Elastic Matrix Research Articles

Modeling the interaction between intra and interlaminar cracking in FRP composites using phase-field regularized interface fracture

Fiber-reinforced polymer composites (FRPCs) exhibit a complex range of failure mechanisms, including matrix cracking, fiber breakage, fiber–matrix debonding, and delamination. Among these failure modes, interlaminar fracture or delamination across the interfaces between the different layers (plies) is commonly observed in experiments. Hence, the fracture behavior of these interfaces plays a critical role in determining the overall fracture performance of the FRPCs. In this work, our aim is to model the effect of interface on the final failure of FRPC laminates. Specifically, the present work focuses on modeling the complex interactions between the bulk FRPC damage and interfacial delamination in the carbon fiber reinforced composites (CFRP) within the realm of phase-field fracture. In the present formulation, the phase fields smear the sharp interface between FRP plies as regularized cohesive zones and also describe the bulk crack surface density eventually allowing interaction between bulk damage and interfacial delamination. For the composite’s constitutive description, the FRPC is treated as a homogenized material, with effective mechanical properties depending on the properties of the individual matrix and fibers with their respective volume fractions. The elastic matrix is assumed to be isotropic, while the fibers are characterized by their orientations. Further, an anisotropic modification is considered in the fracture energy of the FRPC to promote crack growth along the fiber direction. The model is implemented in a commercial finite element package and several numerical examples are presented to illustrate the complex crack path behavior in CFRP. Specifically, crack growth and interactions are simulated when there is a mismatch in the fiber orientation between the adjacent plies, resulting in dissimilar material properties on either side of the interface. The utilization of the regularized interface phase field model in an anisotropic framework to account for the mismatch in fiber orientation and hence material properties between the laminas makes it capable of predicting complex modes of fracture in FRPC laminates as demonstrated in the numerical simulations. We have also compared the model predictions with the experiments to validate their accuracy.

Analytical probabilistic progressive damage modeling of single composite filaments of material extrusion

This research focuses on investigating the elastic and damage characteristics of individual composite beads utilized in additively manufactured (3D printed) composites. A novel analytical probabilistic progressive damage model (PPDM) is introduced to comprehensively capture the elastic and damage attributes of these single 3D printed beads, which constitute the foundational elements of 3D printed composites. The PPDM is formulated based on assumptions of a perfectly elastic, perfectly plastic, and elasto-plastic matrix. For the elasto-plastic matrix, a novel formulation of the damage is developed to offer a more realistic view of the internal mechanics. Furthermore, a novel method of measuring the Young’s modulus of 3D printed composites is assessed. To this end, the Sentmanat extensional rheometer (SER) fixture is used to conduct a series of tensile tests on Kevlar and glass fiber-reinforced nylon beads. The experimental data of the SER are compared with those from an Instron tensile machine. Finally, the results of the PPDM and the experiments are compared and reveal a strong agreement in both the elastic region and the ultimate strength and strain.

Magnetic training of the soft magnetorheological elastomers

The effect of repetitive quasi-static magnetisation of a magnetorheological elastomer on its magnetic response is discussed. Typical components of this material, namely soft silicone rubber and carbonyl iron powder, are used to produce magnetically sensitive composite samples. The composite specimens are examined by vibrating sample magnetometry. The influence of the elasticity of the composite matrix on the change in magnetic differential susceptibility of the material as a function of the number of repeated magnetisation cycles is evaluated. The soft matrix elastomers are characterised by the presence of maxima in the initial part of the differential susceptibility curves. The sample magnetisation values corresponding to such maxima vary with the number of magnetisation cycles. In addition, the initial magnetic susceptibility curves of soft samples obtained at different polarity of the applied field are not symmetrical. Symmetry is obtained by performing several subsequent magnetisation cycles. The differential susceptibility curves are affected by both reversible and irreversible processes related to particle mobility in the matrix. The magnetic response of composite samples with rigid matrices is more similar to that of classical soft magnetic materials.

New Insight into Elastic Mechanical Properties and Anisotropies of Crystal Defect α-Quartz from DFT Calculation.

To reveal the cleavage mechanism of α-quartz in the grinding process of nonferrous metal ores, mechanical and charge properties of α-quartz crystals are investigated using the density functional theory. Based on the elastic constant matrix, the bulk and shear moduli were calculated before and after the α-quartz with oxygen atom defects. The results show that the ratios of bulk and shear moduli (B/G) were 0.87 and 0.95, respectively, which indicated that at the same stress level, it was easier to fracture without O-vacancy defects than with O-vacancy defects. The mapping surfaces indicated that the O-vacancy defect increased the bulk-, shear-, and Young's moduli, and Poisson ratio while decreasing the hardness. The anisotropy index (AL and AU) was calculated which illustrated that the O-vacancy can result in an increased anisotropy; meanwhile, the bulk anisotropy index (AB) increased strongly about two times. The anisotropy analysis shows the dominance crystal cleavage of the (011) plane in the shear stress and the dominance crystal cleavage of the (111) plane in the normal stress. The electron localization function α-quartz show that the O-vacancy defect can decrease the Si-Si length from 3.703 to 2.442 Å, which indicated that the O-vacancy formed the new covalent bonds between silicon atoms. Our work provided a systematic approach containing the mechanical, anisotropic, and electronic properties of mineral crystals to explain the cleavage behavior of crystals.

Optimization study of finite element simulation based on multi-layer structure and anisotropic CFRP

Introduction: Current research has mostly simplified CFRP components as isotropic media or homogenized them as anisotropic media, which fails to present the actual acoustic propagation behavior inside the CFRP components and restricts the accuracy of decoupling sound line tracking results and defect feature information.Method: Based on clarifying the influence of fiber direction on the spatial distribution of CFRP elastic properties, this paper proposes an acoustic modeling method for CFRP multi-directional plates considering the coupling effect of multi-layer structure and elastic anisotropy.Results: There are two main innovations: 1. The model is optimized using the Voigt representation method, which can quantitatively characterize the elastic anisotropy of any homogeneous material with a 6 × 6 elastic stiffness matrix containing 21 independent elastic constants. In this paper, the elastic stiffness matrix only includes five independent elastic constants; 2. Finite element simulation is used to analyze the propagation rules of ultrasonic waves inside CFRP and compare the detection methods with or without sound coupling layer.Discussion: The acoustic characteristics of the sound coupling layer are changed to find the optimal coupling method, reduce the refraction of ultrasonic waves in the specimen layer, and make the sound line path more accurate.

The coupled effects of grain boundary strengthening and Orowan strengthening examined by dislocation dynamics simulations

DD simulations are performed to unravel the coupled effects between grain boundary strengthening and Orowan strengthening. With the simulations of a plastically-deformed grain embedded in elastic matrix, the internal stresses associated with inter- and intragranular obstacles are quantified. First, plastic yielding is controlled by the length of dislocation sources. Then, in plastic deformation, the stress contribution of bypassing mechanism increases significantly with the size and number of precipitates, while the stress contribution of geometrically necessary dislocations at grain boundaries slightly decreases. Compared with regular spatial distribution of precipitates, random distribution induces a higher strengthening effect by reducing the dislocation mobility. Simulations of four-grain aggregates involving grain refinement and precipitation are systematically investigated. The volume fraction of precipitates is the key factor controlling the Orowan strengthening in addition to the grain size effect. A generalized Hall–Petch equation based on the mean free path of dislocations is proposed. At low strain, a relatively uniform internal stress field is found inside the aggregates with weak stress concentrations around grain boundaries and precipitates. The underlying mechanisms identified in this work are essential for understanding the plastic behavior of precipitate-strengthened polycrystals.

Assessing Efficacy of Afatinib toward Elastic Matrix Repair in Aortic Aneurysms.

Abdominal aortic aneurysm (AAA) is a critical, multifactorial cardiovascular disorder marked by localized dilatation of the abdominal aorta. A major challenge to countering the pathophysiology of AAAs lies in the naturally irreversible breakdown of elastic fibers in the aorta wall, which is linked to the poor elastogenicity of adult and diseased vascular smooth muscle cells (SMCs) and their impaired ability to assemble mature elastic fibers in a chronic proteolytic tissue milieu. We have previously shown that these are downstream effects of neutrophil elastase-induced activation of the epidermal growth factor receptor (EGFR) activity in aneurysmal SMCs. The novelty of this study lies in investigating the benefits of an EGFR inhibitor drug, afatinib (used to treat nonsmall cell lung cancer), for proelastogenic and antiproteolytic stimulation of aneurysmal SMCs. In in vitro cell cultures, we have shown that safe doses of 0.5 and 1 nM afatinib inhibit EGFR and p-extracellular signal-regulated kinases 1/2 protein expression by 50-70% and downstream elastolytic matrix metalloprotease 2 (MMP2) versus untreated control cultures. In addition, elastin production on a per cell basis was significantly upregulated by afatinib doses within the 0.1-1 nM dose range, which was further validated through transmission electron microscopy showing significantly increased presence of tropoelastin coacervates and maturing elastic fibers upon afatinib treatment at the above doses. Therefore, our studies for the first time demonstrate the therapeutic benefits of afatinib toward use for elastic matrix repair in small AAAs.

Fracture toughness improvement due to crack deflection and crack trapping by elliptical voids or particles

The paper investigates how voids and particles can be used to deflect and arrest cracks in order to enhance the failure stress and the fracture toughness of intrinsically brittle materials. This is done by investigating crack propagation near single elliptical voids and particles that are located in an elastic matrix material. The shapes of the inhomogeneities are varied, but their cross section is held constant. Uniaxial and biaxial loading conditions are considered and also the Young’s modulus ratio between particle and matrix material is varied. The crack trajectories near the material inhomogeneities are evaluated by applying a computationally very efficient approach, the crack trajectory interpolation (CTI) method, which has been introduced in an earlier work of the authors. With this method, critical distances are determined where an approaching crack runs into an elliptical void and gets trapped. Similarily, zones for crack arrest and crack deflection near stiff particles are found. Combinations of particles and voids are studied, too. A damage-based approach is used to investigate the improvements in failure stress and fracture toughness when a crack runs into a void. The results show that voids and particles that are elongated perpendicular to the crack plane are most useful for crack arrest. The trapping distances increase with increasing ellipticity of the inhomogeneities. However, the improvement in failure stress is highest for voids with moderate ellipticity. The results of this paper will be used to find optimum arrangements of voids or particle-void combinations for the design of structural components with increased fracture toughness.

Polarization-driven reversible actuation in a photo-responsive polymer composite

Light-responsive polymers and especially amorphous azopolymers with intrinsic anisotropic and polarization-dependent deformation photo-response hold great promises for remotely controlled, tunable devices. However, dynamic control requires reversibility characteristics far beyond what is currently obtainable via plastic deformation of such polymers. Here, we embed azopolymer microparticles in a rubbery elastic matrix at high density. In the resulting composite, cumulative deformations are replaced by reversible shape switching – with two reversible degrees of freedom defined uniquely by the writing beam polarization. We quantify the locally induced strains, including small creeping losses, directly by means of a deformation tracking algorithm acting on microscope images of planar substrates. Further, we introduce free-standing 3D actuators able to smoothly undergo multiple configurational changes, including twisting, roll-in, grabbing-like actuation, and even continuous, pivot-less shape rotation, all dictated by a single wavelength laser beam with controlled polarization.

Interaction between an edge dislocation and a circular incompressible liquid inclusion

We use Muskhelishvili’s complex variable formulation to study the interaction problem associated with a circular incompressible liquid inclusion embedded in an infinite isotropic elastic matrix subjected to the action of an edge dislocation at an arbitrary position. A closed-form solution to the problem is derived largely with the aid of analytic continuation. We obtain, in explicit form, expressions for the internal uniform hydrostatic stresses, nonuniform strains and nonuniform rigid body rotation within the liquid inclusion; the hoop stress along the liquid-solid interface on the matrix side and the image force acting on the edge dislocation. We observe that (1) the internal strains and rigid body rotation within the liquid inclusion are independent of the elastic property of the matrix; (2) the internal hydrostatic stress field within the liquid inclusion is unaffected by Poisson’s ratio of the matrix and is proportional to the shear modulus of the matrix; and (3) an unstable equilibrium position always exists for a climbing dislocation.

Structure engineering-enabled multi-direction-reconfigurable, soft, rechargeable lithium-ion battery with tissue-compliance low modulus and high performance

The significant demand for wearable and implantable bioelectronics necessitates high-performance power units. However, conventional batteries typically comprise rigid and bulky metals, or soft materials with conductive fillers (e.g., carbon nanotubes). These materials may induce undesired immune responses and battery failures when subjected to violent deformations due to the mismatch in mechanical properties between biological tissues (<100 kPa) and batteries. Additionally, current research on tissue-compliance soft batteries is based on the material-based low modulus and stretchability, where hydrogels are used as the elastic low modulus matrix. In this study, a structure-based low modulus electrode is developed wherein one-dimension (1D) uniaxial and two-dimension (2D) biaxial Kirigami pattern electrodes were carefully designed to provide both tissue-like modulus and multi-directional reconfigurability. The resulting reconfigurable soft battery exhibits excellent compliance and softness with Young's modulus of 64.1 kPa, which, to our knowledge, is the lowest modulus achieved for batteries with decent performance. The electrochemical performance of the reconfigurable lithium-ion soft battery under various deformations, such as stretching, bending, and twisting was investigated, and a high specific capacity of 83.5 mAh/g was achieved at a current density of 0.5 A/g under 100% stretching strain. The multi-directional stretchability, long-term stability, and biocompatibility of the reconfigurable soft battery were demonstrated. This groundbreaking work paves the way for the designing and manufacturing of soft batteries specifically tailored for wearable and implantable bioelectronics.

In-situ phase separation constructing robust hydrophobic ionogels with multifunction

Ionogels, as the promising alternative to hydrogels, have garnered great attention due to their excellent ionic conductivity, thermal stability, and non-volatility. However, the design and construction of robust hydrophobic ionogel still is a significant challenge at present, especially with a facile method. Herein, inspired by the two-phase structure of the dermis in human skin (stiff collagen fiber scaffold embedded in soft elastin matrix), a one-pot in-situ phase separation design strategy is proposed to construct the robust hydrophobic ionogel through the random copolymerization of hydrophobic monomers with the solubility difference in hydrophobic ionic liquid (IL). The resultant ionogel forms a homogeneously dual phase network containing solvent-rich soft domains and solvent-poor hard domains. The mechanical robustness can be synergistically achieved by the hard domain strong skeleton and the soft domain elastic matrix. Benefiting from multiple reversible interactions including hydrogen bonding, ion–dipole and ion-ion interactions, and physical entanglement, the ionogel shows strong IL retention, excellent self-healing, and regenerating abilities, while can adhere to different substrates. The unique phase separation structure brings temperature-dependent transparency and high-damping features. The ionogel also presents high ionic conductivity due to the abundance of movable ions. As application demonstrations, the ionogel is successfully used for dynamic pattern encryption, shock attenuation, and strain sensing. What’s more, this strategy can be also applied to improve the mechanical properties of hydrophobic ionogels based on other monomers. Hence, this work establishes an effective and general design strategy for hydrophobic ionogels demanding versatility.

Stability of Individual Phases in the Elastic Matrix of a Composite

A methodology for analytical stability assessment of individual compressed flexible phases of discretely heterogeneous composite elements of engineering structures is proposed to ensure their reliable safe operation and minimise the consequences of emergencies. Based on the energy balance equation for the proportional forces of a normal resistance of the medium to the phase displacement, expressions are obtained for determining the critical force, taking into account the possible initial curvature (non-rectilinearity) of a single phase in the elastic medium of the matrix for three possible cases of stability loss. The approbation of the results of the study on the example of deformation features of reinforcing bars in a compressed reinforced concrete column is presented.

Evaluation of elastic constants of particle accelerator cavity materials with Resonant Ultrasound Spectroscopy

European Spallation Source is a multi-nation, interdisciplinary research facility based on the world’s most powerful neutron source that will operate with high standards of availability and reliability minimizing downtime periods. In order to meet these goals, critical component’s performance and ageing need to be constantly monitored and assessed. Resonant Ultrasound Spectroscopy (RUS) is a highly versatile non-destructive technique for the definition of elasticity matrix of materials through the measurement of resonance frequencies. RUS could benefit the characterization of particle accelerator cavity materials exposed to challenging operational environments during project’s design and commissioning phases. This paper demonstrates the methodology and the first results on the implementation of this technique on Radio-Frequency Quadrupole (RFQ) structural copper. Rectangular parallelepiped samples of polycrystal, oxygen free, high purity Cu-OF copper were prepared and RUS measured on a designed experimental set-up. The obtained resonance frequencies were used as an input for the solution of the inverse eigenvalue problem using open-source objective function minimization software. The obtained results are compared with commercially available Finite Element Method (FEM) software defining a repeatable methodology for material property and defect characterization.

JNK2 silencing lipid nanoparticles for elastic matrix repair.

The over-expression of c-Jun N-terminal kinase (JNK2), a stress activated mitogen kinase, in the aortic wall plays a critical role in the formation and progression of abdominal aortic aneurysm (AAA). This triggers chronic downstream upregulation of elastolytic matrix metalloproteinases (MMPs), MMPs2 and 9 to cause progressive proteolytic breakdown of the wall elastic matrix. We have previously shown that siNRA knockdown of JNK2 gene expression in an AAA culture model stimulates downstream elastin gene expression, elastic fiber formation, crosslinking and reduces elastolytic MMPs2 and 9. Since naked siRNA poorly routes to intracellular targets, has poor stability in blood, and could be potentially toxic and immunogenic, this project is aimed to develop PEGylated lipid nanoparticles (LNPs) for delivery of JNK siRNA and to generate evidence of successful JNK2 knockdown and downstream attenuation of MMP2 gene and protein expressions. LNPs were formulated using thin-film hydration technique and had the size of 100-200 nm with zeta-potential ranging between 30 and 40 mV. JNK siRNA loaded PEGylated LNPs successfully knocked down JNK2 in cytokine-activated rat aneurysmal smooth muscle (EaRASMC) cultures. This resulted in a downstream decrease in MMP2 gene and protein expression and an upward trend in expression of genes for proteins critical for elastic fiber assembly such as elastin (ELN) and lysyl oxidase (LOX). Our result indicates cationic LNPs to be potential carriers for JNK siRNA delivery improving potency for elastin homeostasis required for AAA repair which could possibly provide benefits in preventing the progression of small AAAs.

Thermal vibration analysis of cracked nanobeams submerged in elastic foundations by nonlocal continuum mechanics

Understanding the mechanical behavior of nanoscale structures is crucial in the development of advanced nanotechnologies. In this study, a novel approach to investigate the thermal lateral vibration of cracked nanobeams immersed in an elastic matrix is investigated. For this purpose, Reddy’s third-order shear deformation theory (TSDT) is considered. In contrast to Timoshenko beam theory (First-order Shear Deformation Theory, FSDT), TSDT does not depend on a shear correction coefficient. The nano-scale effect is modeled using Eringen’s nonlocal continuum mechanics theory. The nonlocal form of the governing equation is obtained through the application of Hamilton’s principle. The weak form of the finite element global mass and stiffness matrices are obtained using Lagrange linear and Hermitian cubic interpolation. To model the crack in bending vibration, two rotational springs are used for TSDT, unlike the use of a single rotational spring in traditional Bernoulli–Euler (Classical Beam Theory, CBT) and FSDT. The stiffness of the springs is adjusted based on the severity of the crack. The influences of the nonlocal parameter, beam slenderness, position of crack, crack severity, Pasternak and Winkler foundation parameters, thermal effects and boundary conditions on the natural frequencies are investigated. The model’s outcomes are compared with findings from prior publications, demonstrating a strong level of agreement. This study contributes to the growing research on nanostructures by presenting a novel approach to understanding the dynamics of cracked nanobeams using Reddy beam analysis-based solutions.

A representative volume element model to evaluate the effective properties of flexoelectric nanocomposite

In this paper, a computational homogenization approach is developed to investigate the effective material properties of flexoelectric nanocomposites. The analysis incorporates the isogeometric analysis (IGA) to solve an electromechanically coupled system using a 3D representative volume element (RVE) model with periodic boundary conditions. In particular, a micromechanical analysis is carried out to represent the microstructure of a heterogeneous domain composed of an elastic matrix and cylindrical flexoelectric fibers. The numerical simulations indicated that while the effective tensor of piezoelectricity is isotropic, the flexoelectricity tensor is transversely anisotropic concerning the geometry of the composite’s phases. Furthermore, the flexoelectricity coefficients, μ¯3113 and μ¯3333, which couple the polarization to the strain gradients with respect to the longitudinal axis, improved remarkably with increasing the inclusion’s volume fraction. The presented computational methodology and the findings of this study is expected to contribute valuably towards the design of flexoelectric nanostructures and devices.

Matrix Stiffness Regulated Endoplasmic Reticulum Stress-mediated Apoptosis of Osteosarcoma Cell through Ras Signal Cascades.

The modulating effects of matrix stiffness on spreading and apoptosis of tumor cells have been well recognized. Nevertheless, the detail road map leading to the apoptosis and the underlying mechanisms governing the cell apoptosis have remained to be elucidated. To this aim, we provided a tunable elastic hydrogel matrix that promoted cell adhesion by modifying the surface of polyacrylamide with polydopamine, with stiffness value of 1, 10, 30, and 250 kPa, respectively. While the cell spreading increased and the apoptosis decreased with the matrix stiffness, such modulating effect of matrix on cell spreading exhibited different time evolvement behaviors as a function of stiffness, which likely led to surprisingly similar apoptosis rates for the 30 kPa and 250 kPa samples. Matrix stiffness mediated the spreading and apoptosis of MG-63 cells by regulating cell adhesion to matrix and in particular cytoskeletal organization, which was dependent on Ras, Rap1 and PI3K-Akt signaling pathways and finally led to the apoptosis of cancer cells dominated by endoplasmic reticulum stress pathway. Our results provided an insight into the regulation of tumor cell fate by the mechanical clues of ECM, which would have implication for future cancer research and the design of novel anticancer materials.

Sound absorption by a soft medium embedded with complex-shaped hard inclusions

Acoustic coatings for marine applications are commonly designed using a soft elastic matrix embedded with an array of resonant inclusions. In this work, a simple analytical approach to predict the acoustic performance of a soft elastic matrix embedded with hard inclusions of complex shape is presented. Utilizing analogies from fluid dynamics and electrostatics, a small number of well-known lumped parameters such as the added mass and capacitance are employed to relate the dominant dipole component of scattering of a complex-shaped hard inclusion to that of an equivalent sphere. Effective acoustic properties are then derived using a homogenization. The absorption coefficient of the coating for a range of complex shapes is compared with numerical simulations.

Porosity-dependent stability analysis of bio-inspired cellular nanocomposite shells

This paper presents an innovative numerical model to investigate buckling behaviour of bio-inspired continuously graded porous (CGP) nanocomposite cylindrical shells. It is postulated that the shell subjected to combined lateral pressure and axial compressive load is constructed from metal foams with closed-cell structures that possess graded internal pores, which exhibit three types of continuously graded porosity profiles based on a power-law distribution. A scaling relation for the effective Young’s modulus of the cellular structure determined by a variational finite element method (FEM) is used. The effective constitutive law of an elastic isotropic metal matrix containing distributed elastic carbon-nanotubes (CNTs) is estimated in consideration of the impact of CNTs agglomeration using a continuum model based on the Eshelby–Mori–Tanaka (EMT) approach. In contrast to conventional approaches, the study employs Euler–Bernoulli beams to model stiffeners within the CGP shells. This choice allows for a more realistic representation of stiffener effects, as opposed to the prevalent approach of uniform smearing across the shell’s surface. The equilibrium equations of the CGP shell, based on the Reddy higher-order shell theory (RHST), is obtained through the application of the Euler equation. Subsequently, the equations for stability are obtained through the utilization of the variational method. This study emphasizes the effects of geometrical parameters, porosity variability, and distribution of CNTs on the buckling performance of the CGP shells. The intricate interplay between CNTs and porosity distributions critically influences the stability behaviour of CGP shells. CNTs arrangement remarkably impacts buckling behaviour at higher length-to-mean radius ratios, while symmetric porosity near the mid-surface significantly enhances stiffness. These findings provide valuable insights for designing closed-cell cellular stiffened shells with optimal porosity to enhance stability.