering the aerodynamic damping coupling between inplane and outplane rotor motions. Finally, the equations of the tower-nacelle structure, ocean fluid and poroelastic soil are obtained by the classical finite element method. In addition, their interaction is modeled using LLM. The numerical model for monopile and jacked offshore wind turbine is developed in terms of time dynamic response which is evaluated for a range of physical parameters including the wind nature and soil type.

Fracture Load Predictions in Additively Manufactured ABS U-Notched Specimens Using Average Strain Energy Density Criteria.

This paper provides a methodology for the prediction of fracture loads in additively manufactured ABS material containing U-notches. The approach is based on the Average Strain Energy Density (ASED) criterion, which assumes that the material being analysed develops fully linear-elastic behaviour. Thus, in those cases where the material has a certain (non-negligible) amount of non-linear behaviour, the ASED criterion needs to be corrected. In this sense, in this paper, the ASED criterion is also combined with the Equivalent Material Concept (EMC) and the Fictitious Material Concept (FMC), both being corrections in which the non-linear real material is substituted by a linear equivalent or fictitious material, respectively. The resulting methodologies have been applied to additively manufactured ABS U-notched single-edge-notched bending (SENB) specimens combining five different notch radii (0, 0.25, 0.5, 1 and 2 mm) and three different raster orientations (0/90, 45/−45 and 30/−60). The results obtained demonstrate that both the ASED-EMC and the ASED-FMC combined criteria provide more accurate predictions than those obtained directly through the ASED criterion, with the ASED-EMC criterion generally providing safe more accurate predictions, with an average deviation from the experimental fracture loads between +1.0% (predicted loads higher than experimental loads) and −7.6% (predicted loads lower than experimental loads).

Minimum feature size control in level set topology optimization via density fields

A level set topology optimization approach that uses an auxiliary density field to nucleate holes during the optimization process and achieves minimum feature size control in optimized designs is explored. The level set field determines the solid-void interface and the density field describes the distribution of a fictitious porous material using the solid isotropic material with penalization. These fields are governed by two sets of independent optimization variables which are initially coupled using a penalty for hole nucleation. The strength of the density field penalization and projection is gradually increased during the optimization process to promote a 0–1 density distribution. In addition, a second penalty regulates the evolution of the density field in the void phase. The treatment of the density field combined with the second penalty mitigate the appearance of small design features. The minimum feature size of optimized designs is controlled by the radius of the linear filter applied to the density optimization variables. The structural response is predicted by the extended finite element method, the sensitivities by the adjoint method, and the optimization variables are updated by a gradient-based optimization algorithm. Numerical examples investigate the robustness of this approach with respect to algorithmic parameters and mesh refinement. The results show the applicability of the combined density level set topology optimization approach for both optimal hole nucleation and for minimum feature size control in 2D and 3D. This comes, however, at the cost of a more complex problem formulation and additional computational cost due to an increased number of optimization variables.

Development of the Broadband Multilayer Absorption Materials with Genetic Algorithm up to 8 GHz Frequency

A widely used genetic algorithm (GA) is endorsed to improve the design of a multilayer microwave radar absorbing material (MMRAM) which shows good absorption of radar waves over a broad frequency range. In this research, the authors have used genetic algorithm based on MMRAM which plays an important role in defense and civil applications. The scope of multilayer microwave radar absorbing material (MMRAM) is that it can absorb radar signals and reduce or eliminate their reflection. Its primary use is in defense and certain commercial enterprises. The multilayer RAM design demands the superiority of suitable materials to be used in different layers, a decision about multiple layers, and the optimum breadth of an individual layer. The permeability and permittivity of the materials varying with frequency in a fictitious material are used. The effect of change in thickness and the number of layers of RAM on reflectivity is studied. Since the material characteristics are frequency-dependent, different restrained conditions are used for frequency bands to identify the RAM that has good electromagnetic absorption in the frequency range of 1 to 8 GHz.

Mesoscopic modelling of UHPCC material under dynamic tensile loadings

This paper presents a new 3D mesoscopic model of ultra-high performance cement-based composite (UHPCC) to investigate its dynamic tensile behavior. In this model, the UHPCC is regarded as a two-phase material composed of cementitious matrix and randomly distributed fibers. The model is established using the commercial software LS-DYNA and involves generating the randomly distributed fiber elements with considerations of diameter, length, orientation and volume fraction, and then fully constraining them with the matrix. In particular, to capture the slipping effect between fibers and matrix that has a strong influence on the dynamic tensile behavior, the fibers are modelled by a fictitious material represented by the load-slip relation. The strain-rate effect of slipping force neglected in most of previous studies is considered by calibrating constitutive parameters of the fictitious material under different strain-rates based on the single fiber pullout tests. Finally, the 3D mesoscopic model is validated against three sets of tension-dominated experiments covered a wide range of loading intensity. Numerical predictions demonstrate that strain-rate effect of slipping force must be considered, and the neglect of it may lead to a great underestimation of the dynamic tensile strength of UHPCC material and would unavoidably underestimate the blast resistance of UHPCC components.

Modeling of geometric configuration and fiber interactions in short fiber reinforced composites via new modified Eshelby tensors and enhanced mean-field homogenization

Determination of the effective elastic properties of unidirectional short fiber reinforced composites (SFRCs) is a key fundamental requirement which is usually estimated by mean-field homogenization (MFH) methods. Available classical MFH methods only account for volume fraction and aspect ratio of the fibers and do not consider the physical cylindrical geometry of the fibers. Moreover, classical MFHs are not designed for predicting the effective properties of SFRCs with distinct packing configurations and order of fibers. In this work, new modified Eshelby tensors associated with an enhanced MFH are developed which resolve the mentioned limitations of the available MFH methods and preserve their computational efficiency. While classical Eshelby tensors used in MFHs depend only on the aspect ratio of the fictitious ellipsoidal inclusion and material properties of the matrix, the introduced modified Eshelby tensors additionally account for physical cylindrical geometry as well as interactions of the short fibers with different packing configurations. Moreover, non-uniform homogenizing eigenstrains required for accurate homogenization of the short fibers are also incorporated by the proposed analytical treatment. Predictions of the developed enhanced MFH for various packing configurations are compared with those obtained from Finite Element Method implementing periodic boundary conditions and very good agreements are observed. It is shown that packing configuration and geometrical specifications of short fibers can significantly affect the effective properties of the SFRC.

Ultra-low thermal conductivity of nanoparticle chains: A nanoparticle based structure for thermoelectric applications

Nanostructured semiconductors are promising candidates for thermoelectric materials owing to their superior thermal insulating properties over their bulk counterparts. In this study, a one-dimensional, crystalline nanostructure synthesized by sintering Si nanoparticles, called Nano Particle Chain (NPC) structures, is proposed. The structure is systematically analyzed for its thermal transport properties and compared with the nanowire counterparts. Both classical molecular dynamics and lattice dynamics tools were employed to evaluate lattice thermal conductivity (k) and to perform phonon mode level decomposition. A marked reduction in the phonon relaxation time of the NPC structure was observed indicating possible effects of phonon-boundary/constriction scatterings. This has resulted in a two-order reduction in k in NPC structures over bulk Si. Further, one order reduction of k of NPC structures was attained with respect to a nanowire of the same constriction size, indicating the effectiveness of the mismatch of particle and constriction diameters as an efficient thermal suppression mechanism. With the addition of a second material of different mass, the NPC structures can be further diversified to core/shell configurations. It was also identified that a non-monotonic variation of k exists, with a minimum in core/shell NPC structures. This effect is materialized by using a Ge-like fictitious material to coat the original Si nanoparticles, owing to competing effects of two phonon suppression mechanisms. Moreover, these core/shell NPC structures are compared with previously reported diameter modulated core/shell nanowire structures [E. Blandre et al., Phys. Rev. B, 91, 115404 (2015)] to highlight their capability to enhance the thermoelectric performance over conventional one-dimensional nanostructure configurations.

Topology optimization of load-bearing capacity

The present work addresses the problem of maximizing a structure load-bearing capacity subject to given material strength properties and a material volume constraint. This problem can be viewed as an extension to limit analysis problems which consist in finding the maximum load capacity for a fixed geometry. We show that it is also closely linked to the problem of minimizing the total volume under the constraint of carrying a fixed loading. Formulating these topology optimization problems using a continuous field representing a fictitious material density yields convex optimization problems which can be solved efficiently using state-of-the-art solvers used for limit analysis problems. We further analyze these problems by discussing the choice of the material strength criterion, especially when considering materials with asymmetric tensile/compressive strengths. In particular, we advocate the use of a L1-Rankine criterion which tends to promote uniaxial stress fields as in truss-like structures. We show that the considered problem is equivalent to a constrained Michell truss problem. Finally, following the idea of the SIMP method, the obtained continuous topology is post-processed by an iterative procedure penalizing intermediate densities. Benchmark examples are first considered to illustrate the method overall efficiency while final examples focus more particularly on no-tension materials, illustrating how the method is able to reproduce known structural patterns of masonry-like structures. This paper is accompanied by a Python package based on the FEniCS finite-element software library.

Mixed mode I/II crack propagation in stainless steel 316L sheets by large plastic deformations: Prediction of critical load by combining LEFM with fictitious material concept

In this research, the load carrying capacity (LCC) of O-notched diagonally loaded square plate (DLSP) samples with pre-existing cracks emanating from the notch edge is investigated theoretically and experimentally under mixed mode I/II loading. The specimens are made of the stainless steel 316L, which is highly ductile and has great strain-hardening. In order to determine the LCC experimentally, several fracture tests are performed on DLSP specimens. Experimental observations reveal that these specimens experience significant plastic deformations at the onset of crack propagation. For theoretical prediction of the experimental LCCs, the Fictitious Material Concept (FMC) is first employed. By utilizing FMC, the stainless steel 316L with highly ductile behavior and great strain-hardening can be replaced with a virtual brittle material having linear elastic behavior. Then, by coupling FMC with two well-known stress based brittle fracture criteria in the field of the linear elastic fracture mechanics (LEFM), the LCCs of the cracked DLSP samples are estimated. In fact, by using FMC, complex and time-consuming elastoplastic failure analysis can be avoided and by performing only linear elastic analysis, the LCC of ductile DLSP specimens can be estimated. It is shown that combination of FMC with the maximum tangential stress (MTS) and the generalized MTS (GMTS) criteria is quite successful in predicting the crack growth instance in ductile DLSP specimens.

On the use of the Fictitious Material Concept in estimating the ultimate load of keyhole notched AA6061‐T6 specimens under large tension‐torsion deformations

AbstractThis paper examines the fracture of AA6061‐T6 specimens with ductile behavior having notches with keyhole geometry under combined loading of tension/torsion. The investigation is performed by theoretical and experimental methods. New fracture tests are performed using a loading fixture on the samples made of AA6061‐T6 weakened by keyhole notches with different notch tip radii. For theoretically estimating the onset of fracture in the tested notched specimens, a concept called “Fictitious Material Concept (FMC)” is used to equate the ductile material with a fictitious brittle material. Therefore, use of this concept allows use of the linear elastic brittle fracture criteria for ductile materials. The brittle fracture criteria utilized are the “mean stress (MS)” and “maximum tangential stress (MTS)” criteria. The small difference between the theoretical and experimental results confirms that use of the combination of FMC with the two criteria is successful in predicting failure of the keyhole notched AA6061‐T6 samples.

Anisotropic thermal conductivity tensor measurements using beam-offset frequency domain thermoreflectance (BO-FDTR) for materials lacking in-plane symmetry

Many materials have anisotropic thermal conductivity, with diverse applications such as transistors, thermoelectrics, and laser gain media. Yet measuring the thermal conductivity tensor of such materials remains a challenge, particularly for materials lacking in-plane symmetry (i.e., transversely anisotropic materials). This paper demonstrates thermal conductivity tensor measurements for transversely anisotropic materials, by extending beam-offset frequency-domain thermoreflectance (BO-FDTR) methods which had previously been limited to transversely isotropic materials. Extensive sensitivity analysis is used to determine an appropriate range of heating frequencies and beam offsets to extract various tensor elements. This technique is demonstrated on a model transversely anisotropic material, x-cut quartz (<110> α-SiO2), by combining beam offset measurements from different sample orientations to reconstruct the full in-plane thermal conductivity tensor. The technique is also validated by measurements on two transversely isotropic materials, sapphire and highly oriented pyrolytic graphite (HOPG). The anisotropic measurements demonstrated very good self-consistency in correctly identifying isotropic directions when present, with residual anisotropy errors below 4% for sapphire and 2% for HOPG and quartz. Finally, a computational case study (simulated experiment) shows how the arbitrary in-plane thermal conductivity tensor of a fictitious material with high in-plane anisotropy can in principle be obtained from only a single sample orientation, rather than multiple orientations like the experiments on x-cut quartz.

Localized Lagrange Multipliers Mixed (u,p) Formulation Applied in Wind Turbine Analysis

Fluid–structure analysis is frequently used to design offshore structures in a large range of engineering applications. In order to install wind turbines from the seashore, it is required that its towers must be attached at the sea floor or a system needs to be developed that allows the turbine to float. Therefore, the objective of this work is to develop a coupled structural finite element analysis using localized Lagrange multipliers (LLM) at idealized monopile wind turbines. This method enables us to model large structures like wind turbine towers submerged in the ocean and determine the influence of the fluid–structure interaction on the dynamic structural response of these equipments. In this work, the mixed formulation [Formula: see text] developed takes into account the condition of irrotationality of the acoustic fluid. The classical LLM method is modified, thus, a new mixed-formulation for the interface frame has fluid pressure and solid displacement as degree of freedom. In other words, a coupling frame is introduced as fictitious porous material with the aim of non-symmetrical coupling between elastic solid and potential fluid. The solution to the non-matching meshes domain problem is also achieved with this methodology by several numerical strategies. The equations of solid and fluid domains are obtained by classical finite element method and their interaction is modeled with Localized Lagrange Multipliers. The solutions of numerical equations are obtained by direct form in a monolithic approach. The new modeling by using a porous material interface frame algorithm is verified through examples.