Isotropic Material Properties Research Articles

Space–time topology optimization for anisotropic materials in wire and arc additive manufacturing

Wire and Arc Additive Manufacturing (WAAM) has great potential for efficiently producing large metallic components. However, like other additive manufacturing techniques, materials processed by WAAM exhibit anisotropic properties. Assuming isotropic material properties in design optimization thus leads to less efficient material utilization. Instead of viewing WAAM-induced material anisotropy as a limitation, we consider it an opportunity to improve structural performance. This requires the integration of process planning into structural design. In this paper, we propose a novel method to utilize material anisotropy to enhance the performance of structures both during fabrication and in their use. Our approach is based on space–time topology optimization, which simultaneously optimizes the structural layout and the fabrication sequence. To model material anisotropy in space–time topology optimization, we derive the material deposition direction from the gradient of the pseudo-time field, which encodes the fabrication sequence. Numerical results demonstrate that leveraging material anisotropy effectively improves the performance of intermediate structures during fabrication as well as the overall structure.

Influence of interstitial fluid pressure, porosity, loading magnitude, and anisotropy in cortical bone adaptation

Adaptive elasticity in cortical bone has traditionally been modeled using Strain Energy Density (SED). Recent studies have highlighted the importance of interstitial fluid in bone adaptation, yet no research has quantified the role of interstitial fluid pressure and its effects, specifically incorporating both SED and interstitial fluid pressure in the adaptation process. This study introduces a novel formulation combining theory of porous media and theory of adaptive elasticity that considers both SED and interstitial fluid’s pressure in cortical bone adaptation. The formulation is solved using ANSYS Fluent and a MATLAB script, and sensitivity analyses were conducted, analyzing various porosities, loading magnitudes, anisotropic properties of cortical bone, and involvement coefficients of interstitial fluid’s pressure. This study reveals that bones with different vascular porosities (PV) tend to achieve similar density distributions under uniform loading over time. This highlights the significant role of interstitial fluid pressure in accelerating the convergence to optimal bone properties, especially in specimens with larger PV porosities. The findings emphasize the importance of fluid pressure in bone remodeling, aligning with previous studies. Furthermore, this study demonstrates that considering transversely isotropic material properties can significantly alter the remodeling configuration compared to isotropic material properties. This highlights the importance of accurately representing the anisotropic nature of cortical bone in models to better predict its adaptive responses. However, aspects such as fluid density variations and bone geometry changes remain unexplored, suggesting directions for future research. Overall, this research enhances the understanding of cortical bone adaptation and its mechanical interactions.

Spatiotemporally distinct responses to mechanical forces shape the developing seed of Arabidopsis

Organ morphogenesis depends on mechanical interactions between cells and tissues. These interactions generate forces that can be sensed by cells and affect key cellular processes. However, how mechanical forces, together with biochemical signals, contribute to the shaping of complex organs is still largely unclear. We address this question using the seed of Arabidopsis as a model system. We show that seeds first experience a phase of rapid anisotropic growth that is dependent on the response of cortical microtubule (CMT) to forces, which guide cellulose deposition according to shape-driven stresses in the outermost layer of the seed coat. However, at later stages of development, we show that seed growth is isotropic and depends on the properties of an inner layer of the seed coat that stiffens its walls in response to tension but has isotropic material properties. Finally, we show that the transition from anisotropic to isotropic growth is due to the dampening of cortical microtubule responses to shape-driven stresses. Altogether, our work supports a model in which spatiotemporally distinct mechanical responses control the shape of developing seeds in Arabidopsis.

Analytical prediction and numerical verification of stress concentration profile around an in-situ tow break in resin-impregnated filament-wound composites

A new empirical analytical approach is developed for predicting the stress concentration profile around an in-situ tow break in filament-wound composites. A shear-lag analysis is firstly performed to solve for the perturbational axial displacement of the broken tow and resultant debonding lengths. Solution of stress field caused by tangential load on the surface of an elastic half space is then utilized in combination with superposition principle to obtain the overload magnitudes in the neighboring tows. Subsequently, high-fidelity finite element analysis on a representative uni-directional laminate model under different stress states is performed, and excellent overall agreement is observed between analytical and numerical predictions. The proposed method takes into account essential aspects such as transversely isotropic material properties, in-situ stress states and their effect on the interfacial frictional forces in the debonded interfaces, and thus provides a convenient way to evaluate the stress concentration factors in damaged filament-wound composites. In addition, this approach can be applied to yield auxiliary failure evaluation criteria for statistical strength prediction or finite element modeling of filament-wound composites or similar structures.

First and second law analysis of crack propagation in canvas painting

The knowledge of how the craquelures happen and their pattern on historical objects, especially paintings, is interested in the field of cultural heritage. Entropy generation and thermal analysis of crack growth are calculated numerically for the canvas painting. The painting is modeled as a three-layer composite with isotropic material properties. An in-house code is developed to model the plane strain elasto-static structural mechanics with hybrid-Trefftz finite element formulation. The results are benchmarked with numerical and analytical solutions. Entropy generation and temperature fields are simulated throughout stacking in mode I of a delamination process. The parameter study shows that the parameter of entropy has a great influence on the process of expectation of break proliferation in fast and low areas. It is likewise demonstrated that the use of the corruption entropy age hypothesis gives a technique for assessing the steady in the law of crack growth regarding the rate of entropy production.

Rayleigh-Lamb wave propagation in a prestressed transversely isotropic viscoelastic waveguide: Inverse modeling challenges

The functional role and structure of skeletal muscle results in anisotropy in both material properties and imposed stresses, as well as waveguide effects. Dynamic elastography reconstruction methods for estimating muscle tissue viscoelastic properties that are rooted in assumptions of isotropy and bulk wave motion may produce inaccurate estimates. The superposition of axially-aligned orthotropy (transverse isotropy) in material properties and axially-aligned prestress conditions due to passive stretch or muscle activation makes it difficult to independently discern how much of the apparent anisotropy is due to the muscle material or the imposed stress field. Furthermore, this stress field may result in large strain conditions that require use of higher order terms in the stress-strain relationship. The significance of this confounding condition and strategies for decoupling material and stress-based anisotropy are investigated with a series of numerical finite element and experimental elastography studies using scanning laser Doppler vibrometry and magnetic resonance elastography. Shear and Rayleigh-Lamb wave motion is studied in a polymeric muscle phantom that is in the shape of a rectangular rod and has either isotropic or transversely isotropic material properties under zero stress conditions. [Funding support: NIH AR071162]

Unveiling the Electronic Properties of the Strong Isotropic Molecular Materials through the Graph Theory

Unveiling the Electronic Properties of the Strong Isotropic Molecular Materials through the Graph Theory

Regional variation of the cortical and trabecular bone material properties in the rabbit skull.

The material properties of some bones are known to vary with anatomical location, orientation and position within the bone (e.g., cortical and trabecular bone). Details of the heterogeneity and anisotropy of bone is an important consideration for biomechanical studies that apply techniques such as finite element analysis, as the outcomes will be influenced by the choice of material properties used. Datasets detailing the regional variation of material properties in the bones of the skull are sparse, leaving many finite element analyses of skulls no choice but to employ homogeneous, isotropic material properties, often using data from a different species to the one under investigation. Due to the growing significance of investigating the cranial biomechanics of the rabbit in basic science and clinical research, this study used nanoindentation to measure the elastic modulus of cortical and trabecular bone throughout the skull. The elastic moduli of cortical bone measured in the mediolateral and ventrodorsal direction were found to decrease posteriorly through the skull, while it was evenly distributed when measured in the anteroposterior direction. Furthermore, statistical tests showed that the variation of elastic moduli between separate regions (anterior, middle and posterior) of the skull were significantly different in cortical bone, but was not in trabecular bone. Elastic moduli measured in different orthotropic planes were also significantly different, with the moduli measured in the mediolateral direction consistently lower than that measured in either the anteroposterior or ventrodorsal direction. These findings demonstrate the significance of regional and directional variation in cortical bone elastic modulus, and therefore material properties in finite element models of the skull, particularly those of the rabbit, should consider the heterogeneous and orthotropic properties of skull bone when possible.

Quantifying uniaxial prestress and waveguide effects on dynamic elastography estimates for a cylindrical rod.

Dynamic elastography attempts to reconstruct quantitative maps of the viscoelastic properties of materials by noninvasively measuring mechanical wave motion in them. The target motion is typically transversely-polarized relative to the wave propagation direction, such as bulk shear wave motion. In addition to neglecting waveguide effects caused by small lengths in one dimension or more, many reconstruction strategies also ignore nonzero, non-isotropic static preloads. Significant anisotropic prestress is inherent to the functional role of some biological materials of interest, which also are small in size relative to shear wavelengths in one or more dimensions. A cylindrically shaped polymer structure with isotropic material properties is statically elongated along its axis while its response to circumferentially-, axially-, and radially-polarized vibratory excitation is measured using optical or magnetic resonance elastography. Computational finite element simulations augment and aid in the interpretation of experimental measurements. We examine the interplay between uniaxial prestress and waveguide effects. A coordinate transformation approach previously used to simplify the reconstruction of un-prestressed transversely isotropic material properties based on elastography measurements is adapted with partial success to estimate material viscoelastic properties and prestress conditions without requiring advanced knowledge of either.

Information Modeling of Energy Saving Processes in the Field of Design, Construction and Operation

Statement of the problem. Improving energy efficiency at various stages of the life cycle of objects in the construction industry, which is an absolute imperative of the current stage of development of society, can be achieved by integrating information modeling of the life cycle of a capital construction object with energy saving technologies. However, in domestic and foreign practice, the potential of such an integration is realized only to a small extent. In this regard, this work is devoted to the formulation of methods for overcoming this situation. Results. It is shown that the addition of the base vectors of hierarchical information models with data on the thermophysical properties of isotropic materials and orthotropic elements allows solving the research problem. Also, the formats of basic structures and clusters of higher ranks have been developed, which completely determine the information model of the energy efficiency of the life cycle of an object. Methods for optimizing the technology of information transfer between heterogeneous participants in the implementation of the life cycle are formulated. For standard construction objects, methods for simplifying the energy saving information model are formulated, which allow expanding the area of practical application of the developed models. Conclusions. The integration of technologies for information modeling of the life cycle of an object and energy saving makes it possible to optimize managerial and technical decisions to increase the energy efficiency / cost ratio both at the design stage and at the stages of construction and operation. The vector hierarchical model of energy efficiency of the project life cycle allows optimizing the updating and verification of the information model, and the mechanisms for transferring information between project participants.

Acoustic black hole designs for circular beams under axial loading

Acoustic Black Hole (ABH), as a non-reflecting wave effect, has been realised in beams and plates by locally changing their thickness. Geometrical ABH designs stem from their transverse-load bearing properties, assuming isotropic material properties associated with engineering materials (e.g., steels). The underlying physics is to manipulate stiffness locally for a transversely-loaded structure, leading to a change in the elastic wave speed. However, the same ABH would have limitations for axial loading, i.e., slender beams for which longitudinal waves dominate. Here, we present a wave propagation approach using wavefront tracking to identify a potential ABH for axially-loaded circular beams. We study wave propagation in three exponential designs of finite length, monitoring the wave-travel time. Indicative of an effective ABH in finite length sections, the wave-travel time increases compared to the case of a beam without ABH. By employing the wave front tracking method for the design of an ABH with axial loading, it is possible to verify the effectiveness of ABHs. Also, various material models, e.g., orthotropic materials such as wood, and different loading conditions can be considered, which opens a new avenue in applications of ABH phenomena beyond conventional vibro-acoustic control problems.

Influence of Wire Feed Speed and Torch Speed on the Mechanical Properties of Wire Arc Additively Manufactured Stainless Steel

Abstract Wire arc additive manufacturing (WAAM) enables 3D printing of large high-value metal components. However, integrating WAAM into production lines requires a critical understanding of the influence of process parameters on the resulting material characteristics. As such, this research investigates the relationship between WAAM wire feed speed (WFS) and torch speed (TS) on the resulting mechanical characteristics of 316LSi thick parts (2.5 cm (0.98 in.)). The experimental procedure is informed by a training matrix that allows parametric analysis of WFS and TS on the ultimate tensile strength (σult), yield strength (σy), elastic modulus (E), failure strain (εf), hardness (HV0.5), and dimensional accuracy (Da) of the printed samples. The research found that WAAM-processed 316LSi parts feature isotropic material properties despite variations in WFS and TS. The surrogate model developed in this study offers five significant polynomial models capable of accurately predicting the influence of WAAM process parameters on σult, σy, εf, E, and Da. The research found TS to be the most significant WAAM process parameter in comparison to WFS for σult and εf. On the contrary, σy, E, and Da were found to be primarily driven by WFS as opposed to TS. Overall, the paper for the first time presents an accurate surrogate model to predict the mechanical characteristics of WAAM 316LSi thick parts informed by wire feed speed and torch speed. The study demonstrates that the mechanical properties of WAAM-processed steel are primarily influenced by the underlying process parameters offering significant potential for tunable performance.

Modelling guided waves in acoustoelastic and complex waveguides: From SAFE theory to an open-source tool

Guided wave (GW)-based techniques have been extensively investigated and applied in material characterization, damage detection, and structural health monitoring. A comprehensive understanding of GW is the cornerstone for the development of such techniques. Based on the semi-analytical finite element (SAFE) method, an open-source dispersion calculator of GW propagating in acoustoelastic and complex waveguides with both isotropic and anisotropic material properties is developed. First, by assuming the simple harmonic motion along the propagation direction and discretizing along the thickness direction, 1D-GLL-SAFE (one-dimensional Gauss-Lobatto-Legendre SAFE) is adopted for the solution of GW in plate waveguide, which is attributed to its superior performance in terms of computational accuracy and efficiency. Different theories on acoustoelasticity are adopted to calculate GWs under loading. Then 2D-Gauss-SAFE (two-dimensional Gauss SAFE) with triangular meshes filling the cross section is adopted for GW in general waveguides considering the ease of convenience in meshing. Finally, based on the 1D-GLL-SAFE and 2D-Gauss-SAFE algorithms, an open-source tool SAFEDC (SAFE-based dispersion calculator) is developed, which not only provides the solution of GW in pre-stressed isotropic waveguide and general cross section, but also extends to GW in laminates with arbitrary layer stacking configurations and hybrid stacking including multiple materials. Most of the GW features, including phase velocity, group velocity, wave number, wave structure in terms of displacement, stress, and strain, and animation of wave propagation are all offered in SAFEDC, which helps the researchers and engineers to understand and utilize GW.

Quantification of inhomogeneity and anisotropy of bituminous mixtures using biaxial experimental data

Most of the existing mechanical characterization test methods and the analytical models for bituminous mixtures are developed based on the assumption of homogenous and isotropic material properties. However, the extent to which such assumptions hold good for bituminous mixtures is not very clear. A biaxial testing scheme in indirect tension mode can come in handy to collect the experimental data at different test temperature regimes. In this study, a bituminous mixture with a nominal maximum aggregate size (NMAS) of 13.2 mm is used to fabricate cylindrical test specimens with 150 mm diameter and 63.5 mm thickness for conducting the repeated load indirect tension (IDT) test. The input load level is selected as 5 to 13 % of the indirect tensile (ITS) failure load in the form of a haversine pulse of 0.1 s loading and 0.9 s rest period. Such loading is applied on zero-degree and ninety-degree orientations of the specimen. The resulting deformations in different directions are measured using linear variable differential transducers (LVDT) attached to both diametral faces of the specimen. The response of the bituminous mixture specimen is captured at three different temperatures of 20, 25, and 30 °C using two different gauge length (half and quarter gauge of the total diameter). A new framework is introduced in this study to evaluate the extent of inhomogeneity and anisotropy of bituminous mixtures. The deformation response of the test specimen captured in the same orientation at different diametral faces is compared to evaluate the extent of inhomogeneity. The extent of anisotropy is evaluated by comparing the deformation response of the test specimen captured at different orientations within the same diametral face. A 15 % variation in the average peak deformation is chosen as the demarcation for determining the extent of inhomogeneity and anisotropy. From this investigation, it is observed that half gauge length experimental data exhibits homogenous and isotropic behavior for all three test temperatures. The quarter gauge length data exhibit similar behavior at 30 °C, whereas it is observed as homogenous and anisotropic at the other two test temperatures.

Investigation into effective mechanical properties of porous material produced by the additive manufacturing method

Porous materials are defined as materials that contain holes, voids, or spaces in their structures, which can be interconnected or isolated. In the most complex forms of these materials, the holes can have irregular shapes with a random distribution in size, location, and direction, making studying their properties a challenging problem. Additive manufacturing techniques offer opportunities to create complex structures, and in this paper, we investigate the effective mechanical properties of porous material produced by the Fused Displacement Modeling (FDM) technique. We also propose an algorithm for generating a porous body containing irregularly shaped holes with arbitrary distributions in size and location while maintaining specific porosity. Due to the orthotropic properties of bodies created by the FDM technique, Reinforced Isotropic Solid Modeling (RISM) is combined with existing theories that calculate the effective properties of isotropic materials. For the experiments, some modified standard specimen with a porosity of 0.05 to 0.40 has been fabricated, and the elastic modulus and ultimate stress have been calculated using the tensile test. Finally, the results are compared with experimental data.

Biomechanical influence of plate configurations on mandible subcondylar fracture fixation: a finite element study.

Mandible subcondylar fractures have very high complication rate, yet there is no consensus on suitable plate design for optimal patient outcomes. Our study is aimed at comparing single mini, trapezoid, lambda, strut and double mini plates. A finite-element (FE) model of intact mandible was developed based on healthy CT-scan data, which was further virtually osteotomized and fixated with plates. The cortical and cancellous bones were assigned region-specific orthotropic and heterogenous isotropic material properties respectively. The models were subjected to six load cases representing the mastication cycle. Under opposite lateralities, the tensile and compressive mandibular strain distributions were found as the opposite, with tensile strains at the posterior border under ipsilateral molar clenching (RMOL) resulting in lesser mandibular strain in reconstructed mandible with single mini plate under RMOL but highest mandibular strain under the contralateral molar clenching (LMOL). Owing to the reduced mandibular strains under LMOL than RMOL, the contralateral chewing is preferred during the immediate post-surgery period for patients. Under LMOL, the peak von Mises stresses in the plate decreased with increase in the number of screws. Furthermore, the presence of two arms in double mini and trapezoid plates seems beneficial to neutralise the tensile and compressive strains across load cases.

Stress-based topology optimization for fiber composites with improved stiffness and strength: Integrating anisotropic and isotropic materials

Fiber-reinforced materials offer high stiffness- and strength-to-mass ratios to lightweight composite structures. To design stiff, strong, and lightweight fiber-reinforced composite structures, we propose a multimaterial anisotropic stress-constrained topology optimization framework that simultaneously optimizes geometry, distribution of anisotropic (i.e., orthotropic) and isotropic material phases, and local orientations of fiber reinforcements in the anisotropic phase. To achieve high performance in both stiffness and strength, we discover that both isotropic and anisotropic materials are needed: anisotropic materials are preferred in uniaxial members to increase stiffness, while isotropic materials are crucial at multi-axially stressed joints to enhance strength. We introduce multimaterial interpolation schemes to characterize both the stiffness and strength of composites made up of anisotropic and isotropic materials. The characterization of strength is enabled by a novel load factor-based yield function interpolation that consistently integrates anisotropic Tsai–Wu and isotropic von Mises yield criteria. We optimize stress-sensitive domains considering materials with various levels of stiffness and strength anisotropy as well as multiple load cases. The anisotropic stress constraints in the proposed framework effectively inform geometries to reduce stress concentration in fiber composites. The proposed framework provides a rational design paradigm for composite structures, capitalizing on dissimilar stiffness and strength properties of anisotropic and isotropic materials, to potentially benefit various engineering applications.

Accuracy of osseointegrated screw-bone construct stiffness and peri-implant loading predicted by homogenized FE models relative to micro-FE models

Computational predictions of stiffness and peri-implant loading of screw-bone constructs are highly relevant to investigate and improve bone fracture fixations. Homogenized finite element (hFE) models have been used for this purpose in the past, but their accuracy has been questioned given the numerous simplifications, such as neglecting screw threads and modelling the trabecular bone structure as a continuum. This study aimed to investigate the accuracy of hFE models of an osseointegrated screw-bone construct when compared to micro-FE models considering the simplified screw geometry and different trabecular bone material models.Micro-FE and hFE models were created from 15 cylindrical bone samples with a virtually inserted, osseointegrated screw (fully bonded interface). Micro-FE models were created including the screw with threads (=reference models) and without threads to quantify the error due to screw geometry simplification. In the hFE models, the screws were modelled without threads and four different trabecular bone material models were used, including orthotropic and isotropic material derived from homogenization with kinematic uniform boundary conditions (KUBC), as well as from periodicity-compatible mixed uniform boundary conditions (PMUBC). Three load cases were simulated (pullout, shear in two directions) and errors in the construct stiffness and the volume average strain energy density (SED) in the peri-implant region were evaluated relative to the micro-FE model with a threaded screw.The pooled error caused by only omitting screw threads was low (max: 8.0%) compared to the pooled error additionally including homogenized trabecular bone material (max: 92.2%). Stiffness was predicted most accurately using PMUBC-derived orthotropic material (error: -0.7 ± 8.0%) and least accurately using KUBC-derived isotropic material (error: +23.1 ± 24.4%). Peri-implant SED averages were generally well correlated (R2 ≥ 0.76), but slightly over- or underestimated by the hFE models and SED distributions were qualitatively different between hFE and micro-FE models.This study suggests that osseointegrated screw-bone construct stiffness can be predicted accurately using hFE models when compared to micro-FE models and that volume average peri-implant SEDs are well correlated. However, the hFE models are highly sensitive to the choice of trabecular bone material properties. PMUBC-derived isotropic material properties represented the best trade-off between model accuracy and complexity in this study.

Powder reusability in Metal Binder Jetting

Metal binder jetting is a potential mass-production additive manufacturing technique that enables faster production of complex structures with isotropic material properties. In metal binder jetting, the quality of parts is heavily influenced by the powder characteristics, and even small variations in powder feedstock can result in poor-quality parts. Powder management is crucial in this technology because the powder is processed in a high-humidity environment in the machine, and the binder is mixed with the powder as well. In this paper, the characteristics of 316l and 17-4PH stainless steel powders under the machine atmosphere and their reusability are studied in detail. Powder samples were taken from the build box at a fixed interval of time and their moisture content, packing density, and morphology were analysed through scanning electron microscopy. Based on the results obtained, it was observed that moisture content of the powder increases with time up to a few hours when it gets constant. Additionally, it was observed that after the first reuse cycle of the powder, the finest powder particles almost disappear, which may have a detrimental effect on the density of the generated parts. Finally, the recycling of broken green parts was also investigated by means of a new approach. Taking into account that broken green parts are generally scrapped in metal binder jetting, the recyclability of this material could reduce the high material costs related to the process.

The estimation of Poisson’s ratio by time-averaging and Cornu’s method for isotropic beams

Prior research suggests that direct static (e.g., uniaxial testing) and dynamic (e.g., ultrasonic wave propagation analysis) measurements differ in the estimation of Poisson’s ratio because anisotropies and heterogeneities in the sample material affect the two types of tests differently. Even assuming isotropic and homogeneous material properties, prior research further suggests that discrepancies between static/dynamic test results will exist because the error of the diagnostic techniques for the measurand are inherently different. Finally, thermodynamic effects are not present in static tests but can significantly affect dynamic test results. Given the potential for all these variables to produce discrepancies, it would be helpful to have the measurement of Poisson’s ratio obtainable from the same theory and experimental measurements by either static or dynamic testing methods. Our finite element calculations show that by combining time-averaged scanning digital holography with Cornu’s method, it is theoretically possible to estimate the effective Poisson’s ratio from the anticlastic contours at the antinode of the first out-of-plane bending mode shape. This is true regardless of frequency and therefore applicable for both static and dynamic measurements. Our results show that the estimate of Poisson’s ratio by Cornu’s method using data from simulations of mode shapes approaches the true value of Poisson’s ratio. In addition, our research suggests that beam geometry and boundary conditions are fundamental factors limiting the convergence of the estimate of Poisson’s ratio to the true value of Poisson’s ratio regardless of performing a static or dynamic test.