Spatial Variation Of Material Properties Research Articles

Additive manufacturing with varying material properties of thermosetting reactive polymers: a framework and comparison of different modes for implementing material transitions

Additive Manufacturing with Varying Material Properties enables controlled spatial variation of material properties in 3D-printed components, facilitating custom-tailored characteristics, added functionalities and reduced assembly processes. To promote this approach in building façade applications, this paper presents a novel framework for Additive Manufacturing with varying material properties using a thermosetting reactive polymer, specifically polyurethane. By dynamically changing the polyurethane’s chemical composition, the material properties can be precisely controlled. The framework’s individual aspects, including the material, hardware setup and computational system, are described in detail. Additionally, the research explores the implementation of material transitions with this framework, highlighting three different modes (horizontal, vertical and multi plane) and their impact on print time and material consumption. The paper concludes by discussing the potential of this approach for building façade applications, addressing current challenges and outlining future research directions.

Sensitivity of cartilage mechanical behaviour to spatial variations in material properties

Articular cartilage tissue exhibits a spatial dependence in material properties that govern mechanical behaviour. A mathematical model of cartilage tissue under one dimensional confined compression testing is developed for normal tissue that takes account of these variations in material properties. Modifications to the model representative of a selection of mechanisms driving osteoarthritic cartilage are proposed, allowing application of the model to both physiological and pathophysiological, osteoarthritic tissue. Incorporating spatial variations into the model requires the specification of more parameters than are required in the absence of these variations. A global sensitivity analysis of these parameters is implemented to identify the dominant mechanisms of mechanical response, in normal and osteoarthritic cartilage tissue, to both static and dynamic loading. The most sensitive parameters differ between dynamic and static mechanics of the cartilage, and also differ between physiological and osteoarthritic pathophysiological cartilage. As a consequence changes in cartilage mechanics in response to alterations in cartilage structure are predicted to be contingent on the nature of loading and the health, or otherwise, of the cartilage. In particular the mechanical response of cartilage, especially deformation, is predicted to be much more sensitive to cartilage stiffness in the superficial zone given the onset of osteoarthritic changes to material properties, such as superficial zone increases in permeability and reductions in fixed charge. In turn this indicates that any degenerative changes in the stiffness associated with the superficial cartilage collagen mesh are amplified if other elements of osteoarthritic disease are present, which provides a suggested mechanism-based explanation for observations that the range of mechanical parameters representative of normal and osteoarthritic tissue can overlap substantially.

A comprehensive study on static response of agglomerated microstructure-dependent coated functionally graded carbon nanotubes reinforced composite nanoshells rested on complex elastic foundation

An extensive investigation into the bending behavior of nanoshells made of coated functionally graded (FG) carbon nanotubes reinforced composites has been conducted, employing a novel spatial variation in material properties. The study explored Hardcore and Softcore of coated FG nanoshells. The examination includes five distribution patterns: a fully coated tri-directional, two bidirectional patterns, a transverse unidirectional, and an axial unidirectional distribution. The shell is resting on an orthotropic Winkler, Pasternak and Kerr foundations. Galerkin method is employed to establish an analytical solution for the equilibrium equations. This approach is designed to accommodate a variety of different boundary conditions. A comprehensive examination is undertaken to demonstrate the effects of various geometric and material parameters on the deflection and stresses of nanoshells.

Vibration analysis of tri-directionally coated plate via thickness-stretching and microstructure-dependent modeling

In this study, the tri-directionally-coated functionally graded plate has different levels of microstructure and is modeled more accurately using nonclassical mechanics incorporating the intrinsic characteristic lengths as well as using a spatial variation of material properties. The free vibration behavior of the tri-directionally-coated functionally graded plate is investigated using a refined quasi-3D higher-order shear deformation theory in conjunction with nonlocal strain gradient theory. Based on the generalized field of displacement, the quasi-3D higher-order shear deformation theory is employed by reducing the number of variables from six to five variables. The equations of motion are performed based on the principle of Hamilton and solved by applying the Galerkin technique to cover various boundary conditions. Besides, the microstructure-dependent parameters, that is, the nonlocal parameter and the length scale parameter, also affect significantly the frequency of the tri-directionally-coated functionally graded plates. The multi-directionally-coated plate is softened when considering the nonlocal parameter; the multi-directionally-coated plate is, however, hardened when considering the length scale parameter.

A Dynamic Analysis of Porous Coated Functionally Graded Nanoshells Rested on Viscoelastic Medium

Theoretical research has numerous challenges, particularly about modeling structures, unlike experimental analysis, which explores the mechanical behavior of complex structures. Therefore, this study suggests a new model for functionally graded shell structures called “Tri-coated FGM” using a spatial variation of material properties to investigate the free vibration response incorporating the porosities and microstructure-dependent effects. Two types of tri-coated FG shells are investigated, hardcore and softcore FG shells, and five distribution patterns are proposed. A novel modified field of displacement is proposed by reducing the number of variables from five to four by considering the shear deformation effect. The shell is rested on a viscoelastic Winkler/Pasternak foundation. An analytical solution based on the Galerkin approach is developed to solve the equations of motion derived by applying the principle of Hamilton. The proposed solution is addressed to study different boundary conditions. The current study conducts an extensive parametric analysis to investigate the influence of several factors, including coated FG nanoshell types and distribution patterns, gradient material distribution, porosities, length scale parameter (nonlocal), material scale parameter (gradient), nanoshell geometry, and elastic foundation variation on the fundamental frequencies. The provided results show the accuracy of the developed technique using different boundary conditions.

Multiscale mechanical characterization and computational modeling of fibrin gels.

Fibrin is a naturally occurring protein network that forms a temporary structure to enable remodeling during wound healing. It is also a common tissue engineering scaffold because the structural properties can be controlled. However, to fully characterize the wound healing process and improve the design of regenerative scaffolds, understanding fibrin mechanics at multiple scales is necessary. Here, we present a strategy to quantify both the macroscale (1-10mm) stress-strain response and the deformation of the mesoscale (10-1000µm) network structure during unidirectional tensile tests. The experimental data were then used to inform a computational model to accurately capture the mechanical response of fibrin gels. Simultaneous mechanical testing and confocal microscopy imaging of fluorophore-conjugated fibrin gels revealed up to an 88% decrease in volume coupled with increase in volume fraction in deformed gels, and non-affine fiber alignment in the direction of deformation. Combination of the computational model with finite element analysis enabled us to predict the strain fields that were observed experimentally within heterogenous fibrin gels with spatial variations in material properties. These strategies can be expanded to characterize and predict the macroscale mechanics and mesoscale network organization of other heterogeneous biological tissues and matrices. STATEMENT OF SIGNIFICANCE: Fibrin is a naturally-occurring scaffold that supports cellular growth and assembly of de novo tissue and has tunable material properties. Characterization of meso- and macro-scale mechanics of fibrin gel networks can advance understanding of the wound healing process and impact future tissue engineering approaches. Using structural and mechanical characteristics of fibrin gels, a theoretical and computational model that can predict multiscale fibrin network mechanics was developed. These data and model can be used to design gels with tunable properties.

Effect of Precompression and Material Uncertainty on the In-Plane Behavior of URM Pier–Spandrel Systems

Theoretical and experimental studies on loadbearing masonry walls have shown the significant influence of the axial load level (i.e., precompression) and wall aspect ratio on in-plane lateral resistance. Nonetheless, the impact of the precompression and spatial variability of the material properties needs to be further investigated at the scale of walls with openings. This study presents a stochastic analysis of unreinforced (URM) pier–spandrel systems subjected to both axial loads on piers and lateral loads, considering the spatial variation in material properties. A discontinuum-based computational model was utilized to assess the force–displacement behavior of a benchmark pier–spandrel structure under different vertical precompression levels on piers. A total of 750 simulations were carried out to propagate material uncertainties in lateral load analysis. The proposed modeling strategy, based on the discrete element method, explicitly represents joint openings, sliding, and crushing phenomena at the contact points defined between the adjacent discrete rigid blocks. According to the validated computational modeling strategy, meaningful inferences were made regarding the effect of the precompression level on the maximum displacement and ultimate lateral load-carrying capacity of the benchmark URM pier–spandrel system. The results showed that vertical pressure on piers had considerable influence on the displacement ductility of the system while yielding less variation in the displacement capacity. Furthermore, the appealing feature of the spatial probabilistic analysis is noted in the variation in the lateral load-carrying capacity of the structural system.

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.

Modeling of spatial permittivity variations using Karhunen–Loève expansion for stochastic electromagnetic problems

Fabrication tolerance often causes spatial variations in material properties in electromagnetic systems. In this paper, these spatial variations are modeled using Karhunen–Loéve expansion, which is truncated for a finite dimensional representation. Uncertainty quantification is performed by incorporating this model into an intrusive polynomial chaos expansion based spectral stochastic finite element method. Using a numerical example, it has been shown that the stochastic response obtained by the proposed approach is accurate and computationally efficient. The impact of correlation length of the covariance function used in the spectral expansion is analyzed.

A data-driven approach to characterizing nonlinear elastic behavior of soft materials

The Autoprogressive (AutoP) method is a data-driven inverse method that leverages finite element analysis (FEA) and machine learning (ML) techniques to build constitutive relationships from measured force and displacement data. Previous applications of AutoP in tissue-like media have focused on linear elastic mechanical behavior as the target object is infinitesimally compressed. In this study, we extended the application of AutoP in characterizing nonlinear elastic mechanical behavior as the target object undergoes finite compressive deformation. Guided by the prior of nonlinear media, we modified the training data generated by AutoP to speed its ability to learn to model deformations. AutoP training was validated using both synthetic and experimental data recorded from 3D objects. Force–displacement measurements were obtained using ultrasonic imaging from heterogeneous agar–gelatin phantoms. Measurement on samples of phantom components were analyzed to obtain independent measurements of material properties. Comparisons validated the material properties found from neural network constitutive models (NNCMs) trained using AutoP. Results were found to be robust to measurement errors and spatial variations in material properties.

Hybrid phase-field modeling of thermo-elastic crack propagation

Numerical modeling of the thermo-elastic fracture using a hybrid phase-field method is presented. The model’s capability to simulate complex thermo-elastic crack propagation paths under the temperature and mechanical loads’ influence is demonstrated through a few example problems. The evolution of complex crack patterns in a ceramic plate subjected to quenching are simulated. Further, the behavior of functionally graded specimens with a spatial variation of material properties when subjected to thermal shock is investigated. A staggered solution scheme is used to solve the coupled system of multi-field partial differential equations using an open-source finite element software FEniCS.

Analysis of Linear Elastic Fracture Mechanics for Cracked Functionally Graded Composite Plate by Enhanced Local Enriched Consecutive-interpolation Elements

This paper reports the application of consecutive-interpolation procedure into four-node quadrilateral elements for analysis of two-dimensional cracked solids made of functionally graded composite plate. Compared to standard finite element method, the recent developed consecutive-interpolation has been shown to possess many desirable features, such as higher accuracy and smooth nodal gradients it still satisfies the Kronecker-delta property and keeps the total number of degrees of freedom unchanged. The discontinuity in displacement fields along the crack faces and stress singularity around the crack tips are mathematically modeled using enrichment functions. The Heaviside function is employed to describe displacement jump, while four branch functions being developed from asymptotic stress fields are taken as basis functions to capture singularities. The interesting characteristic of functionall graded composite plate is the spatial variation of material properties which are intentionally designed to be served for particular purposes. Such variation has to be taken into account during the computation of Stress Intensity Factors (SIFs). Performance of the proposed approach is demonstrated and verified through various numerical examples, in which SIFs are compared with reference solutions derived from other methods available in literatures.

Topology optimization of functionally graded anisotropic composite structures using homogenization design method

This paper proposes a topology optimization method that is capable of simultaneous design for structural topology, stiff material (i.e. fiber) layout, and its orientations in functionally graded anisotropic composite structures. Functionally graded composites are inhomogeneous materials with continuously varying spatial composition. The spatial variation in material properties might enable better performance than an isotropic multi-material structure or fiber-reinforced composite structure with fixed fiber volume fraction. In order to enable the simultaneous design of composite topology, spatially varying fiber material layout and orientation, a homogenization design method (HDM) is applied together with a solid isotropic material with penalization (SIMP) method taking into account the advantage of each method. The SIMP method is efficient in determining discrete material states while avoiding intermediate states. Thus, it is applied to determine whether a material is void or a composite state. The HDM allows intermediate material states because it considers true anisotropic composite materials. Taking this advantage, the HDM method is applied to optimize spatially varying anisotropic fiber material layout and orientation. The optimization result of the fiber material is visualized using the projection method proposed for periodic composite structures. To validate the effectiveness of the proposed method, numerical examples for compliance minimization problems are provided.

Determination of Shear Wave Velocity Profile Model Considering Uncertainty Caused by Spatial Variation of Material Property in Rockfill Zone of Fill Dam

Determination of Shear Wave Velocity Profile Model Considering Uncertainty Caused by Spatial Variation of Material Property in Rockfill Zone of Fill Dam

Stress Concentration and Damage Factor Due to Central Elliptical Hole in Functionally Graded Panels Subjected to Uniform Tensile Traction.

Functionally graded material (FGM) can optimize the mechanical properties of composites by designing the spatial variation of material properties. In this paper, the stress distribution of functionally graded panel with a central elliptical hole under uniaxial tensile load is analyzed. Based on the inhomogeneity variation and three different gradient directions, the effects of the inhomogeneity on the stress concentration factor and damage factor are discussed. The study results show that when Young’s modulus increases with the distance from the hole, the stress concentration factor decreases compared with that of homogeneous material, and the optimal design of r-FGM is better than that of x-FGM and y-FGM when the tensile load. In addition, when the associated variation of ultimate stress is considered, the choice of scheme to reduce the failure index is related to the strength-modulus exponent ratio. When the strength-modulus exponent ratio is small, the failure index changes with the index of power-law, which means there is an optimal FGM design. But when the strength-modulus exponent ratio is large, the optimal design modulus design is to select a uniform material that maximizes the modulus at each point. These research results have a certain reference value for further in-depth understanding of the inhomogeneous design for FGM.

Two-dimensional adhesion mechanics of a graded coated substrate under a rigid cylindrical punch based on a PWEML model

• A piece-wise exponential multi-layered (PWEML) model is used to simulate the functionally graded materials . • The adhesion effect can be altered by adjusting the gradient index. • The appropriate gradual variation of the shear modulus can improve the performance of the coating. The paper aims at the contact mechanics of functionally graded coated substrate by taking into the adhesion effect. The coating-substrate structure is indented by a cylindrical punch to form a contact region where the adhesion forces are described by using the Maugis adhesion model. A piece-wise exponential multi-layered (PWEML) model is used to simulate the functionally graded materials with arbitrary spatial variation of material properties. This model divided the functionally graded coating into several sub-layers in which the elastic parameter varies as exponential form. Using the Fourier transform technique and the Transfer matrix method, the boundary value problem for adhesive contact of graded coated substrate is reduced to the singular integral equation. Some numerical results are presented to analyze the influence of gradient index on the pull-out force, contact stresses and adhesion region. The results can be applied to improve the performance of the coating by adjusting the gradient index.

Data-Driven Elasticity Imaging Using Cartesian Neural Network Constitutive Models and the Autoprogressive Method.

Quasi-static elasticity imaging techniques rely on model-based mathematical inverse methods to estimate mechanical parameters from force-displacement measurements. These techniques introduce simplifying assumptions that preclude exploration of unknown mechanical properties with potential diagnostic value. We previously reported a data-driven approach to elasticity imaging using artificial neural networks (NNs) that circumvents limitations associated with model-based inverse methods. NN constitutive models can learn stress-strain behavior from force-displacement measurements using the autoprogressive (AutoP) method without prior assumptions of the underlying constitutive model. However, information about internal structure was required. We invented Cartesian NN constitutive models (CaNNCMs) that learn the spatial variations of material properties. We are presenting the first implementation of CaNNCMs trained with AutoP to develop data-driven models of 2-D linear-elastic materials. Both simulated and experimental force-displacement data were used as input to AutoP to show that CaNNCMs are able to model both continuous and discrete material property distributions with no prior information of internal object structure. Furthermore, we demonstrate that CaNNCMs are robust to measurement noise and can reconstruct reasonably accurate Young's modulus images from a sparse sampling of measurement data. CaNNCMs are an important step toward clinical use of data-driven elasticity imaging using AutoP.

3D printing of materials with spatially non-linearly varying properties

Functionally graded materials (FGMs) with spatially varying material properties in 3D space are highly desired for a wide range of applications. Although FGMs are ubiquitous in biological materials, the fabrication of FGMs with continuous non-linear spatial variation of material properties remains a great challenge. Here we present a self-developed extrusion-based additive manufacturing system capable of fabricating FGMs with sophisticated material property distributions. The workflow involves property function modeling, gray-scale representation and control codes generation, digital material feeding and active multi-material mixing. The effectiveness of the technology is demonstrated by the successful printing of a diverse range of objects with complex spatial variations in color and Al2O3 concentration. In addition, by controlling the dynamic change of the different components during reactive 3D printing process, we can fabricate polyurethane (PU) objects with various gradient patterns in material mechanical properties. The results of the cantilever bending test and simulation show that the material gradient can effectively relieve the stress concentration. The proposed gradient 3D printing system opens a new avenue for manufacturing FGMs with exquisite material property distributions thus far only accessible by biological materials grown in nature.

Stochastic Harmonic Function Representation of Random Fields for Material Properties of Structures

AbstractTaking account of the spatial variation of material properties is of paramount importance to the safety and reliability evaluation of engineering structures. This necessitates the highly ef...

Spectral analysis techniques for characterizing cadmium zinc telluride polarization modulators

The low frequency electro-optic characteristics of cadmium zinc telluride are demonstrated in the mid-infrared, in the spectral range 2.5–11 μm. Conventional methods for characterizing the dynamic response by monitoring the amplitude of the time-varying light intensity do not account for spatial variation in material properties. In such cases, a more revealing method involves monitoring two distinct frequency components in order to characterize the dynamic and static contributions to the optical retardation. We demonstrate that, while this method works well for a ZnSe photo-elastic modulator, it does not fully capture the response of a cadmium zinc telluride electro-optic modulator. Ultimately, we show that acquiring the full waveform of the optical response enables a model to be created that accounts for inhomogeneity in the material that results in an asymmetric response with respect to the polarity of the driving voltage. This technique is applicable to broadband and fixed-wavelength applications in a variety of spectral ranges.