Orthotropic Behavior Research Articles

Numerical simulation on structural behavior of FRP profile‐concrete hybrid beams with bolt shear connector

AbstractFRP profile‐concrete hybrid beam, composed of a FRP profile beam, a concrete slab made of normal concrete (NC) or ultra‐high‐performance‐concrete (UHPC), and shear connectors, shows significant potential for employment in large‐span bridges due to its excellent corrosion resistance, lightweight, and easy construction. The structural behavior of such hybrid beam was simulated using a three‐dimensional non‐linear finite element model (FEM) in Abaqus. The Hashin failure model and concrete damage plastic (CDP) model were employed to characterize the progressive failure of FRP, NC, and UHPC, respectively. The FEM considered partial shear connection by utilizing shear load‐slip model and the orthotropic behavior of the FRP profile. The proposed FEM was validated through comparisons with experimental data in terms of load‐midspan deflection curve, load‐end slip curve, and failure modes. A parametric study was subsequently conducted to identify the effects of various factors, including concrete strength, bolt spacing, concrete slab width, concrete slab height, FRP flange and web thickness, and shear span. Based on the results yielded from FEM analysis, the accuracy of the calculation method in Chinese standard (GB‐50608) for predicting the loading capacity of hybrid beams was evaluated and found too conservative.

A covariant formulation for finite strain modelling of orthotropic elasticity and orthotropic plasticity with plasticity-induced evolution of orthotropy: Application to natural fibres

We introduce a rate-independent model for orthotropic elastic and orthotropic plastic material behaviour in a hyper-elasto-plastic framework at finite strains. The model is based on the postulate of covariance and does not rely on a multiplicative decomposition of the deformation gradient. Furthermore, a plastic-deformation-induced evolution of orthotropy is considered, similar to the notion of plastic spin. We propose that the orthotropic strain energy function and the orthotropic yield criterion are guided by identical structural tensors that evolve with plasticity. The modelled material behaviour is significant for natural fibres such as flax, hemp, or pulp fibres. Our formulation has three findings. Firstly, the covariant formulation of plasticity provides rate equations for the plastic variables and the structural tensors suitable for reproducing stress–strain diagrams of natural fibres. Secondly, the introduction of plastic-deformation-induced evolution of orthotropy in the proposed covariant setting results in a non-associative plasticity algorithm. Thirdly, the covariant setting allows the incorporation of suitable constitutive equations for the structural tensors to evolve orthotropy. The latter successfully models the stiffness increase in stress–strain diagrams of cyclic tensile tests of natural fibres.

Fracture predictions in impact three-point bending test of European beech

Hardwood has become widespread in European forests. The strongest factor is climate change and damage to conifers by the bark beetle. The effort to study hardwoods grows with increasing volume of applications. Therefore, European beech wood was investigated under two impact loads in two material directions, resulting in four unique combinations supplemented by the measurement of the friction coefficient. Then, it was computationally simulated to reproduce the cracking, while the material model reflected the orthotropic behaviour in elasticity, plasticity and failure. The model was coded using the user subroutine in Abaqus to initiate and propagate the crack using the element deletion. The resulting reaction forces were in good agreement with those from the experiments. Cracking was numerically simulated in three of four cases as experimentally observed, however, upon larger deflections. Therefore, the model is applicable for further investigations.

Experimental and numerical study of the orthotropic behavior of 3D printed polylactic acid by material extrusion: part two: an analysis about poisson´s ratios

Experimental and numerical study of the orthotropic behavior of 3D printed polylactic acid by material extrusion: part two: an analysis about poisson´s ratios

The shear performance of uniaxially thermoformed auxetic polymer foams

We study the shear behavior of pristine and uniaxially thermoformed auxetic foams using three different shear testing techniques and finite element simulations. A novel simple shear test rig with sliding lateral supports was developed and compared to fixed simple shear and diagonal pure shear rigs. The three rigs yield similar results at shear strains under 8 %, but the fixed simple shear rig shows a significant rise in shear modulus and stiffness at higher strains. In contrast, the sliding simple shear and diagonal pure shear rigs exhibit similar linear results up to 20 % shear strain. The thermoformed auxetic foam displays strong orthotropy, with a shear modulus of 35 kPa along the thermoforming direction and 0.1 MPa in the transverse directions. The pristine foam shows good isotropy under shear, with a similar 50 kPa shear modulus in all directions. The auxetic foam expands slightly along the thermoforming direction at high strains, while the pristine foam and auxetic foam in other directions show noticeable shrinkage. Finite element models based on 3D μ-CT scans, using a new boundary coupling element to apply periodic boundary conditions, closely matched the experimental results. The simulations revealed the deformation mechanisms within the foam cell structures that contributed to the observed orthotropic shear behavior.

Finite Element Analysis of CFFT and CFDTS Columns as a Replacement for CFST Columns in Composite Construction by Using ABAQUS

In the field of composite construction of steel and concrete, concrete filled steel tube CFST columns have been proven to be greater performance structural members. The properties of steel and concrete are used efficiently. But CSFT columns are prone to corrosion in outdoor structures as the outer encasing tube is made up of steel. The outdoor use of CFST column due to its high risk of corrosion requires frequent maintenance and may prove costly. Hence, the possible replacement of steel tubes with fiber-reinforced polymer (FRP) Tubes has to be investigated. FRPs are the most suitable material for encasing concrete columns due to its orthotropic behaviour. In solution to this, the paper is aimed at numerical study of CFST, CFFT and CFDTS short columns to study the axial compression behavior of these short columns analytically and examine the best suitable alternatives of CFST column. The concrete in-fill double tube section CFDTS with better axial compression, stiffness and ductility are also investigated as a suitable replacement of CFST columns. For these three different specimens of CFST columns of steel tube thickness 3mm, 4.5mm and 6mm, CFFT columns of GFRP tube thickness 3mm, 4.5mm and 6mm and CFDTS column with GFRP outer tube of thickness 3mm, 4.5mm and 6mm as well as inner steel tube of thickness 1.5mm, 2mm and 2.5mm are analyzed and compared. Consequently, CFDTS columns, with 1872 kN are proven to be superior to CFST columns with axial capacity 1653 kN and CFFT with axial capacity 689 kN columns. The confinement effect in CFDTS is more than CFST and CFFT column.

Tetrahedral core sandwich panels behavior under bending loading

Abstract Sandwich panel with complex core structure could be represented as a homogenous panel with anisotropic mechanical properties to describe the behavior at the macro level. Effective physical and mechanical characteristics were determined, representing the body as a homogeneous anisotropic continuum. The results of the numerical analysis of sandwich panels in case of bending were performed using ANSYS software. The effective elastic characteristics analysis for the periodicity cell of a sandwich panel shows that, to describe the stress-strain state of a panel with a similar tetrahedral core at the macro level, in addition to the orthotropic behavior in the panel plane, different elastic behavior occurs under tension and compression.

Blast Performance of Polyurea-Coated Modular Structure Composed of Fiber-Reinforced Polymer and Foam Sandwich Panels

Lightweight modular structures have become a requirement in today’s world, especially for areas that are prone to occurrence of extreme events, such as earthquakes and blasts, and are situated in difficult terrains with challenging accessibility. Sandwiched composites can be one of the most suitable building units for construction of these structures due to their engineered mechanical and physical properties. Therefore, in this numerical study, performance assessment of a sandwich modular structure in the shape of a truncated cylinder is conducted under blast load. The sandwich modular structure is composed of flat and curved carbon fiber-reinforced polymer (CFRP) and extruded polystyrene (XPS) foam sandwich panels. A three-dimensional (3D) finite element (FE) model of the sandwich modular structure is developed considering the orthotropic behavior of CFRP facesheets and the crushing foam behavior is accounted for the XPS foam core in the FE modeling. The damage assessment in the CFRP facesheet is performed using Hashin’s damage criterion. Furthermore, the effect of polyurea with varying thicknesses on the blast-resistance of the structure is investigated. The polyurea is modeled as hyperelastic material using the Mooney-Rivlin model. The influence of polyurea positioning is studied when (a) applied externally to flat and curved walls of the structure directly exposed to the blast and (b) applied internally to flat and curved walls of the structure opposite to the exposure of the blast (rear face). It is observed that the flat walls of the structure are more vulnerable to the blast load than the curved walls of the structure. Moreover, a quadratic and linear reduction in the deflection of flat and curved walls with increasing thickness of polyurea coating is obtained, respectively. In addition, with increasing thickness of the additional polyurea coating, a logarithmic reduction in the kinetic energy of the sandwich modular structure is reported.

Identification, uncertainty quantification and validation of orthotropic material properties for additively manufactured polymers

The mechanical behavior of polymeric parts manufactured by fused filament fabrication is often characterized as orthotropic because of the layer-wise extrusion of the material. To perform reliable simulations of the mechanical response of these parts subjected to certain loads, the material parameters have to be known. This leads to the task of material parameter identification from suitable experimental data. In this work, the identification of the material parameters for orthotropic material behavior is studied in detail with a focus on the specific characteristics of additively manufactured parts. This comprises working out the differences that arise compared to the parameter identification for classical orthotropic composite materials. Moreover, the material parameters are identified from tensile and shear test information together with full-field displacement data from digital image correlation measurements. Then, the obtained parameters are compared for analytical and numerical approaches, where a non-linear least-squares method with finite elements is drawn on. The parameters are not only identified, but also an uncertainty analysis is carried out and, subsequently, the different methods are validated. Further, a clear derivation of commonly applied analytical equations is provided with a special focus on the underlying assumptions. It turns out that the analytical parameter identification procedures cannot be easily transferred to numerical procedures, especially when using full-field data, because of correlations between the parameters. Moreover, the identified parameters are employed to prove the reasonability of orthotropic material behavior for specimens manufactured by fused filament fabrication. Finally, during validation it turns out that all parameter identification methods provide a good agreement with experimental data, showing only small differences between the results of the different calibration strategies.

Interlocking Joints with Multiple Locks: Torsion-Shear Failure Analysis Using Discrete Element and Equilibrium-Based SiDMACIB Models

SiDMACIB (Structurally informed Design of Masonry Assemblages Composed of Interlocking Blocks) is the first numerical model capable of extending the equilibrium problem of limit analysis to interlocking assemblies. Adopting the concave formulation, this model can compute the stress state at the corrugated faces with orthotropic behaviour, such as their combined torsion-shear capacity. Generally speaking, finding the plastic torsion-shear capacity of planar faces shared between conventional blocks is still a fresh topic, while investigating this capacity for interlocking interfaces is particularly rather unexplored. Upon the authors’ previous works that focused on interlocking blocks with a single lock, in this paper, an extension to blocks composed of several locks (multi-lock interfaces) is presented and the SiDMACIB model is upgraded accordingly. For this purpose, the shear-torsion results obtained from the original SiDMACIB formulation are validated and subsequently compared with those derived from distinct element analysis conducted using the 3DEC 7.0 software. Based on this comparison, revisions to the SiDMACIB model are proposed, involving a reduction in the number of locks affecting torsion-shear capacity.

Elastic behaviour of bamboo at nano- and microscale

This paper presents an anatomy-based numerical multiscale approach for modelling the mechanical behaviour of Moso bamboo, addressing limitations in previous research where the intricate microstructure was often simplified. The mechanical response of bamboo culms is predicted at the nano and microscale considering the orthotropic behaviour of cellulose microfibrils in different layers of tissues, deviating from conventional isotropic assumptions. Through nano and microscale finite element models, the impact of chemical composition and microfibril angle on elastic properties of different layers of the fibre and parenchyma cells are explored at two different levels of moisture content. At low moisture content, fibres within vascular bundles exhibit significantly higher longitudinal and transverse elastic moduli compared to parenchyma cells. When the moisture content is high, the properties of the fibre and parenchyma cells are less different. Anisotropic behaviour at the nanoscale contributes to a more accurate prediction of the mechanical properties of bamboo culms at the microscale, particularly in the transverse direction in moist conditions. This study lays the groundwork for forthcoming research in modelling the mechanical behaviour of bamboo culm at meso and macroscales.

Additive Manufacturing of Composite Polymers: Thermomechanical FEA and Experimental Study.

This study presents a comprehensive approach for simulating the additive manufacturing process of semi-crystalline composite polymers using Fused Deposition Modeling (FDM). By combining thermomechanical Finite Element Analysis (FEA) with experimental validation, our main objective is to comprehend and model the complex behaviors of 50 wt.% carbon fiber-reinforced Polyphenylene Sulfide (CF PPS) during FDM printing. The simulations of the FDM process encompass various theoretical aspects, including heat transfer, orthotropic thermal properties, thermal dissipation mechanisms, polymer crystallization, anisotropic viscoelasticity, and material shrinkage. We utilize Abaqus user subroutines such as UMATHT for thermal orthotropic constitutive behavior, UEPACTIVATIONVOL for progressive activation of elements, and ORIENT for material orientation. Mechanical behavior is characterized using a Maxwell model for viscoelastic materials, incorporating a dual non-isothermal crystallization kinetics model within the UMAT subroutine. Our approach is validated by comparing nodal temperature distributions obtained from both the Abaqus built-in AM Modeler and our user subroutines, showing close agreement and demonstrating the effectiveness of our simulation methods. Experimental verification further confirms the accuracy of our simulation techniques. The mechanical analysis investigates residual stresses and distortions, with particular emphasis on the critical transverse in-plane stress component. This study offers valuable insights into accurately simulating thermomechanical behaviors in additive manufacturing of composite polymers.

Meso-FE modelling for homogenization of the nonlinear orthotropic behavior of PTFE-coated fabric based on virtual fiber method

Compared to traditional textile composites, the coated fabric used in fabric membrane structures is much more flexible. Its macroscopic mechanical behavior is highly nonlinear, anisotropic, and shows stress ratio dependence during the loading process. The main reason is that the yarns within the coated fabric are not completely solidified, and there is a significant crimp interchange process in the yarns under load. This paper proposes a novel mesoscopic finite element (FE) model to predict the nonlinear orthotropic mechanical behavior of PTFE-coated fabric using the virtual fiber method (VFM). By comparing with experimental data, it is shown that the virtual fiber defined by the truss element can visually and effectively simulate the mechanical behavior of the internal fibers and reflect the crimp interchange process between two-way yarns. Combined with PBCs, it can effectively predict the uniaxial and biaxial tensile behaviors of the PTFE-coated fabric. Moreover, a new multi-scale model suitable for structural scale analysis of fabric membrane structures has been attempted by combining the direct FE2 (D-FE2) method with the proposed mesoscopic FE model. Local deformation mechanisms and macro response of fabric membrane structures can be observed simultaneously from these analyses, which provide a better understanding of the mechanical behavior of the fabric membrane structures.

Evaluation of Moisture-Induced Stresses in Wood Cross-Sections Determined with a Time-Dependent, Plastic Material Model during Long-Time Exposure

In recent years, the use of timber as a building material in larger construction applications such as multi-story buildings and bridges has increased. This requires a better understanding of the material to realize such constructions and design them more economically. However, accurate computational simulations of timber structures are challenging due to the complexity and inhomogeneity of this naturally grown material. It exhibits growth inhomogeneities such as knots and fiber deviations, orthotropic material behavior and moisture dependence of almost all physical parameters. Describing the creep response of wood under real climate conditions is particularly difficult. Changes in moisture content, plasticity and viscoelasticity affect moisture-induced stresses and potentially lead to cracks and structural damage. In this paper, we apply a material model that combines time and moisture-dependent behavior with multisurface plasticity to simulate cross-sections of different dimensions over a 14-month climate period. Our findings indicate that considering this long-term behavior has a minor impact on moisture-induced stresses during the drying period. However, during the wetting period, neglecting the time- and moisture-dependent material behavior of wood leads to a significant overestimation of tensile stresses within the cross-section, resulting in unrealistic predictions of wetting-induced fracture. Therefore, simulations during wetting periods require a sophisticated rheological model to properly reproduce the stress field.

Evaluating Airborne Sound Insulation in Dwellings Constructed with Hollow Ceramic Blocks under Brazilian Housing Policies

In Brazil, there is a shortage of approximately 5.80 million residences, a challenge that intensified during the pandemic. Since 2013, there has been a mandate to implement specific performance criteria in residential constructions. However, many construction firms face difficulties in meeting these standards, especially concerning sound insulation in partition elements. This work aims to assess the airborne sound insulation performance and compliance with legal standards in new residential buildings through measurements and simulations. In particular, subsidized housing units for low-income populations are studied, which are eligible for reduced taxes on building loans. These buildings are typically made of hollow ceramic blocks with vertical perforations as separating walls, a commonly used national building material. Three buildings located in Guarapuava, a southern city in Brazil with a population of approximately 183,000 residents, were selected for this purpose. Measurements were conducted following ISO 16283-1 guidelines, whereas simulations were performed using ISO 12354-1, initially assuming a uniform plate but also exploring an alternative model that considers orthotropic behavior with analytical expressions. The calculations considered both static and dynamic moduli of elasticity. The results indicated that all the units failed to meet the specified standards. The measured DnT,w values were below the required thresholds, obtaining 42 < 45 dB for Building B1, 40 < 45 dB for Building B2, and 38 < 40 dB for Building B3. The predicted DnT,w values agreed well with the measured values when considering orthotropy with a dynamic elastic modulus. However, discrepancies were observed in the spectral analysis, especially at lower and higher frequencies. The findings suggest refraining from employing single-leaf partition walls made of vertical hollow ceramic blocks in such buildings. Improving sound insulation necessitates embracing a comprehensive strategy that takes into account the separating element, flanking paths, and the room geometries.

NUMERICAL MODELING OF TIMBER‐STEEL HYBRID STRUCTURES: CHALLENGES AND INNOVATIVE STRATEGIES

AbstractThe increasing diffusion of timber as a structural material asks for major detailing concerning numerical modelling; timber is commonly used with other construction materials in order to create hybrid structures exploiting each material's strengths and smoothing less efficient features. In this way – combining timber and steel – structural performances are guaranteed while lightness and sustainability of only‐timber structures are maintained. Some specific issues linked to timber material – e.g., orthotropic behaviour – and contact with steel are specifically addressed, exploring different techniques according to the scale of the problem. Finally, a complete steel‐timber hybrid beam‐to‐column joint is assembled, with a clear understanding of each interaction and insights for future adjustments to the benchmark model.

Experimental and numerical studies on low-velocity impact of laminated C/SiC structures

Laminated C/SiC(carbon fiber reinforced silicon carbide composites) has the complicated nature of composite failure which include cracks for void defects at the meso and micro scales, complex cracks propagation of tunnel cracks, matrix cracks, delaminations and fiber cracks, orthotropic, and pseudoplastic behavior. It has technical challenge to solve all of them for complicated-mechanics problems by using multi-scale methodology. This paper focused tackling it by a model that lies between macro and meso scales, and proposed a new conceptual 3D FE-PDM(Finite Element - Progressive Damage Method). 3D FE-PDM was validated by the experiments of low-velocity impact of 2D C/SiC and 3D needled C/SiC. Damage initiation and evolution were controlled by strain in order to preventing stress chaos which could occur as cracks leading local stress relief. The multi-linear constitutive relations were adopted in orthotropic directions. The coupled effects of stresses between in-plane and out-of-plane were computed by adding damage coefficients into stiffness matrix. Cohesive Zone Method was used for delamination. The PDM approach was introduced for the 3D elements for intralaminar and cohesive elements for the interfaces. A parametric inversion methodology was put forward to determine the model parameters iteratively by comparing simulation results with the load-time curves, damage CT details of the experiments. Validation implies that, with small number of parameters, 3D FE-PDM is able to predict damage initiation of each phase knee, damage evolution, and load–displacement curve with good convergence for the low-velocity impact case. 2D woven and 3D needled non-woven C/SiC both have impact energy threshold and different damage evolution types.

Overall elastic characterization of equivalent FE models for aluminum foams through computational homogenization approach and genetic algorithm optimization

Aluminum foams are gaining increasing interest because of their widespread set of functional attributes combined with highly specific structural properties and affordable manufacturing processes. The finite element analysis of foam materials is typically performed with complex and time-consuming 3D models. Here, a beam FE model strategy is utilized to obtain a precise and time-saving simulation instrument for open-cell aluminum foams. The beam FE modeling is based on the Kelvin cell as a fundamental unit and provides a simplified geometrical description of the intersection node between ligaments whose elastic properties need to be adjusted through a calibration procedure. The beam FE model elastic properties are measured through a homogenization procedure that evaluates the elastic constants of an equivalent material. The issue of model calibration is formulated as an optimization problem exploiting the NSGA-II genetic algorithm. This procedure allows obtaining the full elastic calibration of the beam FE model, reproducing the orthotropic elastic behavior of the aluminum foams with reduced computational efforts.

Influence of Topological Defects on the Mechanical Response of Unit Cells of the Tetrachiral Mechanical Metamaterial

The primary benefit of metamaterials is that their physical and mechanical properties can be controlled by changing the structure geometry. Numerical analysis tools used in this work offer a few advantages over full-scale testing, consisting of an automated process, as well as lower material and time costs. The investigation is concerned with the behavior of unit cells of the tetrachiral mechanical metamaterial under uniaxial compression. The base material is studied within an elastic mathematical model. The influence of topological defects of the unit cell on the metamaterial properties is studied for the first time. Defects, and especially topological defects, play a decisive role in the mechanical behavior of materials and structures. The unit cell without defects reveals orthotropy of properties. Torsion of a cell with a chiral structure is induced by the rotation of all tetrachiral walls, and therefore it is sensitive to the introduction of defects. There are cases of increased torsion as well as of no compression–torsion coupling effect. In the latter case, the unit cell experiences only shear. The effective Young’s modulus is calculated to vary in the range from 23 to 57 MPa for unit cells of different topologies. With the successive introduction of defects in two walls, the studied characteristics increase, correlating with each other. A further increase in the number of defects affects the characteristics in different ways. The introduction of two more defects in the walls decreases torsion and increases Young’s modulus, after which both characteristics decrease. The introduction of topological defects in all walls of the unit cell leads to the orthotropic behavior of the cell with the opposite sign of torsion.

Characterization of wave propagation in complex composite structures (CCS) using a robust inverse analysis method

This paper presents the application of wave propagation characterization for complex composite structures through the Algebraic K-space Identification technique in the Cartesian coordinate system (AKSI-C). The proposed method is a novel development since the developed methodology uses adequate partial differential algebraic operations to provide a robust and low-cost framework for identifying wave propagation parameters of the structures with multidimensional signals for the first time. Additionally, the proposed method has been experimentally applied to identify the complex wave propagation phenomenon of different complex composite structures: (i) honeycomb sandwich composite structure: variability of orthotropic behavior and damping properties with frequency and direction is identified by wavenumber space, 3D dispersion curves, and damping loss factor surface. Then, the contribution of individual layer properties on the changes in dynamic behavior is studied by estimating transition frequency; (ii) locally resonant meta-structure: the effect of the local resonator-induced band gap on the wave attenuation is investigated; (iii) periodic rib-stiffened composite plates: the inner resonance phenomena and their remarkable elastic wave manipulation ability are explored by designing 3D-printed resonators and identifying the mixed-resonance-induced band gap. The proposed method has been compared with other inverse methods to assess its reliability under complex conditions.