Constitutive Material Properties Research Articles

Numerical Modeling and Nonlinear Finite Element Analysis of Conventional and 3D-Printed Spinal Braces

This study aims to describe the numerical modeling and nonlinear finite element analysis of typical spinal braces as a first step towards optimizing their topology for 3D printing. Numerical simulation was carried out in Abaqus CAE software Version 2021, utilizing a CAD (Meshmixer Version 3.5.474) scan of an actual spinal brace. Boundary conditions were defined by means of contact surfaces between the human body and the supporting pads located in the interior of the brace. The process of tightening the straps on the rear face of the brace was simulated via appropriate imposed displacements. The response is described through the deformations and developing stresses of the brace and the contact pressures in the areas of interaction with the human body. Parametric analysis indicated that increasing the cross-sectional thickness or elastic modulus of the brace material results in higher maximum von Mises stresses and lower displacements. The comparison between 3D-printed and conventional braces highlighted the potential of 3D-printing technology to achieve comparable performance with customized designs, leveraging the constitutive properties of 3D-printed material obtained from tension tests. The tension tests demonstrated that the 3D-printed material achieved higher values of modulus of elasticity compared to traditional brace materials. Finally, the topology optimization criteria to be applied for the design of spinal braces in the next step of this ongoing research are briefly described.

Nonlinear dynamical characteristics of carbon nanotube-reinforced composite beams with piezoelectric actuators and elastically restrained ends under thermo-electro-mechanical loads

Nonlinear free vibration and dynamical responses of carbon nanotube (CNT) reinforced composite beams with surface-bonded piezoelectric layers and tangentially restrained ends under thermo-electro-mechanical loads are investigated in this paper. The properties of constitutive materials are assumed to be temperature-dependent and effective properties of nanocomposite are estimated using an extended rule of mixture. Unlike previous studies, the present work considers the effects of tangentially elastic constraints of two ends on the nonlinear dynamic characteristics of hybrid beams. Motion equation is established within the framework of Euler-Bernoulli beam theory taking into account von Kármán nonlinearity. Analytical solution is assumed to satisfy simply supported boundary conditions and Galerkin procedure is employed to obtain a time ordinary differential equation including both quadratic and cubic nonlinear terms. This differential equation is numerically solved employing fourth-order Runge-Kutta scheme to determine the frequencies of nonlinear free vibration and nonlinear transient response. Parametric studies are executed to examine numerous influences on the nonlinear dynamical characteristics of hybrid nanocomposite beams. The study reveals that tangential constraints of ends substantially effect the frequencies and dynamic response of the beam, especially at elevated temperatures. The results also indicate that nonlinear dynamic responses can be controlled effectively by means of piezoelectric actuators and elasticity of tangential constraints of ends should be considered in design of piezo-CNTRC beams.

Estimating viscoelastic, soft material properties using a modified Rayleigh cavitation bubble collapse time

Accurate determination of high strain rate (>103 1/s) constitutive properties of soft materials remains a formidable challenge. Albeit recent advancements among experimental techniques, in particular inertial microcavitation rheometry (IMR), the intrinsic requirement to visualize the bubble cavitation dynamics has limited its application to nominally transparent materials. Here, in an effort to address this challenge and to expand the experimental capability of IMR to optically opaque materials, we investigated whether one could use the acoustic signature of the time interval between the bubble's maximum radius and first collapse time point, characterized as the bubble collapse time, to infer the viscoelastic material properties without being able to image the bubble directly in the tissue. By introducing a modified Rayleigh collapse time for soft materials, which is strongly dependent on the stiffness of the material at hand, we show that, in principle, one can obtain an order of magnitude or better estimate of the viscoelastic material properties of the soft material under investigation. Using a newly developed energy-based theoretical framework, we show that for materials stiffer than 10 kPa the bubble collapse time during a single bubble cavitation event can provide quantitative and meaningful information about the constitutive properties of the material at hand. For very soft materials (i.e., shear modulus less than 10 kPa), our theory shows that unless the collapse time measurement has very high precision and low uncertainties, the material property estimates based on the bubble collapse time only will not be accurate and require visual resolution of the full cavitation kinematics.

基于CAE仿真计算的堆栈式PZT材料本构特性的研究

基于CAE仿真计算的堆栈式PZT材料本构特性的研究

Finite Element Analysis-Based Soft Robotic Modeling: Simulating a Soft Actuator in SOFA

Soft robotics modeling is a research topic that is evolving fast. Many techniques are present in literature, but most of them require analytical models with a lot of equations that are time consuming, hard to resolve, and not so easy to handle. For this reason, the help of a soft mechanics simulator is essential in this field. This article presents a tutorial on how to build a soft-robot model using an open source finite element analysis (FEA) simulator, called SOFA. This software is able to generate a simulation scene from a code written in Python or XML, so it can be used by people with different fields of competence, like mechanical knowledge, knowledge of material properties, and programming skills. As a case study, a Python simulation of a cable-driven soft actuator that makes contact with a rigid object is considered. The basic working principles of SOFA required to make a scene are explained step by step. In particular, this article shows how to simulate the mechanics and animate the bending behavior of the actuator and the importance of knowledge of the constitutive material properties for good modeling of the mechanical system. Furthermore, we will also show how to retrieve and save data from simulation, demonstrating that SOFA can easily adapt to a multidisciplinary subject, such as research in soft robotics, but can also be useful for teaching simulation and programming language principles to engineering students.

Multiscale modeling of nanoindentation and nanoscratching by generalized particle method

Most concurrent multiscale methods that expand atomistic region by continuum domain suffer from inconsistent material constitutive properties, which affect the integrity of model in the interface of atomistic and continuum domains. In this paper, the Generalized Particle (GP) method is employed to simulate nanoindentation and nanoscratching of a single-crystal aluminum sample. The main advantage of the GP method lies in its ability to extend the simulation model while maintaining consistent atomic properties across all scales. Coarsening of the atomic domain has been conducted through two-scale and three-scale GP model. The results showed a strong consistency between the results of full atomic simulations and those achieved through the GP method for both nanoindentation and nanoscratch simulations. Also, wave reflections were not seen at the interfaces. The study revealed that an increase in the number of distinct particle domains led to a reduction in the accuracy of multiscale simulations.

Computational synthesis of wheeled vehicles via multi-layer topology optimization

In current engineering practice, computer-aided design (CAD) tools play a key role in the design and fabrication of most mechanical systems, including the design of most vehicles. This software tends to rely heavily on human designers to provide the basic design concept, with the software being used to computationally render an existing design, or to perform modifications to a design to achieve incremental improvements in performance. However, an emerging class of computational methods, known as topology optimization methods, offers the potential for true black box computational design. Under this general framework, practitioners provide the algorithm with the constitutive properties of the design materials, and the mechanical function being designed for (e.g. maximum stiffness under a given loading condition), and the algorithm autonomously generates a description of the corresponding structure. With some exceptions, existing topology optimization methods are limited to generating static, single-body designs. In this study, we present a novel method that builds upon the current state of the art by combining multiple collocated planar design domains to achieve automated computational synthesis of multi-body wheeled vehicles. This capability represents an important step on the path toward automated computational design of increasingly complex, innovative and impactful mechanical systems.

Critical Review of Nanoindentation-Based Numerical Methods for Evaluating Elastoplastic Material Properties

It is well known that the elastoplastic properties of materials are important indicators to characterize their mechanical behaviors and are of guiding significance in the field of materials science and engineering. In recent years, the rapidly developing nanoindentation technique has been widely used to evaluate various intrinsic information regarding the elastoplastic properties and hardness of various materials such as metals, ceramics, and composites due to its high resolution, versatility, and applicability. However, the nanoindentation process of indenting materials on the nanoscale provides the measurement results, such as load-displacement curves and contact stiffness, which is challenging to analyze and interpret, especially if contained in a large amount of data. Many numerical methods, such as dimensionless analysis, machine learning, and the finite element model, have been recently proposed with the indentation techniques to further reveal the mechanical behavior of materials during nanoindentation and provide important information for material design, property optimization, and engineering applications. In addition, with the continuous development of science and technology, automation and high-throughput processing of nanoindentation experiments have become a future trend, further improving testing efficiency and data accuracy. This paper critically reviewed various numerical methods for evaluating elastoplastic constitutive properties of materials based on nanoindentation technology, which aims to provide a comprehensive understanding of the application and development trend of the nanoindentation technique and to provide guidance and reference for further research and applications.

Origins of brain tissue elasticity under multiple loading modes by analyzing the microstructure-based models.

Constitutive behaviors and material properties of brain tissue play an essential role in accurately modeling its mechanical responses. However, the measured mechanical behaviors of brain tissue exhibit a large variability, and the reported elastic modulus can differ by orders of magnitude. Here we develop the micromechanical models based on the actual microstructure of the longitudinally anisotropic plane of brain tissue to investigate the microstructural origins of the large variability. Specifically, axonal fiber bundles with the specified configurations are distributed in an equivalent matrix. All micromechanical models are subjected to multiple loading modes, such as tensile, compressive, and shear loading, under periodic boundary conditions. The predicted results agree well with the experimental results. Furthermore, we investigate how brain tissue elasticity varies with its microstructural features. It is revealed that the large variability in brain tissue elasticity stems from the volume fraction of axonal fiber, the aspect ratio of axonal fiber, and the distribution of axonal fiber orientation. The volume fraction has the greatest impact on the mechanical behaviors of brain tissue, followed by the distribution of axonal fiber orientation, then the aspect ratio. This study provides critical insights for understanding the microstructural origins of the large variability in brain tissue elasticity.

On the Regularity of Non-scattering Anisotropic Inhomogeneities

In this paper we examine the necessary conditions for an anisotropic inhomogeneous medium to be non-scattering at a single wave number and for a single incident field. These conditions are expressed in terms of the regularity of the boundary of the inhomogeneity. We assume that the coefficients, characterizing the constitutive material properties of the medium, are sufficiently smooth, and that the incident wave is appropriately non-degenerate. Our analysis utilizes the Hodograph transform as well as regularity results for nonlinear elliptic partial differential equations. Our approach requires that the boundary a-priori is of class $$C^{1,\alpha }$$ for some $$0<\alpha <1$$ .

High-fidelity modeling of dynamic origami folding using Absolute Nodal Coordinate Formulation (ANCF)

Origami has evolved into a framework for creating engineering systems at vastly different scales: from large deployable airframes to architected materials to small DNA machines. These emerging applications require us to develop high-fidelity models that can simulate and examine folding-induced mechanical responses, especially those involving significant facet rotation, non-uniform deformation, and complex dynamics. To this end, this study formulates and experimentally validates a new origami mechanics model based on Absolute Nodal Coordinate Formulation (ANCF), which has unique advantages for predicting the nonlinear dynamics of multibody systems with large rotation and deformation. This new model treats origami facets as ANCF thin plate elements rotating around compliant creases. Moreover, Torsional Spring Damper Actuator (TSDA) connectors are developed to represent crease folding. After careful calibration with experimentally measured constitutive material properties, this study provides the first reported quantitative agreement between simulation predictions and experiment results involving complex and non-uniform facet deformation and transient dynamic responses. Therefore, this model can help deepen our knowledge of folding-induced mechanics and dynamics, fostering future applications for origami.

Mechanical characterization of additively manufactured polymers using ultrasonic nondestructive testing

Ultrasonic nondestructive testing (NDT) can be used to relate the print settings of additively manufactured polymers to their macroscopic elastic properties. We present a comparison of the measurement of angle- and frequency-dependent ultrasonic transmission through a flat plate to predictions using a multiscale model that considers infill geometry and constitutive material properties. The experiment is an immersion test that uses a point source and synthetic linear array to measure the transmission coefficient from 0.2 to 1 MHz over a wide range of incident angles. Samples were fabricated using fused deposition modeling (FDM) to print infilled plates with polylactic acid (PLA) filament. Transmission measurements were compared to predictions from a multiscale model consisting of a finite element model to predict the effective anisotropic stiffness based on an assumed infill geometry and PLA material properties and an acoustic reflection-transmission model for an anisotropic elastic plate submerged in water based on the work of Rokhlin and Wang [J. Acoust. Soc. Am. 112, 822 (2002)]. Minimization of the difference between the measured and modeled transmission coefficient for all angles and frequencies by varying model inputs provides an improved understanding of the effects of the print settings on the as-built mechanical properties for 3D-printed materials.

Non-reciprocal wave propagation in time-modulated elastic lattices with inerters

Non-reciprocal wave propagation in acoustic and elastic media has received much attention of researchers in recent years. This phenomenon can be achieved by breaking the reciprocity through space- and/or time-dependent constitutive material properties, which is an important step in overcoming the limitations of conventional acoustic- and phononic-like mechanical lattices. A special class of mechanical metamaterials with non-reciprocal wave transmission are latices with time-modulated mass and stiffness properties. Here, we investigate the non-reciprocity in elastic locally resonant and phononic-like one-dimensional lattices with inerter elements where mass and stiffness properties are simultaneously modulated through inerters and springs as harmonic functions of time. By considering the Bloch theorem and Fourier expansions, the frequency-band structures are determined for each configuration while asymmetric band gaps are found by using the weighting and threshold method. The reduction in frequency due to introduced inerters was observed in both phononic and locally resonant metamaterials. Dynamic analysis of finite-length lattices by the finite difference method revealed a uni-directional wave propagation. Special attention is given to phononic-like lattice based on a discrete-continuous system of multiple coupled beams. Moreover, the existence of edge modes in the discrete phononic lattice is confirmed through the bulk-edge correspondence and their time evolution quantified by the topologically invariant Chern number. The proposed methodology used to investigate non-reciprocal wave transmission in one-dimensional inerter-based lattices can be extended to study more complex two-dimensional lattices.

Nondeterministic multiobjective optimization of 3D printed ceramic tissue scaffolds

Despite significant advances in the design optimization of bone scaffolds for enhancing their biomechanical properties, the functionality of these synthetic constructs remains suboptimal. One of the main challenges in the structural optimization of bone scaffolds is associated with the large uncertainties caused by the manufacturing process, such as variations in scaffolds’ geometric features and constitutive material properties after fabrication. Unfortunately, such non-deterministic issues have not been considered in the existing optimization frameworks, thereby limiting their reliability. To address this challenge, a novel multiobjective robust optimization approach is proposed here such that the effects of uncertainties on the optimized design can be minimized. This study first conducted computational analyses of a parameterized ceramic scaffold model to determine its effective modulus, structural strength, and permeability. Then, surrogate models were constructed to formulate explicit mathematical relationships between the geometrical parameters (design variables) and mechanical and fluidic properties. The Non-Dominated Sorting Genetic Algorithm II (NSGA-II) was adopted to generate the robust Pareto solutions for an optimal set of trade-offs between the competing objective functions while ensuring the effects of the noise parameters to be minimal. Note that the nondeterministic optimization of tissue scaffold presented here is the first of its kind in open literature, which is expected to shed some light on this significant topic of scaffold design and additive manufacturing in a more realistic way.

Dimensionless Analysis to Determine Elastoplastic Properties of Thin Films by Indentation

By assuming the elastoplastic properties of thin-film materials, a reverse analysis method is proposed by deriving a dimensionless function for the indentation process. The substrate effect is taken into account by assuming a perfect interface between thin-film and substrate materials. In order to obtain the applied load–penetration depth (P-h) curves, the indentation process is numerically modeled as an axisymmetric problem with a rigid-body Berkovich indenter on the semi-infinite substrate when performing finite element (FE) simulations. As a typical soft film/hard substrate problem, the elastic substrate is assumed and the power–law model is used to describe the constitutive properties of thin-film materials. Varying elastic modulus (10–50 GPa), yield strength (60–300 MPa), and hardening exponent (0.1–0.5) characterize different elastoplastic mechanical properties of thin-film materials with film thickness of 10–30 μm. Owing to the good trending P-h curves with the maximum indentation depth up to the 2/3 film thickness for different elastoplastic thin-film materials, a dimensionless function is derived and validated based on the predictions by reliable FE simulations. The proposed dimensionless function elegantly elucidates the essential relationship between the elastoplastic mechanical properties of the thin-film material and indentation responses (e.g., loading and unloading variables). The elastoplastic constitutive curves predicted by the proposed reverse method are confirmed to be in good agreement with the stress-strain curves of materials by FE simulations with the randomly selected elastoplastic mechanical properties and film thicknesses. This study provides a theoretical guidance to understand the explicit relationship between elastoplastic mechanical properties of the thin-film material and indentation responses.

Topology Optimization for Hybrid Lattice Compliant Mechanisms with Multiple Microstructures.

Hybrid lattice compliant mechanisms (HLCMs) composed of multiple microstructures have attracted widespread interest due to their superior compliant performance compared to the traditional solid compliant mechanisms. A novel optimization scheme for HLCMs is presented using the independent continuous mapping (ICM) method. Firstly, the effective properties of multiple orthogonal and anisotropic lattice microstructures are obtained by taking advantage of homogenization theory, which are used to bridge the relationship between the macrostructure layout and microstructure recognition. Then, a new parallel topology optimization model for optimizing HLCMs is built via a generalized multi-material, recognizing interpolation scheme with filter functions. In addition, the characterization relationship between independent continuous variables and performance of different elements is established. Sensitivity analysis and linear programming are utilized to solve the optimal model. Lastly, numerical examples with a displacement inverter mechanism and compliant gripper mechanism demonstrate the effectiveness of the proposed method for designing HLCMs with various lattice microstructures. Anisotropic lattice microstructures (ALMs) significantly facilitate the efficient use of constitutive properties of materials. Hence, HLCMs consisting of various ALMs achieve superior compliant performance than counterparts comprising different orthogonal lattice microstructures (OLMs). The presented method offers a reference to optimize HLCMs, as well as promotes the theoretical development and application of the ICM method.

Determine the unique constitutive properties of elastoplastic materials from their plastic zone evolution under nanoindentation

The evolution of the plastic zone underneath the indenter is challenging to be described during nanoindentation, which is recently known to be crucial to establish a constitutive model that features the plastic properties of the substrate materials based on their indentation responses. Using molecular dynamics and axisymmetric finite element (FE) simulations in this study, we show that the plastic zone shape in the elastoplastic materials is hemispherical in a broad range of length scales under a three-sided pyramid-shaped Berkovich indenter. By considering the critical factors of the applied load–penetration depth (P–h) curve, dimensional analysis is performed to derive dimensionless functions regarding the radius of the hemispherical plastic zone. For the loading and unloading stages in extensive FE simulations, a set of polynomial functions are proposed by associating the instantaneous and residual plastic zone radii with constitutive parameters. In addition to Young's modulus and the hardening exponent, the ratio of the representative stress to the reduced modulus is found to be crucial for predicting the plastic deformation. Lastly, the proposed dimensionless function reveals that the plastic zone radii are drastically different for three representative materials with identical P–h curves as confirmed by three independent methods. This result suggests that the proposed plastic zone radius in the dimensionless analysis helps to overcome the challenging uniqueness issue for decades to determine the unique elastoplastic properties of materials based on nanoindentation responses.

Probing bonded interfaces with finite-element resonant ultrasound spectroscopy

Resonant ultrasound spectroscopy (RUS) has long been applied for non-destructive quantification of elasticity, geometry, and density in material samples. Improvements in mode imaging and finite element analysis now provide validation and predictive models for a growing range of sample types. We build on recent work which applied finite-element RUS to characterize layered samples. Our study takes a closer look at the utility of RUS to evaluate the bonded interface between layers, with extension to thin films. Forward modeling of bond properties provided insights into mode-dependent frequency shifts for various types of homogeneous bond changes such as thickness and stiffness. Experimental work consisted of RUS testing on Al-Ti samples diffusion-bonded at different pressures. Despite identical base materials, samples bonded at 2 MPa and 15 MPa exhibit spectral differences not explained by geometry variance alone, indicating sensitivity to the bond interface. Though highly geometry and material dependent, the sensitivity of RUS to interface properties appears to be roughly an order of magnitude smaller than to the constitutive material properties, emphasizing careful experimentation.

A complex-variable finite element method-based inverse methodology to extract constitutive parameters using experimental data

This paper presents the use of full-field kinematic measurements obtained using the digital image correlation (DIC) procedure and load–displacement data to determine constitutive material properties by solving an inverse finite element optimization problem. A key ingredient in the proposed approach is computing accurate sensitivities with respect to the unknown parameters. These sensitivities were used to solve the optimization problem using an accurate, efficient, gradient-based method, and were computed using the complex-variable finite element method, ZFEM. The use of ZFEM’s gradients to inversely determine material properties is demonstrated with two examples. First, the elastic–plastic material properties of DP-590 steel are obtained using a tensile test specimen. Second, the cohesive material parameters of an adhesive are determined using a double cantilever beam test. A significant outcome of this paper is that the use of a weighted residual formulation of the interfacial strain fields and the load–displacement data within the optimization procedure provides better estimates of the constitutive properties than using only the load–displacement data. This technique minimizes the relative error in both the strain fields and the load–displacement curve, which is important to obtain accurate interfacial properties.

Thermal oxidative aging of satin weave and thin‐ply polyimide composites

AbstractThe weight loss and damage development of satin weave and thin‐ply carbon fiber‐reinforced polyimide composites are studied during high temperature (288 and 320°C) aging in air. Two distinct regions are identified in the weight loss measurements—a rapid initial desorption and a subsequent slower weight loss, which is attributed to matrix degradation. The initial desorption stage is modeled by combining material constitutive properties from literature, micro‐mechanics and a one‐dimensional Fickian diffusion model. Two different damage patterns are observed by using optical microscopy and X‐ray computed tomography on specimens before and after aging. Crack clusters form a network in satin weave composites, while edge delaminations are observed in thin‐ply laminates, which are known for their enhanced resistance to matrix cracking.