Apparent Material Properties Research Articles

Probabilistic analysis of homogenized elastic property for resin products fabricated by additive manufacturing based on three-dimensional random field modeling of microstructure

Additive manufacturing (AM) techniques have been used in several fields of science and industry, and fabrication techniques are being updated. For this fact, especially, for industrial use, mechanical property evaluation methodologies for AM products and standards for product quality assessment should also be well established. In this paper, a probabilistic evaluation of the homogenized elastic properties of a resin product fabricated by a material extrusion-based AM technique is attempted by considering the randomness of both material and microscopic geometrical quantities. This AM method fabricates a resin structure by piling up melted resin, and to decrease consumed material and influence of thermal deformation, the inner structure of the fabricated products will include many pores and its geometry is difficult to be well controlled. From this fact, the products will be regarded as a heterogeneous material with complex random microstructure. This will cause difficulty in the evaluation of its apparent material properties and therefore a probabilistic homogenization analysis is attempted for their quantitative estimation in this study. In particular, to investigate probabilistic properties of microscopic geometry, a random field modeling technique is employed for the evaluation of autocorrelation of the microscopic geometrical parameter, and the results of the autocorrelation identified by experimental observation are introduced to the probabilistic homogenization analysis. The two-dimensional or three-dimensional random field modeling is attempted, and the effectiveness of this approach is investigated by comparing it with the experimental result.

The effect of random field parameter uncertainty on the response variability of composite structures

The accurate quantification of the random spatial variation of material properties at different scales is crucial for the systematic propagation of uncertainties through engineering models. In a previous work, the spatial variability of the apparent material properties of two-phase composites has been quantified in a Bayesian framework. This framework enables a consistent modeling of the statistical uncertainty in the parameters of the respective mesoscale random fields and also allows selecting the most plausible correlation model among different models belonging to the Matérn family. In this work, the most plausible random field model is employed in the context of uncertainty propagation of composite structures. Sample functions of the mesoscale random fields are generated using a covariance decomposition approach and the response variability of various composite structures is computed through Monte Carlo simulation. Parametric investigations are conducted to highlight the effect of the identified parameter uncertainty on structural response variability.

Evaluation of the unconfined uniaxial compression test to study the evolution of apparent printable mortar properties during the early age transition regime

The aim of this study is the evaluation of the unconfined uniaxial compression test (UUCT) to study the evolution of the apparent material properties of the printable mortar during the early age transition regime between the non-Newtonian fluid and the cohesive frictional material. For this application it is important to establish validated and reliable test procedures. The main focus lies on the determination of the apparent static Young's modulus, which defines limitations for stability failure of 3D printed structures. The results of UUCT beyond the apparent elastic range help to better distinguish between ductile and brittle behavior. A numerical simulation of the UUCT by the Mohr-Coulomb material model with apparent material properties determined by UUCT and direct shear test is able to reproduce the behavior at different ages, including material stiffness and deformation patterns, which is considered as an additional validation of the test procedure.

Random Field Modeling of Microstructure in Unidirectional Fiber‐Reinforced Plastic Using SEM‐Image and Image Processing for Multiscale Stochastic Stress Analysis Considering Random Fiber Arrangements

Herein, an image‐processing‐based random field modeling of microstructure in an actual specimen of a unidirectional fiber‐reinforced composite material and multiscale stochastic stress analysis with considering a random fiber arrangement having the random field identified from an actual specimen is described. Multiscale stochastic stress analysis will be effective for evaluation of uncertainty propagation through the different scales in heterogeneous materials. It will be important when a microscopic randomness has a significant influence on apparent material properties. Some mechanical properties of heterogeneous materials take an influence of the microscopic randomness, and such multiscale stochastic analysis has been attracted. In this article, a random field modeling technique for a digital image of microstructure of a unidirectional fiber‐reinforced plastic (FRP) is presented, and the multiscale stochastic stress analysis with considering a random fiber arrangement in FRP based on the random field model identified by the presented method is attempted. For this purpose, a method for generating a set of realizations according to the identified random field is also developed. From the results, effectiveness of the presented approach is discussed.

Multiscale Stochastic Stress Analysis of Unidirectional FRP Considering Random Fiber Location Variation by an Improved Successive Local Approximation

Herein, a multiscale stochastic stress analysis of a unidirectional fiber reinforced composite material considering random fiber location variation in microscale is discussed. Since a microscopic quantity has an influence on the apparent material properties of heterogeneous materials, and a microscopic geometrical feature has a significant influence on microscopic stresses in composites. When microscopic randomness or uncertainty is observed, an apparent material property such as strength will become a random response, and therefore the uncertainty propagation through the different scales should be investigated for more reliable design of composite structures. For this problem, the Monte Carlo simulation‐based approach will be effective but expensive because many fibers should be considered for more accurate analysis, and the successive local approximation‐based approach has been proposed. However, accuracy of this approach depends on the local surrogate of the stresses for random variables, and an improved approach is proposed herein. In the proposed approach, a numerical condition for constructing a lower order surrogate is adjusted to minimize the estimation error to a reference solution obtained from a higher‐order surrogate. Herein, the problem settings and outline of the methods are introduced. Then, numerical results are provided for discussing effectiveness of the proposed approach.

Predicting post-impact compression strength of composite structures using the inverse method

The application of carbon fiber-reinforced laminated composites is restricted due to the dramatic decrease of compression strength after impact, which can reach 70% at most. So far, there is no method of predicting the post-impact material performance that has been widely accepted by researchers, aircraft manufactures and aviation safety administrations. Recently, an inverse method was proposed for post-impact strength prediction by modeling impact damage as a soft inclusion with apparent material properties from experiment. This study aims to explore the inverse method in compression-after-impact (CAI) strength prediction of aircraft structures. First, a model and computer program to implement the validation of the inverse method was developed to determine the damage area properties. Then, experiments were conducted with the help of digital image correlation technology and the optimization program to measure the displacement field around damage zones and calculate the apparent material properties. Finally, a strategy of predicting post-impact compression strength of laminated composites was proposed based on the investigation of the compression properties of T700/M21.

Bayesian identification and model comparison for random property fields derived from material microstructure

This paper provides a Bayesian framework for determining the spatial variability of the apparent material properties of two-phase composites. Bayesian analysis is applied to learn the parameters of the random fields that characterize the mesoscale material properties using computer-simulated images of the material microstructure. The information from such images is used to define the likelihood function of the random field parameters given the homogenized microscale data. The uncertainty in the parameter estimates is quantified through determining their full posterior distribution instead of a point estimate by application of an adaptive sampling algorithm. In addition, the Bayesian approach allows for assessing the plausibility of different correlation models belonging to the Matérn class through computing their respective marginal likelihoods for various choices of the smoothness parameter. The framework is applied to a composite material with large inclusion/matrix stiffness ratio and useful conclusions are derived with regard to the most appropriate correlation model and its parameters.

A meta-analysis of the size-weight and material-weight illusions.

The current study comprises the first systematic meta-analysis of weight illusions. We obtained descriptive data from studies in which subjective heaviness estimates were made for pairs or groups of objects that had the same mass and different volumes (size-weight illusion; SWI) or different apparent material properties (material-weight illusion; MWI). Using these data, we calculated mean effect sizes to represent illusion strength. Other study details, including stimulus mass, volume, density, and degree of visual and somatosensory access to the stimuli were also recorded to quantify the contribution of these variables to effect sizes for the SWI. The results indicate that the SWI has a larger mean effect size than the MWI and that the former is consistent in strength when information about stimulus size is gained through somatosensory channels, regardless of visual access. The SWI is weaker when only the visual system provides size information. Effect sizes for the SWI were larger when there was a greater difference in volume across the stimuli. There was also a positive correlation between SWI strength and the difference in physical density across the different experimental stimuli, even after controlling for volume differences. Together, we argue that these findings provide support for theories of weight illusions that are based on conceptual expectancies as well as those that are based on bottom-up processing of physical density. We further propose that these processes, which have been considered dichotomously in the past, may not be mutually exclusive from each other and could both contribute to our perception of weight when we handle objects in everyday life.

An explicit micro-FE approach to investigate the post-yield behaviour of trabecular bone under large deformations.

Homogenised finite element (FE) analyses are able to predict osteoporosis-related bone fractures and become useful for clinical applications. The predictions of FE analyses depend on the apparent, heterogeneous, anisotropic, elastic, and yield material properties, which are typically determined by implicit micro-FE (μFE) analyses of trabecular bone. The objective of this study is to explore an explicit μFE approach to determine the apparent post-yield behaviour of trabecular bone, beyond the elastic and yield properties. The material behaviour of bone tissue was described by elasto-plasticity with a von Mises yield criterion closed by a planar cap for positive hydrostatic stresses to distinguish the post-yield behaviour in tension and compression. Two ultimate strains for tension and compression were calibrated to trigger element deletion and reproduce damage of trabecular bone. A convergence analysis was undertaken to assess the role of the mesh. Thirteen load cases using periodicity-compatible mixed uniform boundary conditions were applied to three human trabecular bone samples of increasing volume fractions. The effect of densification in large strains was explored. The convergence study revealed a strong dependence of the apparent ultimate stresses and strains on element size. An apparent quadric strength surface for trabecular bone was successfully fitted in a normalised stress space. The effect of densification was reproduced and correlated well with former experimental results. This study demonstrates the potential of the explicit FE formulation and the element deletion technique to reproduce damage in trabecular bone using μFE analyses. The proper account of the mesh sensitivity remains challenging for practical computing times.

Size effects in lattice structures and a comparison to micropolar elasticity

This work models periodic thin walled cellular materials using either a discrete beam element lattice model or nominally equivalent micropolar elastic model. When the material properties of cellular materials are tested, small samples may have different apparent material properties than large samples. This difference is known in the literature as a size effect. The predictions of size effects from discrete and micropolar simulations are examined. Although the literature explains size effects arising from the effects simulated in the micropolar model, the micropolar model typically under predicts the stiffness due to size effects seen in the lattice model by an order of magnitude. The lattice size effects are examined for patterns and the size effect patterns found can be explained by the shape of the free edges, and by the specifics of how material is distributed within the material domain. These are causes for size effects that are not captured in the micropolar model.

On the Elastic Plates and Shells with Residual Surface Stresses

Recently the interest grows to development of the theory of surface elasticity with respect to nanotechnologies. Nanostructured materials demonstrate very promising properties which are different from whose of bulk materials, in general. In particular, nanosized specimens exhibit size-effect that is dependence of apparent (effective) material properties such as Young's modulus on specimen's size. One of possible explanation of these phenomena is the consideration of surface-related phenomena and their influence on the effective properties at the macroscale. In fact, surface elasticity may dramatically change effective (apparent) properties of nano- and microstructure materials.We discuss here the effective properties of thin-walled structures that are tangential and bending stiffness parameters taking into account surface/interfacial initial stresses. We consider the Gurtin-Murdoch model of surface elasticity. We show that the surface elasticity results in positive size-effect that is stiffening of nano-sized bodies in comparison with their bulk counterparts. Special attention will be paid to residual surface stresses. Unlike to surface elastic moduli there are no restrictions for values of residual stresses. In particular, we show that the compressive residual stresses may lead to negative size-effect that is to decreasing of an effective stiffness for nano-sized specimens.

Effect of waviness and orientation of carbon nanotubes on random apparent material properties and RVE size of CNT reinforced composites

A computational procedure is proposed in this paper for the determination of mesoscale random fields and of the representative volume element (RVE) size of carbon nanotube reinforced composites (CNT-RCs). To this purpose, computer-simulated images of composites with specific weight fraction (wt) of randomly scattered CNTs are examined. The cases of randomly oriented and unidirectionally aligned CNTs with random wavy and straight geometry are considered. A stochastic description of the random CNT waviness is adopted based on real measurements. The proposed approach takes into account the local weight fraction variability by processing statistical volume elements (SVEs) extracted directly from the composite images using the moving window technique. Computational homogenization is applied on various SVE finite element models using both kinematic and static uniform boundary conditions. The response statistics of the SVE models are obtained with Monte Carlo simulation. In this way, the statistical characteristics of the upper and lower bounds of the apparent material properties are effectively computed. The RVE size is defined within a prescribed tolerance, by examining the convergence of these two bounds. The effect of waviness and orientation of CNTs on the mechanical responses, mesoscale random fields and RVE size of CNT-RCs is particularly highlighted.

Determination of RVE size for random composites with local volume fraction variation

In this paper, a novel computational procedure is proposed for the determination of the representative volume element (RVE) size for random composites, which is the basis of homogenization methods. The proposed approach takes into account the local volume fraction variation by processing computer-simulated images of composites with randomly scattered inclusions. A variable number of microstructure models are derived directly from the images using the moving window technique. Each microstructure model contains different amount of inclusions, measured by image analysis tools. The proposed computational procedure is based on the solution of multiple boundary value problems under kinematic and static uniform boundary conditions using the extended finite element method (XFEM) coupled with Monte Carlo simulation (MCS). In this way, the statistical characteristics of the upper and lower bounds of the apparent material properties are computed. The RVE is attained within a prescribed tolerance by examining the convergence of these two bounds with respect to the mesoscale size. The numerical results clearly demonstrate the significant effect of matrix/inclusion stiffness ratio and volume fraction on the convergence rate. The proposed computational procedure leads to RVEs which can give more realistic results when used in homogenization problems. Mesoscale random fields describing the spatial variation of the components of the apparent elasticity tensor are also determined using the proposed approach.

Variability response functions for apparent material properties

The computation of apparent material properties for a random heterogeneous material requires the assumption of a solution field on a finite domain over which the apparent properties are to be computed. In this paper the assumed solution field is taken to be that defined by the shape functions that underpin the finite element method and it is shown that the variance of the apparent properties calculated using the shape functions to define the solution field can be expressed in terms of a variability response function (VRF) that is independent of the marginal distribution and spectral density function of the underlying random heterogeneous material property field. The variance of apparent material properties can be an important consideration in problems where the domain over which the apparent properties are computed is smaller than the representative volume element and the approach introduced here provides an efficient means of calculating that variance and performing sensitivity studies with respect to the characteristics of the material property field. The approach is illustrated using examples involving heat transfer problems and finite elements with linear and nonlinear shape functions and in one and two dimensions. Features of the VRF are described, including dependency on shape and scale of the finite element and the order of the shape functions.

Material properties derived from three-dimensional shape representations

Retinal image structure is due to a complex mixture of physical sources that includes the surface’s 3D shape, light-reflectance and transmittance properties, and the light field. The visual system can somehow discriminate between these different sources of image structure and recover information about the objects and surfaces in the scene. There has been significant debate about the nature of the representations that are used to derive surface reflectance properties such as specularity (gloss). Specularity could be derived either directly from 2D image properties or by exploiting information that can only be derived from representations in which 3D shape has been made explicit. We recently provided evidence that 3D shape information can play a critical role in the perception of material specularity, but the shape manipulation in our prior study also significantly changed 2D image properties (Marlow, Todorović, & Anderson, 2015). Here, we held fixed all monocularly visible 2D image properties and manipulated 3D shape stereoscopically. When binocularly fused, the depicted 3D shapes induced striking transformations in the surfaces’ apparent material properties, which vary from matte to ‘metallic’. Our psychophysical measurements of perceived specularity reveal that 3D shape information can play a critical role in material perception for both singly-curved surfaces and more complex geometries that curve in two directions. These results provide strong evidence that the perception of material specularity can depend on physical constraints derived from representations in which three-dimensional shape has been made explicit.

Invisible Losses and the Logics of Resettlement Compensation

The necessity of compensating people negatively affected by conservation and other development projects has been widely acknowledged. It is less widely acknowledged that because conventional compensation assessments focus on material resources and their economic equivalents, many important losses incurred by resettlers are invisible to project authorities. Through ethnographic observations and interviews, we documented losses identified by people facing resettlement from Mozambique's Limpopo National Park. We also examined resettlement planning documents to determine why decision makers' assessments of natural resource use and value neglect losses residents identified as critical. Identifying, preventing, and mitigating invisible losses in resettlement planning necessitates a better understanding of intangible benefits residents derive from resources, which are often as or more important than their readily apparent material properties. These benefits include but are not limited to decision-making authority linked to owning land versus having the use of fields; ancestral identity and social belonging linked to gravesites; the importance of tree roots that provide a powerful sense of security because they suppress hunger in periods of scarcity; and the importance of people's location within social networks and hierarchies as they determine the benefits versus risks that will be incurred through resettlement.

Finite element modeling to estimate the apparent material properties of trabecular bone

The in-vivo micro-structure and corresponding material property of trabecular bone is important to simulate the mechanical behavior of macroscopic bone structure. In order to simulate the mechanical behavior of bone numerically, the apparent Young’s modulus of trabecular bone should be available. Generally a high-resolution finite-element model based on micro-CT-images could be was used to estimate this value. However, all the previous works regarding this issue have employed either eight-noded voxel elements or four-noded tetrahedral elements, which usually produces large amount of error in estimating an apparent material property. Therefore, rigorous studies on the accuracy of element type for predicting the material properties of cancellous bone have been made in this paper. Micro-CT-data were extracted from a femoral neck to construct three-dimensional finite-element models with three different element types and compression analyses were performed numerically (up to 1.3% strain) to estimate the apparent modulus. Compression tests using the specimens extracted from a cadaver were also performed to validate the simulated apparent material properties using different element types. As a result, ten-noded tetrahedral elements are recommended to obtain reliable material properties of cancellous bone instead of eight-noded voxel elements or four-noded tetrahedral elements.

Fiber-aligned polymer scaffolds for rotator cuff repair in a rat model

Repair techniques of rotator cuff tendon tears have improved in recent years; nonetheless, the failure rate remains high. Despite the availability of various graft materials for repair augmentation, there has yet to be a biomechanical study using fiber-aligned scaffolds invivo. The objective of this study was to evaluate the efficacy of fiber-aligned nanofibrous polymer scaffolds as a potential treatment-delivery vehicle in a rat rotator cuff injury model. Scaffolds with and without sacrificial fibers were fabricated via electrospinning and implanted to augment supraspinatus repair in rats. Repairs without scaffold augmentation were also performed to serve as controls. Rats were sacrificed at 4 and 8 weeks postoperatively, and repairs were evaluated histologically and biomechanically. Both scaffold formulations remained in place, with more noticeable cellular infiltration and colonization at 4 and 8 weeks after injury and repair for scaffolds lacking sacrificial fibers. Specimens with scaffolds were larger in cross-sectional area compared with controls. Biomechanical testing revealed no significant differences in structural properties between the groups. Some apparent material properties were significantly reduced in the scaffold groups. These reductions were due to increases in cross-sectional area, most likely caused by the extra thickness of the implanted scaffold material. No differences were observed between the 2 scaffold groups. No adverse effect of surgical implantation of overlaid fiber-aligned scaffolds on structural properties of supraspinatus tendons in rat rotator cuff repair was demonstrated, validating this model as a platform for targeted delivery.

Conventional Vickers and true instrumented indentation hardness determined by instrumented indentation tests

We evaluate Vickers hardness and true instrumented indentation test (IIT) hardness of 24 metals over a wide range of mechanical properties using just IIT parameters by taking into account the real contact morphology beneath the Vickers indenter. Correlating the conventional Vickers hardness, indentation contact morphology, and IIT parameters for the 24 metals reveals relationships between contact depths and apparent material properties. We report the conventional Vickers and true IIT hardnesses measured only from IIT contact depths; these agree well with directly measured hardnesses within ±6% for Vickers hardness and ±10% for true IIT hardness.

Numerical simulation of a permittivity probe for measuring the electric properties of planetary regolith and application to the near‐surface region of asteroids and comets

Abstract— We present a numerical simulation technique for the retrieval of the electric properties relative permittivity and conductivity of planetary, asteroid, and cometary regolith. Our simulation techniques aim at accompanying hardware development and conducting virtual experiments, e.g., to assess the response of arbitrary heterogeneous conductivity and permittivity distributions or to scrutinize possibilities for spatial reconstruction methods using inverse schemes. In a first step, we have developed a finite element simulation code on the basis of unstructured, adaptive triangular grids for arbitrary two‐dimensional axisymmetric distributions of conductivity and permittivity. The code is able to take into account the spatial geometry of the probe and allows for possible inductive effects. In previous studies, the non‐inductive approach has been used to convert potential and phase data into apparent material properties. By our simulations, we have shown that this approach is valid for the frequency range from 102 Hz to 107 Hz and electric conductivities of 10−8 S/m that are typical for the near‐surface region of asteroids and comets composed of chondritic materials and/or frozen volatiles such as H2O and CO2 ice. We prove the accuracy of our code to be better than 10%, using mixed types of boundary conditions and present a simulated vertical log through a horizontally stratified subsurface layer as a representative example of a heterogeneous distribution of the electrical properties. Resolution studies for the given electrode separation reveal that the material parameters of layers having thicknesses of less than about half the electrode spread are not reconstructible if only apparent quantities are considered. Therefore, spatial distributions of the complex sensitivity are presented having in mind a future data inversion concept that will permit the multi‐dimensional reconstruction of material parameters in heterogeneous environments.