Showing papers on "Orthotropic material published in 2021"

Design and Optimization of Conforming Lattice Structures

Abstract: Inspired by natural cellular materials such as trabecular bone, lattice structures have been developed as a new type of lightweight material. In this paper we present a novel method to design lattice structures that conform with both the principal stress directions and the boundary of the optimized shape. Our method consists of two major steps: the first optimizes concurrently the shape (including its topology) and the distribution of orthotropic lattice materials inside the shape to maximize stiffness under application-specific external loads; the second takes the optimized configuration (i.e., locally-defined orientation, porosity, and anisotropy) of lattice materials from the previous step, and extracts a globally consistent lattice structure by field-aligned parameterization. Our approach is robust and works for both 2D planar and 3D volumetric domains. Numerical results and physical verifications demonstrate remarkable structural properties of conforming lattice structures generated by our method.

The effect of variable properties and rotation in a visco-thermoelastic orthotropic annular cylinder under the Moore–Gibson–Thompson heat conduction model:

Abstract: The present contribution aims to address a problem of thermoviscoelasticity for the analysis of the transition temperature and thermal stresses in an infinitely circular annular cylinder. The inner...

Experimentally-validated orthotropic elastic model for Wire-and-Arc Additively Manufactured stainless steel

Abstract: Wire-and-Arc Additively Manufactured (WAAM) alloys are characterized by specific mechanical properties which can largely differ from the conventionally-manufactured alloys. In detail, the printing process results in a peculiar microstructure, characterized by preferential crystallographic orientation with reference to the printing direction, that leads to an anisotropic mechanical behavior of the printed part. Previous experimental tests on WAAM-produced stainless steel plates showed in particular a strong anisotropic elastic behavior. Based on the above, the present work formulates a specific anisotropic elastic model for a WAAM-processed austenitic stainless steel, considering an orthogonally anisotropic (or orthotropic) constitutive law and a procedure to calibrate the elastic parameters based on the experimental results. In detail, the procedure is applied to calibrate the numerical values of the elastic parameters of a specific WAAM 304L austenitic stainless steel. For this aim, specific investigations on both the mechanical and microstructural features were carried out. Experimental tensile tests were performed on specimens with different orientations with reference to the printing direction. In detail, Young’s modulus and Poisson’s ratios were evaluated for samples oriented along three different orientations with regard to the printing deposition layers: longitudinally (L), transversally (T) and diagonally (D) to them. Digital Image Correlation (DIC) optical measuring system was used to acquire the full strain fields during the test. Microstructural analysis was also carried out to study the inherent microstructure, characterized by a distinctive grain growth direction, and to assess the preferred crystallographic orientations of specimens extracted along the three considered directions. The experimental results are used to calibrate the orthotropic elastic model. From the calibrated model additional material properties in terms of Young’s and shear modulus for any printing direction are derived. The resulting values exhibit very large variations with the printing angle, with ratios between minimum to maximum values around 2 for the Young’s modulus and 3.5 for the shear modulus. This marked orthotropic behavior could open unexplored design possibilities based on deformability issues. Additionally, the calibrated orthotropic model can also be used for future experimental explorations of the mechanical properties of WAAM alloys and for stiffness-based structural design optimizations.

Hygrothermal modeling of the buckling behavior of sandwich plates with nanocomposite face sheets resting on a Pasternak foundation

Abstract: In this work we investigate the buckling response of sandwich plates with a polymeric core and two face sheets reinforced by carbon nanotubes (CNTs). The problem is tackled analytically by means of a higher-order sandwich plate theory, where the face sheets are modeled according to a classical plate theory and modified strain gradient theory with temperature-dependent and moisture-dependent material properties. A Mori–Tanaka method is applied to determine the mechanical properties associated with the face sheets, while considering the agglomeration effect of CNTs. The governing equations of the problem are derived from the Hamilton’s principle, whose solutions are recovered by means of a Navier–Stokes method. A thorough sensitivity study of the structural response to different parameters includes the agglomeration and volume fraction of CNTs, the material length scale parameter, the side and aspect ratios, together with the temperature variation and humidity conditions. The sandwich plates are assumed to be immersed within an orthotropic Pasternak foundation, whose normal and shear moduli can affect the overall buckling response of the structure. Numerical experiments show that sandwich plates with nanocomposite face sheets, resting on orthotropic elastic foundations, feature an increased stiffness, where the proposed formulation yields accurate results, due to the possibility of considering the variation in temperature, humidity and agglomeration of the reinforcing CNTs within the solution.

Modelling full-culm bamboo as a naturally varying functionally graded material

Abstract: The mechanical behaviour of bamboo is greatly influenced by its transverse properties, which are not easily measured by experiment. This study develops a framework and the computational tools required to evaluate the material and mechanical properties of bamboo in its full-culm form. A numerical model of bamboo as a transversely isotropic material with functionally graded material properties in the radial direction is developed. The random field method was introduced as a means of quantifying the measured uncertainty of bamboo with respect to the mechanical characterisation of its full-culm state. Four increasingly complex approaches to model circumferential compression tests of bamboo are presented: a theoretical evaluation using Castigliano’s theorem; an orthotropic model neglecting the graded nature of the culm wall; and, two models—one discrete and one continuum-based that define a transversely isotropic graded material. Output from each model is compared, calibrated and validated with experimental results. While the models developed were robust, their application has drawn into question the fundamental hypothesis that the functionally graded behaviour of bamboo can be captured using the rule of mixtures.

Model parameterization and amplitude variation with angle and azimuthal inversion in orthotropic media

Abstract: Horizontal layered formations with a suite of vertical or near-vertical fractures are usually assumed to be an approximate orthotropic medium and are more suitable for estimating fracture p...

Effects of scanning pattern on the grain structure and elastic properties of additively manufactured 316L austenitic stainless steel

Abstract: The present paper aims to contribute to the understanding of the process-(micro)structure-property linkage in additively manufactured materials. The scanning pattern effects on the microstructure and elastic properties of 316L austenitic stainless steel produced by the powder bed based additive manufacturing are explored. A multiphysics methodology adapted for this purpose combines the physically-based cellular automata for simulation of the grain structure evolution, finite-difference heat transfer calculations in a simplified way following the concept of a moving melt pool, and elastic anisotropy modeling based on the orientation distribution functions and Reuss, Voigt, and Hill schemes. Unidirectional and bidirectional scanning strategies strongly influence the texture and elastic properties of as-built components. The grain structures obtained are characterized by bi-component crystallographic textures. While the specimen printed using a bidirectional strategy demonstrates the major { 011 } 100 Goss and minor { 001 } 100 cube texture components, the unidirectional scanning pattern leads to the rotation of both grain arrangement in space and crystallographic texture. The specimen produced with a unidirectional strategy tends to have coarser grains, more severe texture and more pronounced anisotropy of elastic properties than that printed using a bidirectional scanning pattern. The latter is concluded to exhibit the orthotropic behavior based on the calculated stiffness tensor. In addition, the present study reports stiffness tensors for the additively manufactured steel components.

Ritz method analysis of rectilinear orthotropic composite circular plates undergoing in-plane bending and torsional moments

Abstract: In this article, the elastic problem of composite circular plates with rectilinear orthotropic characteristics, in case of in-plane bending and torsional moments applied, is resolved. According to ...

A new deformation measure for micropolar plates subjected to in-plane loads

Abstract: This work aims to analyze the effect of a new deformation measure in the response of 2D plates subjected to in-plane loads. The proposed formulation allows to clearly distinguish the energetic contribution of every involved deformation mechanism. The action functional is supposed to depend on a strain, a wryness and a new relative rotation tensor in the nonlinear hypothesis; therefore, the suggested approach seems to have a considerable potential to study granular materials. Some 2D samples characterized by complicated geometries are analyzed by means of the finite element method; parametric analyses are performed to test the role played by each material constant which appears in the new constitutive laws: both isotropic and orthotropic models are investigated.

Non-linear anisotropic damage rheology model: Theory and experimental verification

Abstract: We extend the isotropic non-linear damage rheology model with a scalar damage parameter to a more complex formulation that accounts for anisotropic damage growth under true triaxial loading. The model takes account of both the anisotropy of elastic properties (associated with textural rock structure) and the stress- and damage-induced anisotropy (associated with loading). The scalar, isotropic model is modified by assuming orthotropic symmetry and introducing a second-order damage tensor, the principal values of which describe damage in three orthogonal directions associated with the orientations of the principal loading axes. Different damage components, accumulated under true triaxial loading conditions, allows us to reproduce both stress-strain curves and damage- and stress-induced seismic wave velocity anisotropy. The suggested model generalization includes a non-classical energy term similar to the isotropic non-linear scalar damage model, which allows accounting for the abrupt change in the effective elastic moduli upon stress reversal. For calibration and verification of the model parameters, we use experimental stress-strain curves from deformation of dry sandstone under both conventional and true triaxial stress conditions. Cubic samples were deformed in three orthogonal directions with independently controlled stress paths. To characterize crack damage, changes in ultrasonic P-wave velocities in the three principal directions were measured, together with the bulk acoustic emission output. The parameters of the developed model were constrained using the conventional triaxial test data, and provided good fits to the stress-strain curves and P-wave velocity variations in the three orthogonal directions. Numerical simulation of the true triaxial test data demonstrates that the anisotropic damage rheology model adequately describes both non-linear stress-strain behavior and P-wave velocity variations in the tested Darley Dale sandstone.

Functional mechanical metamaterial with independently tunable stiffness in the three spatial directions

Abstract: Mechanical metamaterials with variable stiffness recently gained a lot of research interest, as they allow for structures with complex boundary and load conditions. Herein, we highlight the design, additive manufacturing, and mechanical testing of a new kind of bending-dominated metamaterial. By advancing from well-established mechanical metamaterials, the proposed geometry allows for varying the stiffness in the three spatial directions independently. Therefore, structures with different orientational properties can be designed, ranging from isotropic to anisotropic structures, including orthotropic structures. The compression modulus can be varied in the range of several orders of magnitude. Gradual transitions from one unit cell to the next can be realized, enabling smooth transitions from soft to hard regions. Specimens have been additively manufactured with acrylic resins and polylactic acid using Digital Light Processing and Fused Filament Fabrication, respectively. Two different numerical models have been employed using ABAQUS to describe the mechanical properties of the structure and verified by the experiments. Compression tests were performed to investigate the linear elastic properties of isotropic structures. Numerical models, based on three-point-bending test data, have been employed to study orthotropic structures. Compression test results for orthotropic and anisotropic structures are shown to highlight the independent variability. The manufacturing of the structures is not limited to the presented techniques and materials but can be expanded to all available additive manufacturing techniques and their respective materials. For a video of the compression tests of a specimen with three different compression moduli along the spatial axes, see the Supplementary Data available online.

On the source of the thermoelastic response from orthotropic fibre reinforced composite laminates

Abstract: In thermoelastic stress analysis (TSA) of orthotropic laminated polymer composites, heat transfer influences the measured stress induced temperature change, or ‘thermoelastic response’. The composite constituents, including different fibre types, fibre geometry, ply thickness and resin systems, in combination with the manufacturing process means that, even for nominally identical materials, different conditions are generated for heat transfer. Hence, definitively identifying the ‘source’ of the thermoelastic response for a general composite laminate has remained elusive. A procedure based on the simultaneous application of digital image correlation (DIC) and TSA is devised that enables the source of the thermoelastic response to be established categorically. In glass fibre laminates, it is shown that heat conduction cannot take place so the thermoelastic response emanates from the surface resin rich layer. In similar carbon fibre laminates, adiabatic conditions are only met at higher frequencies with the response emanating from the orthotropic surface ply.

On the nonlinear vibration of heterogenous orthotropic shallow shells in the framework of the shear deformation shell theory

Abstract: In this study, the nonlinear vibration of heterogeneous orthotropic shallow shells (HTOSSs) is investigated. The first order shear deformation theory (FSDT) is generalized to the non-linear vibration problem of HTOSSs for the first time. After the presentation of visual and mathematical models of HTOSSs, the von-Karman type nonlinear basic relations of HTOSSs are created and then the non-linear equations of motion are derived depending on the rotation angles, Airy stress and deflection functions. Then, applying superposition, Galerkin and semi-inverse methods to the nonlinear differential equations, the frequency-amplitude relation of non-linear vibration of HTOSSs is obtained. The frequency-amplitude relation within the classical shell theory (CST) is obtained in a special case. After checking the reliability of the proposed formulation and the accuracy of the results in accordance with the available literature, a systematic study is aimed at checking the sensitivity of the dynamic response to the shear stresses, nonlinearity, heterogeneity, orthotropy and different geometric characteristics.