Elastic Matrix Research Articles

Plasticity of Expression of Stem Cell and EMT Markers in Breast Cancer Cells in 2D and 3D Culture Depend on the Spatial Parameters of Cell Growth; Mathematical Modeling of Mechanical Stress in Cell Culture in Relation to ECM Stiffness

The majority of the current cancer research is based on two-dimensional cell cultures and animal models. These methods have limitations, including different expressions of key factors involved in carcinogenesis and metastasis, depending on culture conditions. Addressing these differences is crucial in obtaining physiologically relevant models. In this manuscript we analyzed the plasticity of the expression of stem cell and epithelial/mesenchymal markers in breast cancer cells, depending on culture conditions. Significant differences in marker expression were observed in different growth models not only between 2D and 3D conditions but also between two different 3D models. Differences observed in the levels of adherent junction protein E-cadherin in two different 3D models suggest that spatial parameters of cell growth and physical stress in the culture may affect the expression of junction proteins. To provide an explanation of this phenomenon on the grounds of mechanobiology, these parameters were analyzed using a mathematical model of the 3D bioprinted cell culture. The finite element mechanical model generated in this study includes an extracellular matrix and a group of regularly placed cells. The single-cell model comprises an idealized cytoskeleton, cortex, cytoplasm, and nucleus. The analysis of the model revealed that the stress generated by external pressure is transferred between the cells, generating specific stress fields, depending on growth conditions. We have analyzed and compared stress fields in two different growth conditions, each corresponding to a different elasticity of extracellular matrix. We have demonstrated that soft matrix conditions produce more stress than a stiff matrix in the single cell as well as in cellular spheroids. The observed differences can explain the plasticity of E-cadherin expression in response to mechanical stress. These results should contribute to a better understanding of the differences between various growth models.

Unlocking high hole mobility in diamond over a wide temperature range via efficient shear strain

As a wide bandgap semiconductor, diamond holds both excellent electrical and thermal properties, making it highly promising in the electrical industry. However, its hole mobility is relatively low and dramatically decreases with increasing temperature, which severely limits further applications. Herein, we proposed that the hole mobility can be efficiently enhanced via slight compressive shear strain along the [100] direction, while the improvement via shear strain along the [111] direction is marginal. This impressive distinction is attributed to the deformation potential and the elastic compliance matrix. The shear strain breaks the symmetry of the crystalline structure and lifts the band degeneracy near the valence band edge, resulting in a significant suppression of interband electron–phonon scattering. Moreover, the hole mobility becomes less temperature-dependent due to the decrease of electron scatterings from high-frequency acoustic phonons. Remarkably, the in-plane hole mobility of diamond is increased by ∼800% at 800 K with a 2% compressive shear strain along the [100] direction. The efficient shear strain strategy can be further extended to other semiconductors with face-centered cubic geometry.

Super elastic and negative triboelectric polymer matrix for high performance mechanoluminescent platforms

Mechanoluminescence platforms, combining phosphors with elastic polymer matrix, have emerged in smart wearable technology due to their superior elasticity and mechanically driven luminescent properties. However, their luminescence performance often deteriorates under extreme elastic conditions owing to a misinterpretation of polymer matrix behavior. Here, we unveil the role of the polymer matrices in mechanoluminescence through an interface-triboelectric effect driven by elasticity, achieving both high elasticity and brightness. By investigating interactions between elastic polymers and copper doped zinc sulfide microparticles, we reveal that elasticity significantly governed triboelectric effects for mechanoluminescence. In particular, high negative triboelectricity emerged as the key to overcoming poor triboelectric effect in extreme elastic conditions. This led to the discovery of polybutylene adipate-co-terephthalate silane and polycarbonate silane, achieving remarkable elasticity over 100% and a brightness of 139 cd/m2. These findings offer fundamental insights to select the optimal polymer matrix based on systematic parameters for various smart wearable applications.

Advanced microgrid optimization using price-elastic demand response and greedy rat swarm optimization for economic and environmental efficiency

In this paper, a comprehensive energy management framework for microgrids that incorporates price-based demand response programs (DRPs) and leverages an advanced optimization method—Greedy Rat Swarm Optimizer (GRSO) is proposed. The primary objective is to minimize the generation cost and environmental impact of microgrid systems by effectively scheduling distributed energy resources (DERs), including renewable energy sources (RES) such as solar and wind, alongside fossil-fuel-based generators. Four distinct demand response models—exponential, hyperbolic, logarithmic, and critical peak pricing (CPP)—are developed, each reflecting a different price elasticity of demand. These models are integrated with a flexible elasticity matrix to assess the dynamic consumer response to fluctuating electricity prices. The study evaluates four operational scenarios, focusing on grid participation, DER utilization, and the impact of real-time pricing (RTP), time of use (TOU), and critical peak pricing strategies. Quantitative results demonstrate the significant cost-saving potential of integrating DRPs with microgrid operations. In the optimal scenario, the GRSO achieved a minimum generation cost of 882¥ for the base load profile. Further, when critical peak pricing (CPP) was applied, the generation cost was reduced to 746¥, representing a 15.4% reduction. For a scenario where the grid’s participation was limited, the logarithmic-based demand response model decreased the generation cost to 817¥, while full grid interaction led to higher cost reductions. Additionally, our results show a significant reduction in peak load, with load factor improvements of up to 87.7% across the studied demand profiles. Furthermore, limiting the grid’s upstream power capacity to 30 kW resulted in a 7% increase in generation cost across all cases, confirming the importance of grid participation in reducing operational costs. The GRSO algorithm outperformed traditional metaheuristics in terms of both execution time and convergence, making it a viable solution for real-time microgrid optimization. In conclusion, the proposed GRSO-based framework provides an efficient approach for microgrid cost minimization, achieving up to a 15.4% reduction in operational costs and notable environmental benefits by reducing emissions. This study highlights the importance of dynamic demand response strategies and grid participation for sustainable and cost-effective microgrid management.

Quantifying Anisotropic Properties of Old–New Concrete Interfaces Using X-Ray Computed Tomography and Homogenization

The interface between old and new concrete is a critical component in many construction practices, including concrete pavements, bridge decks, hydraulic dams, and buildings undergoing rehabilitation. Despite various treatments to enhance bonding, this interface often remains a weak layer that compromises overall structural performance. Traditional design methods typically oversimplify the interface as a homogeneous or empirically adjusted factor, resulting in significant uncertainties. This paper introduces a novel framework for quantifying the anisotropic properties of old–new concrete interfaces using X-ray computed tomography (CT) and finite element-based numerical homogenization. The elastic coefficient matrix reveals that specimens away from the interface exhibit higher values in both normal and shear directions, with normal direction values averaging 33.15% higher and shear direction values 39.96% higher than those at the interface. A total of 10 sampling units along the interface were collected and analyzed to identify the “weakest vectors” in normal and shear directions. The “weakest vectors” at the interface show consistent orientations with an average cosine similarity of 0.62, compared with an average cosine similarity of 0.23 at the non-interface, which demonstrates directional features. Conversely, the result of average cosine similarity at the interface shows randomness that originates from the anisotropy of materials. The average angle between normal and shear stresses was found to be 88.64°, indicating a predominantly orthogonal relationship, though local stress distributions introduced slight deviations. These findings highlight the importance of understanding the anisotropic properties of old–new concrete interfaces to improve design and rehabilitation practices in concrete and structural engineering.

Uniform elastic field within a parabolic inhomogeneity obeying Neuber’s nonlinear stress-strain law under generalized plane strain deformations

We use complex variable methods to derive a closed-form solution to the generalized plane strain problem of an incompressible nonlinear elastic parabolic inhomogeneity obeying Neuber’s special nonlinear stress-strain law embedded in an infinite linear isotropic elastic matrix subjected to uniform remote in-plane and anti-plane stresses. We prove that the internal in-plane and anti-plane stresses and strains within the parabolic inhomogeneity remain uniform. The uniform effective strain within the parabolic inhomogeneity is obtained in closed-form. Consequently, the uniform elastic field within the parabolic inhomogeneity and the non-uniform elastic field in the matrix are completely determined.

Full-Spectrum Mechanochromic Photonic Films with Large Interparticle Distance.

Non-close-packed crystalline arrays of colloidal particles in an elastic matrix exhibit mechanochromism. However, small interparticle distances often limit the range of reversible color shifts and reduce reflectivity during a blueshift. A straightforward, reproducible strategy using matrix swelling to increase interparticle distance and improve mechanochromic performance is presented. Photonic composites are initially prepared with silica particle arrays embedded in an elastomer matrix at volume fractions of 0.35-0.5. To increase interparticle distance, the composites are immersed in an elastomer-forming monomer, causing the matrix to swell, followed by photopolymerization, thereby producing liquid-free composites. The degree of swelling is controllable up to 3.16, depending on monomer choice, matrix volume fraction, and crosslinking density. The process can be repeated to further increase swelling up to 10.36. This method can reduce the volume fraction of silica particles from 40% to 3.8%, while interparticle distance increases from 53 to 257nm. The swollen photonic composites exhibit a full visible spectrum under compression, while minimizing reflectivity loss. This allows red-colored photonic composites to be transformed into vivid multicolor patterns when compressed with stamps featuring spatial height variations.

Shape Functions Development for Beam-Column Element with Semi-Rigid Connections in Second-Order Steel Frame Analysis

The objective of this paper is to provide a novel method for developing the shape functions of a beam-column element with semi-rigid connection ends, thereby establishing a static analysis method for semi-rigid steel frames. This method takes into account the influence of the P-Delta effect, according to the finite element method based on displacement (FEM). The shape function is established directly from a third-order Hermitian displacement function polynomial combined with the bending element deflection differential equation. The linear elastic stiffness matrix, the geometric stiffness matrix of a semi-rigid connection beam-column, and the equilibrium equation of the element in a local coordinate system are simultaneously obtained by applying Castigliano’s theorem (Part 1) for elastic deformation potential energy expression. The computational program was developed using Matlab software, and the calculation results are verified against published research results, showing that the derived shape functions and the steel frame analysis method are reliable and trustworthy. In addition, this article also derives stiffness matrices and an equivalent nodal load vector for specific cases where the semi-rigid connection is fully rigid (FR) or a pin connection. The derived shape functions are polynomial expressions with coefficients that are simply calculated from the connection stiffness and the geometric and material characteristics of the element, making them highly convenient to use. Doi: 10.28991/CEJ-2025-011-01-021 Full Text: PDF

Miniaturized Liver Disease Mimics to Gain Insights into MMP Expression during Disease Progression.

Nonalcoholic fatty liver disease (NAFLD) encompasses a spectrum of liver conditions, ranging from hepatic steatosis to steatohepatitis, fibrosis, and severe outcomes such as cirrhosis or cancer. The progression from hepatic steatosis to fibrosis involves significant extracellular matrix (ECM) remodeling, characterized by increased collagen deposition and cross-linking of ECM proteins, causing increased tissue stiffness and altered MMP expression patterns. Dysregulated MMP expression and extracellular acidosis are key contributors to NAFLD progression. Unlike other MMPs, which may be relevant only at specific disease stages, MMP-9 serves as a universal marker, allowing for monitoring of its expression in relation to disease states and ECM parameters. Understanding dysregulated MMP-9 expression across different NAFLD stages can provide crucial insights into disease progression and serve as both a diagnostic and a prognostic biomarker, identifying potential therapeutic targets. This study introduces a three-dimensional (3D) collagen/alginate-based liver disease model designed to investigate how matrix collagen content, elasticity, and diseased cell conditions influence MMP expression and pH levels in situ using nanoprobes. The platform offered an understanding of the relationships between these factors and their role in NAFLD progression, offering valuable insights into disease progression and potential resolution. To examine how various physicochemical and biological factors, particularly MMP expression and collagen deposition, drive NAFLD progression, three 3D NAFLD models were developed, simulating healthy (HL), steatotic (SL), and fibrotic (FL) liver matrices. Additionally, the role of collagenase treatment in the FL matrix in enhancing MMP expression and potentially mitigating fibrosis was also explored. By employing dual-sensitive fluorescent nanoprobes to monitor real-time in situ changes in MMP-9 expression and pH levels, this platform offers a novel approach to understanding the in vitro roles of matrix stiffness, collagen deposition, and diseased cell conditions in NAFLD pathogenesis.

Structural, morphological, mechanical, and electrical studies of N. nucifera fibres.

The Powder X-ray diffraction (PXRD) data of Nelumbo Nucifera fibre is utilized to study multifaceted properties. Rietveld refinement was carried out along with cellulose phase. The crystallite size was computed using the Scherrer equation, and through first principle calculations, it has been illustrated and concluded that the size is not ellipsoidal, as previously suggested by other researchers; rather, it exhibits a multidimensional shape. Treloar's principle was used to create a 6×6 elastic tensor matrix, which was analysed with the Elastic Tensor Analysis (EALTE) tool that showed the fibre is anisotropic. The dielectric properties were measured in relation to frequency and temperature. It was found that conductivity increases with an increase in frequency and temperature. Functional Data Analysis (FDA) and regression analyses were employed to determine the correlation among various parameters. Fourier Transform Infrared Spectroscopy (FTIR) studies confirm that the lotus fibre is made up of cellulose. Scanning Electron and Transmission Electron Microscopy images unveiled that the lotus fibre exhibits structural stability characterized by both crystalline and amorphous regions. The energy gap calculated from UV-Vis data using the Kubelka-Munk method is 3.8eV. The constituents of N. nucifera fibre are identified to be carbon and oxygen through Energy Dispersive X-ray Spectroscopy (EDS) analysis.

Research on the Elastic Properties of Deep Rock Composites Under High Pressure

This paper presents a three-dimensional model of the definitive structure of gypsum, calcite and quartz crystals, which are the primary components of deep rock mass. The optimization of the primary components of deep rock mass material was performed under pressures ranging from 0 to 120 MPa using the first principles method. This led to the determination of the structural constants of the primary component crystals within the deep rock material. Furthermore, the variation rule of mechanical parameters, including elastic constants, for the primary components of deep-seated rock materials under different pressures was also investigated. The findings indicate a clear downward trend in the partial crystal structure parameters of deep-seated rock materials with increasing pressure. The primary components of each rock mass material display disparate compressibility properties in distinct directions when subjected to uniaxial compression. In conclusion, the anisotropic elastic properties of gypsum crystals, calcite crystals and quartz crystals under different pressures were investigated. The anisotropic cloud diagrams of bulk modulus, elastic modulus and shear modulus were presented for the three types of rock material at 0 MPa, 60 MPa and 120 MPa, respectively. In conclusion, we derived the theoretical equations for the elastic tensor matrix of composite materials using the principle of superposition. Furthermore, we studied and obtained the elastic tensor matrix for composite materials within the deep rock mass. These results provide essential theoretical guidance for the development of underground space and the analysis of deep rock dynamics.

A Neutral Isotropic Elastic Ellipsoidal Inhomogeneity with a Spring-Type Imperfect Interface

Summary We study the design of an imperfectly bonded neutral isotropic elastic ellipsoidal inhomogeneity that does not disturb the prescribed uniform normal stresses in an isotropic elastic matrix. The imperfect inhomogeneity-matrix interface is modeled by a spring-type imperfect interface characterized by a single imperfect interface function. The same degree of interface imperfection is realized in both the normal and tangential directions. The two loading parameters and the imperfect interface function are determined by solving a resulting cubic equation for each one of the three types of elastic constants of the composite. All three roots of the cubic equation are permissible provided that the Young’s modulus (for the first two types) or the Poisson’s ratio (for the third type) of the inhomogeneity is higher or lower than that corresponding to the matrix. The design of a neutral superellipsoidal or paraboloidal elastic inhomogeneity with another kind of spring-type interface that does not sustain shear traction under a prescribed uniform hydrostatic stress field in the matrix is also achieved.

A Model of Interaction of Rigid Fibers in an Orthotropic Composite Rope

The purpose of research is to construct an algorithm for calculating a stress-strain state of a multilayer orthotropic composite rope. Research methodology involves constructing and solving the interaction model of parallel reinforcing rigid fiber elements regularly placed in layers connected through an elastic material. A method for calculating a stress-strain state of a multilayer orthotropic composite rope is developed. The scientific novelty of research is in the establishment of a dependency for distribution of internal loading forces in reinforcing rigid fibers on stay rope parameters. The distribution of internal loading forces in reinforcing fibers depends on the amount and relative location of fibers in a stay rope. Along the length, the stress-strain state of a rope depends on a square root of the ratio of shear modulus of elastic matrix and tensile rigidity of fibers. The practical value of the research is in that the presented method allows determining the rope stress-strain state during the designing stage of a permanent structure. This is based on structural parameters and mechanical properties of components of a composite rope and conditions of its interaction with the structure, thereby increasing reliability and operation efficiency of the structure, in particular, the cable-stayed bridge.

Strategies for the development of finite elements for non-prismatic frames

Non-prismatic structural elements, often referred to as beams with variable cross-sections, constitute a special class of slender structures. These types of structures capture the interest of engineers and architects due to their ability to optimize geometry to meet specific needs, such as weight reduction, material consumption, environmental impact, and costs. Despite the advantages that engineers can gain from using non-prismatic structural elements, modeling these structures poses non-trivial challenges, resulting in inaccuracies that may compromise the benefits offered by such structures. Taking this into consideration, this work presents an innovative approach to obtain the displacement solution for non-prismatic beams, obtaining the elastic stiffness matrix through the virtual work principle, using the kinematics of Timoshenko's theory. This proposed formulation is independent of bar discretization to achieve an analytical result. This is due to the absence of considering any additional approximations beyond those already contained in the analytical idealization of bar behavior, resulting in a nearly natural discretization of the structure.

Asymptotic homogenization, domain decomposition and finite elements combined for calculating effective elastic properties of periodic fiber-reinforced composites with imperfect interfaces

A methodology is presented for calculating the effective elastic properties of periodic multi-phase composites made of an anisotropic linear elastic matrix reinforced with a periodical distribution of unidirectional fibers and exhibiting spring-type imperfect contacts at the interfaces. The periodicity cell contains any finite number of parallel fibers and exhibits arbitrary cross-section. Fibers also exhibit arbitrary cross-sections and are made of a different anisotropic linear elastic material each. The methodology uses asymptotic homogenization (AH) to obtain the mathematical expressions of the effective properties and to formulate the so-called local problems on the periodicity cell on whose solutions the effective properties depend on. In order to deal with the discontinuities arising from the spring-type interfaces, the local problems are then restated via domain decomposition (DD) in a way allowing for an iterative resolution scheme in which the solution of the problem to be solve in each iteration is obtained via finite elements (FE). Results in the examples are obtained via a computational implementation of the methodology based on the FreeFEM open-source software, which allows for the variational formulation of the iteration problem to be dealt with directly.

A constitutive model for brittle rock subjected to dynamic loadings

Abstract The constitutive model of rock serves as the foundation for researching its mechanical responses under impact and explosion loads, and holds significant academic value and military significance. With the help of the basic solution to Eshelby’s matrix-inclusion problem and meso-damage mechanics, a new constitutive model was developed to describe the dynamic behaviour of brittle rock subjected to impact loadings. Brittle rock was considered here as heterogeneous solids composed of elastic solid matrix and imbedded penny-shaped microcracks. A rate-dependent constitutive relation, considering meso-structural damage mechanism of brittle rock, was derived based on the Ponte-Castaneda and Willis method. Further, micro-damage evolution equations with clear physical concept and fewer parameters were presented. In order to illustrate the predictive ability of the proposed model, comparisons are performed between the model predictions and experimental data from Split Hopkinson pressure bar tests on sandstone. The results show a generally good agreement, thus verifying its rationality and practicability.

A symmetric liquid lip inclusion in an infinite isotropic elastic matrix

We study the plane strain problem of a symmetric compressible liquid lip inclusion with two cusps in an infinite isotropic elastic matrix subjected to uniform remote in-plane normal stresses. The pair of analytic functions characterizing the elastic field in the matrix is derived in closed form. Explicit, elementary, and concise expressions in terms of the two Skempton’s induced pore-pressure coefficients are obtained for the internal uniform hydrostatic tension within the liquid inclusion and the mode I stress intensity factor at the cusp tip. When the two remote normal stresses satisfy a single condition, the external loading will not induce any singular stress field at the cusp tips.

Elastic properties of a magnetic elastomer

Magnetoactive (aka magnetorheological) elastomer is a composite material consisting of an elastic matrix and magnetic filling substance. A study dedicated to the relationship between its viscoelastic parameters and the strength of the external magnetic field has been done. Under the influence of a field, the material can demonstrate elasticity and viscosity increased by ten folds. The elastic properties of the composite remaining under those conditions heavily depend on the degree of deformation of the sample. Thus, this type of magnetic composite is a prospective material for being used as the working body in controllable dampers.

The plastic behavior of matrix and its effect on the interface stress transfer in fiber-reinforced composites

ABSTRACT Existing shear-lag models for fiber-reinforced elasto-plastic composites always assume a rectangular-shaped plastic zone in the matrix, which is not consistent with numerical simulations. In this paper, a shear-lag model considering a more realistic parabolic shape of the plastic zone in an elasto-plastic matrix is proposed, in order to investigate the effect of matrix plasticity on the interface stress transfer. A closed-form solution to the profile of parabolic shape related to the applied stress is obtained so that the plastic zone evolution can be analytically characterized. Compared with the case with a purely elastic matrix, a plastic matrix could lead to a decrease in the interfacial shear stress (ISS) and an increase in the fiber stress. The smaller the plastic tangent modulus of the matrix, the lower the ISS is and the larger the fiber stress becomes, and the ISS and fiber stress keep being on same magnitudes of yielding strength and Young’s modulus of matrix, respectively. The present model with a parabolic plastic shape is more accurate to describe the mechanical behaviors of plasticity in matrix, which is of guiding value for the design of elasto-plastic composites used in vehicle accessories, medical devices, civil engineering and so on.

Molecularly Designed and Nanoconfined Polymer Electronic Materials for Skin-like Electronics.

Stretchable electronics have seen substantial development in skin-like mechanical properties and functionality thanks to the advancements made in intrinsically stretchable polymer electronic materials. Nanoscale phase separation of polymer materials within an elastic matrix to form one-dimensional nanostructures, namely nanoconfinement, effectively reduces conformational disorders that have long impeded charge transport properties of conjugated polymers. Nanoconfinement results in enhanced charge transport and the addition of skin-like properties. In this Outlook, we highlight the current understanding of structure-property relationships for intrinsically stretchable electronic materials with a focus on the nanoconfinement strategy as a promising approach to incorporate skin-like properties and other functionalities without compromising charge transport. We outline emerging directions and challenges for intrinsically stretchable electronic materials with the aim of constructing skin-like electronic systems.