Spatial Distribution Of Material Properties Research Articles

Exploring the potential of transfer learning for metamodels of heterogeneous material deformation

From the nano-scale to the macro-scale, biological tissue is spatially heterogeneous. Even when tissue behavior is well understood, the exact subject specific spatial distribution of material properties is often unknown. And, when developing computational models of biological tissue, it is usually prohibitively computationally expensive to simulate every plausible spatial distribution of material properties for each problem of interest. Therefore, one of the major challenges in developing accurate computational models of biological tissue is capturing the potential effects of this spatial heterogeneity. Recently, machine learning based metamodels have gained popularity as a computationally tractable way to overcome this problem because they can make predictions based on a limited number of direct simulation runs. These metamodels are promising, but they often still require a high number of direct simulations to achieve an acceptable performance. Here we show that transfer learning, a strategy where knowledge gained while solving one problem is transferred to solving a different but related problem, can help overcome this limitation. Critically, transfer learning can be used to leverage both low-fidelity simulation data and simulation data that is the outcome of solving a different but related mechanical problem. In this paper, we extend Mechanical MNIST, our open source benchmark dataset of heterogeneous material undergoing large deformation, to include a selection of low-fidelity simulation results that require ≈ 2 − 4 orders of magnitude less CPU time to run. Then, we show that transferring the knowledge stored in metamodels trained on these low-fidelity simulation results can vastly improve the performance of metamodels used to predict the results of high-fidelity simulations. In the most dramatic examples, metamodels trained on 100 high fidelity simulations but pre-trained on 60,000 low-fidelity simulations achieves nearly the same test error as metamodels trained on 60,000 high-fidelity simulations (1 − 1.5% mean absolute percent error). In addition, we show that transfer learning is an effective method for leveraging data from different load cases, and for leveraging low-fidelity two-dimensional simulations to predict the outcomes of high-fidelity three-dimensional simulations. Looking forward, we anticipate that transfer learning will enable us to better capture the influence of tissue spatial heterogeneity on the mechanical behavior of biological materials across multiple different domains.

A study of supervised combined neural-network-based ultrasonic method for reconstruction of spatial distribution of material properties

This paper examines the performance of the commonly used neural-network-based classifiers for investigating a structural noise in metals as grain size estimation. The biggest problem which aims to identify the object structure grain size based on metal features or the object structure itself. When the structure data is obtained, a proposed feature extraction method is used to extract the feature of the object. Afterwards, the extracted features are used as the inputs for the classifiers. This research studies is focused to use basic ultrasonic sensors to obtain objects structural grain size which are used in neural network. The performance for used neural-network-based classifier is evaluated based on recognition accuracy for individual object. Also, traditional neural networks, namely convolutions and fully connected dense networks are shown as a result of grain size estimation model. To evaluate robustness property of neural networks, the original samples data is mixed for three types of grain sizes. Experimental results show that combined convolutions and fully connected dense neural networks with classifiers outperform the others single neural networks with original samples with high SN data. The Dense neural network as itself demonstrates the best robustness property when the object samples not differ from trained datasets.

Semantic instance segmentation using convolutional networks for reconstruction of spatial distribution of material properties

The general objective of this research is non-destructive assessment of the grain size in the metals. The authors suggest a new way of applying neural network technology when the neural network is used for analysis of the ultrasonic structural noise. It was assumed that the signals of ultrasonic structural noise are measured at several frequencies. In order to address structural noise issues, a convolutional neural network is designed to process ultrasonic sensor data, to learn structural noise features and to achieve direct grain size estimation simultaneously. To ensure minimum data gathering of metal samples, the design focuses on neural network with concept of semantic instance segmentation, for data extrapolation. Experimental results show that proposed methods as semantic instance segmentation with combined convolutional and fully connected dense neural networks with classifiers outperform the other single neural networks with original samples with high signal to noise ratio (SN) data.

On the Numerical Prediction of Process-Dependent Properties of Current High-Performance Materials with Material Model *MAT_254 in LS-DYNA

Over the last years, the forecast quality in production and especially (cold) forming simulations has reached a high level at least for standard materials. It has become state-of-the-art to take the results of these process simulations into account e.g. for crashworthiness analyses. For most of the currently used high-performance materials, however, the manufacturing processes do not only result in plastic deformation and thinning of the parts. There usually is a thermal component to these processes, which significantly influences the microstructure of the material and results in a spatial distribution of material properties within the final part. In order to predict the later behavior of the part with the same quality as for standard materials and standard processes, the virtual process chain has to be closed and material models have to be used that are able to simulate the microstructure evolution during the process. The press-hardening of the manganese-boron steel grade 22MnB5 is, for example, a standard in automotive industry. For this material FEM software for process simulation tools like LS-DYNA were extended in the past to take the microstructure evolution into account. The implemented material models are tailored for this certain alloy and process. To ensure the usability of the simulation tool the material models were generalized. In LS-DYNA, material model *MAT_GENERALIZED_PHASECHANGE (*MAT_254) has been devised to serve this purpose. Core of the model is a phase evolution table that takes into account up to 24 individual phases and consequently defines up to 552 possible phase transformations, not all of which have to be defined. The appropriate transformation law for each of the phase changes can be chosen from a list of generic phase change mechanisms. Due to its relatively flexible input structure and generality of the implementation, the model has been successfully used for different processes such as press-hardening, welding, additive manufacturing, and heat treatment, and for different materials, such as ultra-high strength steels, aluminum 6xxx alloys and titanium. This contribution will introduce the material formulation in detail and show the recent extensions based on the microstructure evolution of titanium.

FEM Simulation of Subintimal Angioplasty for the Treatment of Chronic Total Occlusions

Subintimal angioplasty is a highly challenging technique for percutaneous treatment of chronic total occlusion (CTO) in blood vessels, and the development of predictive tools for preliminary evaluation of potential outcomes and risks could be very useful for clinicians. While finite element (FE) simulation is a well-established approach to investigating partial occlusions, its extension to CTO has not been investigated yet, because of several additional issues that have to be addressed. In this work, we discuss the implementation of a FE model to simulate the main steps of the procedure, i.e., subintimal insertion of an initially folded balloon in a false lumen, inflation from eccentric position, deflation, and extraction. The model includes key morphological features of the CTO and possibility of varying spatial distribution of material properties to account for different constituents and degree of calcification. Both homogeneous and heterogeneous CTO configurations were analyzed, comparing arterial stress state, plaque compression, and postprocedural recoil. For a peak inflation pressure of 12 bar, the degree of lumen restoration was in the range 65-80%, depending on plaque heterogeneity. After balloon extraction, homogeneous highly calcified plaques exhibited substantial recovery of original shape. For homogeneous and heterogeneous CTO, values of peak von Mises stress in the arterial wall were of the same order of magnitude (range 1-1.1 MPa) but at different locations. Results compared favorably with data reported in literature for postprocedural lumen restoration and arterial stress data, confirming potential usefulness of the approach.

Identification of Heterogeneous Elastoplastic Behaviors Using the Constitutive Equation Gap Method

Recent developments in imaging techniques now facilitate local field measurements (e.g. strain, temperature, etc.). In this study, we identify the spatial distribution of material properties and local stress fields using an inverse identification method based on the constitutive equation gap (CEG). The CEG concept is based both on minimization of a cost function equal to the sum of the potential and complementary energies, and on the deviation between the measured and computed strain fields. We propose a new approach for identifying heterogeneous property fields (mechanical parameters and stress) using a secant elastoplastic tensor and a measured strain field obtained by full-field measurement. The reliability of the method is checked using finite element simulation data as reference full-field measurements. The method is then applied on noisy displacement fields to assess its robustness. Finally, the developed inverse method is tested on real measured data.

Production and Reliability Oriented SOFC Cell and Stack Design

This paper reports the results from the European project PROSOFC (funded by FCH-JU, FP7). Within the project an innovative methodology for a production and reliability oriented SOFC cell and stack design is developed. In particular the PROSOFC project aims at improving the robustness, manufacturability, efficiency and cost of SOLIDpowers state-of-the-art SOFC stacks so as to reach market entry requirements. The key issues are the mechanical robustness of solid oxide fuel cells (SOFCs), and the delicate interplay between cell properties, stack design, and operating conditions of the SOFC stack. The novelty of the project lies in combining state of the art methodologies for cost-optimal reliability-based design (COPRD) with actual production optimization. To achieve the COPRD beyond state of the art multi-physical modeling concepts were developed and validated for significantly improved understanding of the production and operation of SOFC stacks. The most critical failure modes for stack operation were identified in order to align the experimental investigations to generate suitable data for modelling these failures. The multi-physics model allows a probabilistic approach to consider statistical variations in production, material and operating parameters for the optimization phase. The project provides a methodology for 3D description of spatial distribution of material properties based on a random field models. The key for the whole methodology are validating experiments, homogenized models on multiple levels of the SOFC system (cell, interconnect, sealings) and introduction of extensive test programs specified by the COPRD methodology. The probabilistic models were related to the experimentally obtained properties of base materials to establish a statistical relationship between the material properties and the most relevant load effects in view of potential damage/failure based on multi-physics simulation can be established. Software algorithms for meta models that allow the detection of relationships between input parameters (materials, loading, etc.) and output parameters and to perform a sensitivity analysis were developed and implemented. The capabilities of the methodology for COPRD being developed is illustrated on two practical cases. A procedure based on meta models has been developed to estimate elastic, primary and secondary creep model parameters from 4-point bending tests. The goal is to (i) account for the effects of the friction between the sample and the rollers, anticlastic curvature, contact point shift and large deflection, which can affect the accuracy of the measurements, and (ii) measure properties which cannot be obtained using closed-form analytical solutions. This could be achieved by model-based parameter estimation with a 3-D continuum finite-element (FE) model, at the cost of very high running time. The proposed approach is computationally much more efficient. It starts with a sensitivity analysis to generate distributed meta models of the displacement at the inner rollers during loading-unloading cycles and creep measurements simulated by the 3-D FE model. The optimization problem for parameter estimation is then solved using the meta models. The accuracy of the approach was tested using a set of numerical experiments and comparison with results from 3-D imaging and computational homogenization. The experiments on Ni-YSZ samples were then analyzed. For the stochastic investigation of the thermo-electrochemical behavior of the stack a multi-physics stack model implemented in gPROMS and Fluent was linked and controlled automatically by optiSlang to perform a sensitivity analysis. The outcome is (i) the identification of the most relevant production and operating parameters which can have a significant impact on the stack lifetime and (ii) meta models of the efficiency and of the 3-D temperature distribution generated in the view of optimization. The tests show for instance that the accuracy of the 3-D meta model of the temperature distribution is sufficient to identify the minimum of variations in the spatial distribution of the temperature during cycling between full and part load by using sets of operating conditions for optimization.

Production and Reliability Oriented SOFC Cell and Stack Design

The paper presents an innovative development methodology for a production and reliability oriented SOFC cell and stack design aiming at improving the stacks robustness, manufacturability, efficiency and cost. Multi-physics models allowed a probabilistic approach to consider statistical variations in production, material and operating parameters for the optimization phase. A methodology for 3D description of spatial distribution of material properties based on a random field models was developed and validated by experiments. Homogenized material models on multiple levels of the SOFC stack were established. The probabilistic models were related to the experimentally obtained properties of base materials to establish a statistical relationship between the material properties and the most relevant load effects. Software algorithms for meta models that allow the detection of relationships between input and output parameters and to perform a sensitivity analysis were developed and implemented. The capabilities of the methodology is illustrated on two practical cases.

Extension and application of dynamic mechanical analysis for the estimation of spatial distribution of material properties

The paper presents a unique extension and application of the dynamic mechanical analysis (DMA) technique for the determination of heterogeneous mechanical material properties. Their values as well as their spatial distribution are major interest when analysing properties of post-damage materials. The proposed procedure incorporates longer than typical beam-shaped test samples enclosing the zone with locally varied material properties. The mechanical properties are estimated for the extended sample at defined positions while the sample is iteratively shifted along its axis. The procedure was successfully validated in various tests incorporating standardised and extended samples.The preliminary investigations regarding the application of the proposed procedure were conducted on composite specimens with heterogeneous distribution of material properties introduced by impact load. The results show, on the one hand, a monotonic relation between the storage modulus and the damage extent. On the other hand, a non-monotonic relation between the loss modulus and damage severity has been observed.

Spatial Distribution of Material Properties in Load Bearing Femur as Characterized by Evolutionary Structural Optimization

This works aims to simulate bone formation under natural loading using evolutionary structural optimization. Unlike material elimination by hard-kill approach applied previously, the current presentation implements material replacement defined as soft-kill method. A numerical analysis platform was developed and finite element model of sheep femur was constructed using computer tomography data. Quadruple material properties governing soft medullary canal, cancellous as well as plexiform and haversian cortical structures were considered as the main material constituents of the femur. An iterative algorithm was designed for determining the spatial distribution of these tissue types throughout the femur. The model initially started with a homogenous plexiform design and iteratively converged to a final state with heterogeneous density profile, nearly similar to a natural femur. The inefficient regions were gradually changed with mechanically lower grade and lighter tissues and thus the final construct had the least weight but still supported the load. The convergence was achieved successfully. The tissue types were distributed in a mechanically optimum fashion to counteract the applied forces. The resulting internal material assignments provided insights into the structural remodeling of femur within the context of Wolff’s law. Using the developments, bone formation can be simulated numerically under different mechanical loading conditions. Such investigations may provide useful information about the vulnerability of bone as its material properties change with osteoporosis or the fracture risk as a result of malfunction in muscles attached to the femur.

Manipulation of the propagation of out-of-plane shear waves

For a given elastic medium, there is a one-to-one correspondence relation between material properties (elastic moduli and density) and the propagation path of elastic waves. Based on this idea, we propose a new method for designing a cylindrical cloak invisible to out-of-plane shear waves. We begin by writing the Hamiltonian governing the path trajectory of out-of-plane shear waves in an inhomogeneous orthotropic medium. Based on Hamilton’s equations of motion, we derive the ray equation for out-of-plane shear waves and the differential equation that describes the optimal spatial distribution of material properties in the cylindrical cloak. To solve these two differential equations, two boundary conditions are imposed in terms of the continuity conditions of displacement and traction on the outer boundary of the cylindrical cloak. The two differential equations and two boundary conditions constitute a solvable system from which various cloak profiles can be designed. The proposed approach, which differs from the transformation optics approach, provides an intuitive and flexible design platform and allows considerable freedom to construct invisibility cloaks with a specific spatial distribution of material properties. The effects of the material properties and boundary conditions on cloak invisibility are analyzed in detail. Numerical simulations show that optimized cylindrical cloaks with finite material properties can be easily constructed.

Interactive Material Design Using Model Reduction

We demonstrate an interactive method to create heterogeneous continuous deformable materials on complex three-dimensional meshes. The user specifies displacements and internal elastic forces at a chosen set of mesh vertices. Our system then rapidly solves an optimization problem to compute a corresponding heterogeneous spatial distribution of material properties using the Finite Element Method (FEM) analysis. We apply our method to linear and nonlinear isotropic deformable materials. We demonstrate that solving the problem interactively in the full-dimensional space of individual tetrahedron material values is not practical. Instead, we propose a new model reduction method that projects the material space to a low-dimensional space of material modes. Our model reduction accelerates optimization by two orders of magnitude and makes the convergence much more robust, making it possible to interactively design material distributions on complex meshes. We apply our method to precise control of contact forces and control of pressure over large contact areas between rigid and deformable objects for ergonomics. Our tetrahedron-based dithering method can efficiently convert continuous material distributions into discrete ones and we demonstrate its precision via FEM simulation. We physically display our distributions using haptics, as well as demonstrate how haptics can aid in the material design. The produced heterogeneous material distributions can also be used in computer animation applications.

Determination of the distribution of electrical resistivity in reinforced concrete structures using electrical resistivity tomography

Concrete resistivity is an important durability related material parameter. It correlates with various properties, e.g., the reinforcement corrosion rate, the water saturation degree and the porosity. The resistivity is typically determined on a structure by using the Wenner probe. Unfortunately the results can strongly be influenced by heterogeneities, e.g., reinforcement bars or inhomogeneous moisture distributions. Neglecting these effects can lead to significant misinterpretations. In order to consider these influences quantitatively the applicability of the electrical resistivity tomography (ERT) on reinforced concrete has been studied. The aim of the method is to determine the distribution of the concrete resistivity perpendicular to the concrete surface. Based on this data the spatial distribution of material properties can be derived and the influence of an inhomogeneous resistivity distribution on the corrosion rate of the reinforcement can be studied. ERT can be applied to determine the resistivity distribution of reinforced concrete within certain resolution limits. Within this work the influence of different electrode configurations and rebar positions as well as the improvement of the resolution by considering prior information are exemplarily shown. Compared to the Wenner configuration the resolution and accuracy can be improved significantly with dipole–dipole measurements.

Portland Cement Pervious Concrete: A Field Experience from Sioux City

Portland Cement Pervious Concrete (PCPC) is becoming more utilized across the U.S. due to increased re- quirements for stormwater management. This paper details the experience of the installation of a PCPC test sec- tion/parking area in Sioux City, Iowa. In order to evaluate a large number of mixture designs, the test section incorporated five different mixtures, each placed with and without air entraining agent, for a total of ten sections. Cylinder samples were prepared during construction and compared with core data. The samples were tested for void ratio, permeability, unit weight, compressive strength development with time, and spatial distribution of material properties across the pavement profile. The results show a high degree of variability in material properties between the top and bottom layers, especially in the bottom five cm (two in.). Strong relationships between unit weight, permeability, strength, and void ratio suggest that void ratio criteria determined from unit weight testing has the potential for use as QA/QC criteria for pervious con- crete field placement.

Solution of the nonlinear elasticity imaging inverse problem: the compressible case

We discuss and solve an inverse problem in nonlinear elasticity imaging in which we recover spatial distributions of hyperelastic material properties from measured displacement fields. This problem has applications to elasticity imaging of soft tissue because the strain dependence of the apparent stiffness may potentially be used to differentiate between malignant and normal tissues. We account for the geometric and material nonlinearity of the tissues by assuming a known hyperelastic model for the soft tissue. We formulate the problem as the minimization of a cost function representing the difference between the measured and predicted displacement fields. We minimize the cost function with respect to the spatial distribution of material properties using a gradient-based (quasi-Newton) optimization approach. We calculate the gradient efficiently using the adjoint method and a continuation strategy in the material properties. We present numerical examples that demonstrate the feasibility of the approach.

Modelling mechanical behaviour of continuously graded vulcanised rubbers

Tailoring the spatial distribution of material properties is a well-established concept in materials engineering and referred as functional grading. Vulcanised rubbers have been graded very recently using a construction-based (layering) method. Although these studies have indicated the possibility of continuously grading the mechanical and chemical properties, there is little information available in the literature regarding the mechanical behaviour of so-produced rubbers. The present study attempts to close this knowledge gap via mathematical modelling of the stress–strain fields in graded rubbers. Rectilinear shearing of graded rubber slabs is theoretically analysed as it allows us to obtain closed-form analytical solutions. It is found that the slabs can develop highly localised stress–strain fields depending on the spatial variation of the shear modulus. The results indicate the need for a design code to grade rubbers with a mechanical functionality and the potential risks in the absence of such a code.

Resonant bar simulations in media with localized damage

As a rule, problems of wave propagation in finite media with non-uniform spatial distribution of material properties can only be tackled by numerical models. In addition, the modeling of damage features in a material requires the introduction of locally non-linear and––more important––non-unique equations of state. Using a multiscale approach, we have implemented a non-linear hysteretic stress–strain relation based on the Preisach–Mayergoyz (PM) model, into a numerical elastodynamic finite integration technique program, which has originally been developed for linearly elastic wave propagation in inhomogeneous media. The simulation results show qualitatively good agreement with data of non-linear resonant bar experiments in homogeneously non-linear and hysteretic media. When the PM density distribution of hysteretic units at the mesoscopic level is not uniform and/or confined to a finite area in stress–stress space, the response at high amplitude excitation tend to deviate from the quasi-analytical results obtained in the case of a uniform PM-space density. Localized microdamage features in an intact medium can be modeled by conceiving finite zones with pronounced hysteretic stress–strain relations within a “linear” surrounding. Forward calculations reveal a significant influence of the amplitude dependent resonance behavior on the location (edge versus center of a bar), the extend (width of the zone) and the degree (density of hysteretic units) of damage.

Non-destructive, three-dimensional monitoring of water absorption in polyurethane foams using magnetic resonance imaging

Non-destructive techniques to monitor the dynamics and spatial distribution of material properties are of critical importance in the development and assessment of future technical applications. The water absorption of polyurethane foams was investigated for the first time using magnetic resonance imaging. Small amounts of water were detected with high sensitivity. The dynamics of water penetration in the samples were recorded over an interval of 67 days and quantified gravimetrically. Different patterns of water absorption were visualized. Irregularities in the samples facilitated water absorption. The interfaces between foams, embedded structures and surrounding materials, as well as their resistance to water penetration, was studied. Magnetic resonance imaging, with its high spatial and temporal resolution, proved to be a valuable tool for precisely and non-destructively analyzing the behavior of polyurethane foams against water penetration.

Effect of specimen thickness on the statistical properties of fatigue crack growth resistance in BS4360 steel

In this paper the effect of specimen thickness on fatigue crack growth with the spatial distribution of material properties is presented. Basically, the material resistance to fatigue crack growth is treated as a spatial stochastic process, which varies randomly on the crack surface. The theoretical autocorrelation functions of fatigue crack growth resistance with specimen thickness are discussed for several correlation lengths. Constant ΔK fatigue crack growth tests were also performed on CT type specimens with three different thicknesses of BS 4360 steel. Applying the proposed stochastic model and statistical analysis procedure, the experimental data were analyzed for different specimen thicknesses for determining the autocorrelation functions and probability distributions of the fatigue crack growth resistance.

Stochastic finite element method for spatial distribution of material properties and external loading

In this paper, a stochastic finite element method is presented for the analysis of structures having statistical uncertainities in both material properties and externally applied loads, which are modelled as a homogeneous Gaussian stochastic process. The Neumann expansion technique has been used for the inversion of a stochastic stiffness matrix. The digital simulation technique was adopted to generate the deviatoric part of the stiffness matrix and load vector. A beam problem was taken up for comparison of results obtained by Neumann expansion and the direct Monte Carlo simulation technique. The comparison of the results shows that the values approach those obtained by direct Monte Carlo solutions as the order of expansion of the Neumann series is increased. An excellent agreement was achieved for cases when the coefficient of variation is comparatively small.