Isotropic Research Articles

Sensitivity analysis of fibrous thick-walled tubes with mechano-sensitive remodeling fibers in homeostasis

AbstractIn this article, we apply the sensitivity analysis method to capture the influence of various parameters on the inflation pressure, axial force, and the deformation for an inflated and axially stretched cylinder. The material consists of an isotropic ground substance material reinforced with fibers that undergo a continuous and mechano-sensitive remodeling process. The input parameters of the mechanical system are assumed to be distributed according to the uniform probability distribution function. In the sensitivity analysis, we apply the Sobol method to determine how the variations of input parameters affect the inflation as well as the axial force in the cylinder. Special attention is given to the fiber remodeling process associated with a homeostatic balance between the constant fiber creation process and the strain-stabilized fiber dissolution. The results may help to understand the importance of the effect of material parameter changes, for example, due to remodeling processes in the context of diseases or recovering processes, on the overall tissue behavior.

Demonstration of the Optical Isotropy of TiO2 Thin Films Prepared by the Sol–Gel Method

Titanium dioxide (TiO2) thin films prepared by the sol–gel technique have been shown to be optically isotropic and, unlike the films obtained by competitive methods, do not exhibit measurable birefringence. A series of submicrometer-thin titanium dioxide films were prepared using the sol–gel technique and then thermally annealed at different temperatures. The samples were analyzed by spectroscopic ellipsometry using the Mueller matrix formalism, X-ray diffractometry and scanning electron microscopy. The conversion of amorphous titanium dioxide to polycrystalline anatase occurred at 400 °C or higher. Crystallites of a few percent of the film thickness were observed. Nevertheless, the crystallization process did not trigger the appearance of birefringence. These observations demonstrate that high-quality planar optical waveguides can be successfully fabricated on flexible substrates, in particular those composed of efficient polymers that can withstand the aforementioned temperatures.

3D Bulk Metamaterials with Engineered Optical Dispersion at Terahertz Frequencies Utilizing Amorphous Multilayered Split-Ring Resonators.

A 3D bulk metamaterial (MM) containing amorphous multilayered split-ring resonators is proposed, fabricated, and evaluated. Experimentally, the effective refractive index is engineered via the 3D bulk MM, with a contrast of 0.118 across the frequency span from 0.315 to 0.366 THz and the index changing at a slope of 2.314 per THz within this frequency range. Additionally, the 3D bulk MM exhibits optical isotropy with respect to polarization. Moreover, the peak transmission and optical dispersion are tailored by adjusting the density of the split-ring resonators. Compared to reported conventional approaches for constructing bulk MMs, this approach offers advantages in terms of the potential for large-scale manufacturing, the ability to adopt any shape, optical isotropy, and rapid optical dispersion. These features hold promise for dispersive optical devices operating at THz frequencies, such as high-dispersive prisms for high-resolution spectroscopy.

Real-time topology optimization based on multi-scale convolutional attention mechanism

This article proposes a deep learning model based on a multi-scale convolutional attention mechanism network SegNext for improving Topology Optimization (TO-Next), aimed at addressing the computational challenges associated with finite element iterations in traditional density-based methods. TO-Next is trained on diverse topology structures with varying loads, constraints and enriched physical information after initial iterations to enhance its generalization. Following training on three distinct decoder architectures, the optimal encoder–decoder network structure is determined. This study also investigates the algorithm's generalization capability under both single and multiple load constraints. The results indicate the superior performance and efficiency of the proposed method compared with the Solid Isotropic Material with Penalization (SIMP) method, enabling real-time generation of near-optimal topology structures within a short timeframe.

An Efficient Method to Compute Capillary Pressure Functions and Saturation-Dependent Permeabilities in Porous Domains Spanning Several Length Scales

AbstractA method for calculating capillary pressure functions and saturation-dependent permeabilities of geometries containing several length scales is presented. The method does not require the exact geometries of the smaller length scales. Instead, it requires the effective two-phase flow parameters. It does this by generating phase distributions that form static equilibria at a selected capillary pressure value, similar to pore-morphology methods. Within a porous material, the effective parameters are used to obtain the corresponding phase saturation. It is shown how these phase distributions can be used in geometries spanning several length scales to calculate the capillary pressure function and saturation-dependent permeabilities. The method is tested on a geometry containing a simple isotropic porous material and it is applied to a complex textile stack geometry from a liquid composite molding process. In this geometry, three different length scales can be distinguished. The effective two-phase flow parameters of the textile stack are calculated by the proposed method, avoiding expensive simulations.

Supercontinuum laser-based gonio-scatterometer for in and out-of-plane spectral BRDF measurements

The hyperspectral component of bidirectional reflectance measurements, namely from several hundred wavelengths upwards, is attracting growing interest for numerous applications in both optics and computer graphics. In this paper, we present a motorized hyperspectral bidirectional reflectance measurement bench that performs in-plane and out-of-plane measurements for isotropic materials using a supercontinuum laser covering the visible and near infrared range, with a sub-nanometer spectral accuracy. We describe the complete data processing chain, including a method for assessing the alignment error of the measurement bench. From these measurements, we verify the principles of non-negativity, energy conservation and Helmholtz reciprocity. We introduce criteria also to evaluate the validity of the Lambertian hypothesis for the bidirectional reflectance and its deviation from reciprocity, obtained from the measurements directly. We show the need for spectral bidirectional reflectance measurements for certain materials, rejecting the separable function approximation.

Discovering 3D Hidden Elasticity in Isotropic and Transversely Isotropic Materials with Physics-informed UNets.

Three-dimensional variation in structural components or fiber alignments results in complex mechanical property distribution in tissues and biomaterials. In this paper, we use a physics-informed UNet-based neural network model (El-UNet) to discover the three-dimensional (3D) internal composition and space-dependent material properties of heterogeneous isotropic and transversely isotropic materials without a priori knowledge of the composition. We then show the capabilities of El-UNet by validating against data obtained from finite-element simulations of two soft tissues, namely, brain tissue and articular cartilage, under various loading conditions. We first simulated compressive loading of 3D brain tissue comprising of distinct white matter and gray matter mechanical properties undergoing small strains with isotropic linear elastic behavior, where El-UNet reached mean absolute relative errors under 1.5% for elastic modulus and Poisson's ratio estimations across the 3D volume. We showed that the 3D solution achieved by El-UNet was superior to relative stiffness mapping by inverse of axial strain and two-dimensional plane stress/plane strain approximations. Additionally, we simulated a transversely isotropic articular cartilage with known fiber orientations undergoing compressive loading, and accurately estimated the spatial distribution of all five material parameters, with mean absolute relative errors under 5%. Our work demonstrates the application of the computationally efficient physics-informed El-UNet in 3D elasticity imaging and provides methods for translation to experimental 3D characterization of soft tissues and other materials. The proposed El-UNet offers a powerful tool for both in vitro and ex vivo tissue analysis, with potential extensions to in vivo diagnostics. STATEMENT OF SIGNIFICANCE: Elasticity imaging is a technique that reconstructs mechanical properties of tissue using deformation and force measurements. Given the complexity of this reconstruction, most existing methods have mostly focused on 2D problems. Our work is the first implementation of physics-informed UNets to reconstruct three-dimensional material parameter distributions for isotropic and transversely isotropic linear elastic materials by having deformation and force measurements. We comprehensively validate our model using synthetic data generated using finite element models of biological tissues with high bio-fidelity-the brain and articular cartilage. Our method can be implemented in elasticity imaging scenarios for in vitro and ex vivo mechanical characterization of biomaterials and biological tissues, with potential extensions to in vivo diagnostics.

Legendre–Ritz solutions for vibration characteristics of three-dimensional double-layer lattice truss sandwich plates

In this paper, Legendre–Ritz solutions for vibration characteristics of double-layer lattice truss sandwich plates are proposed based on three-dimensional (3-D) elasticity theory. Double-layer lattice truss sandwich plates consist of three face sheets and two cores. The face sheets are composed of fiber-reinforced composites and the cores are composed of pyramidal lattice trusses made of isotropic materials. The pyramidal lattice core is equated to a homogeneous plate according to equivalence principle. Based on 3-D elasticity theory and pseudo excitation method (PEM), each layer's energy expressions of double-layer lattice truss sandwich plates are constructed. After that, Legendre polynomials are adopted to describe displacement components in length, width and thickness directions. On this basis, the Rayleigh-Ritz method is used to solve energy functions to obtain motion equations of double-layer lattice truss sandwich plates. The accuracy and validity of the present method are corroborated by comparisons with references and finite element method (FEM). Additionally, in order to find out effects of relevant parameters on dynamical characteristics of double-layer lattice truss sandwich plates, parametric studies are carried out by means of some numerical examples.

Size Matters: Rethinking Hertz Model Interpretation for Cell Mechanics Using AFM

Cell mechanics are a biophysical indicator of cell state, such as cancer metastasis, leukocyte activation, and cell cycle progression. Atomic force microscopy (AFM) is a widely used technique to measure cell mechanics, where the Young modulus of a cell is usually derived from the Hertz contact model. However, the Hertz model assumes that the cell is an elastic, isotropic, and homogeneous material and that the indentation is small compared to the cell size. These assumptions neglect the effects of the cytoskeleton, cell size and shape, and cell environment on cell deformation. In this study, we investigated the influence of cell size on the estimated Young’s modulus using liposomes as cell models. Liposomes were prepared with different sizes and filled with phosphate buffered saline (PBS) or hyaluronic acid (HA) to mimic the cytoplasm. AFM was used to obtain the force indentation curves and fit them to the Hertz model. We found that the larger the liposome, the lower the estimated Young’s modulus for both PBS-filled and HA-filled liposomes. This suggests that the Young modulus obtained from the Hertz model is not only a property of the cell material but also depends on the cell dimensions. Therefore, when comparing or interpreting cell mechanics using the Hertz model, it is essential to account for cell size.

Structural Study of Four-Layered Cylindrical Shell Comprising Ring Support

In this work, the vibration analysis of a layered, cylinder-shaped shell is undertaken. The structure of the shell layers is composed of functionally graded and isotropic materials. The vibrations of four-layered cylindrical shells with a ring support along the axial direction are investigated in this research. The two internal layers are composed of isotropic materials, and the external two layers are composed of functionally graded materials. The outer functionally graded material layers considered are stainless steel, zirconia, and nickel. The inner two isotropic layers considered are aluminum and stainless steel. The shell frequency equation is acquired by employing the Rayleigh–Ritz method under the shell theory of Sanders. The trigonometric volume fraction law is used to sort the functionally graded material composition of the FGM layers. The natural frequencies are attained under two boundary conditions, namely simply supported–simply supported and clamped–clamped.

Data-driven and physics-based methods to optimize structures against delamination

Composite materials and multi-material components often fail at their internal interfaces/adhesive joints, and hence special attention should be given to such catastrophic delamination events to guarantee the system’s functional requirements. So far, however, the majority of structural topology optimization problems have focused on optimal distribution of the bulk materials by considering interfaces as perfectly bonded. This motivates the introduction of optimization methods that explicitly take into account the role of the material interfaces to optimize structures against delamination. In this work, we propose a data-driven heuristic optimization approach for the identification of optimal cohesive interfaces with linearly graded fracture properties to increase the ability of the composite structure to withstand peeling. Moreover, for given cohesive interface properties, we investigate the applicability of the physics-based Solid Isotropic Material with Penalty (SIMP) topology optimization approach to optimize the internal structure of a substrate in problems where the stress field is affected by interface delamination.

Задача нелинейной теории упругости о растяжении и кручении составного цилиндра с предварительно напряжённым включением, содержащим винтовую дислокацию

The problem of large torsional and tension-compression deformations of a composite circular cylinder of incompressible Bartenev-Khazanovich material is considered. The cylinder contains a central circular cylindrical inclusion in which a concentrated screw dislocation is formed. It is pre-twisted and stretched (or compressed) along the axis and bonded to an unstressed external hollow cylinder. A single reference configuration is used when solving a problem for a composite body. This configuration is natural (unstressed) for the outer hollow cylinder and prestressed for the inner solid cylinder. The large deformation superposition theory is used to write the determining ratios of the material of the inner cylinder. The nonlinear theory of torsion of elastic cylinders containing a screw dislocation is used to solve the problem of the prestressed state of the internal inclusion. This theory is physically correct not for any models of isotropic elastic materials, but only for those for which the screw dislocation in the cylinder has a finite linear energy and creates a longitudinal force of finite value. The Bartenev-Khazanovich model belongs to this class. The problem for a composite cylinder is solved by a semi-inverse method. Using this method, it is reduced to nonlinear ordinary differential equations. The assumption of isotropy and incompressibility of the material makes it possible to find an exact solution to the problem.

Topology optimised novel lattice structures for enhanced energy absorption and impact resistance

ABSTRACT This study evaluates topologically optimized lattice structures for high strain rate loading, crucial for impact resistance. Using the BESO (Bidirectional Evolution Structural Optimisation) topology optimisation algorithm, CompIED and ShRIED topologies are developed for enhanced energy absorption and impact resistance. Micromechanical simulations reveal CompIED surpasses theoretical elasticity limits for isotropic cellular materials, while the hybrid design ShRComp achieves theoretical maximum across all relative densities. Compared to TPMS, truss, and plate lattices, the proposed structures exhibit higher uniaxial modulus. Manufactured via fused deposition modeling with ABS thermoplastic, their energy absorption capabilities are assessed through compression tests and impact simulations. The ShRComp lattice demonstrates superior energy absorption under compression compared to CompIED. Impact analyses of CompIED and ShRComp sandwich structures at varying velocities show exceptional resistance to perforation and higher impact absorption efficiency, outperforming other classes of sandwich structures at similar densities. These findings position these new and novel topologies as promising candidates for impact absorption applications.

Negative refraction in isotropic achiral and chiral materials

Negative refraction in isotropic achiral and chiral materials

A fully coupled system of generalized thermoelastic theory for semiconductor medium

This study presents a new mathematical framework for analyzing the behavior of semiconductor elastic materials subjected to an external magnetic field. The framework encompasses the interaction between plasma, thermal, and elastic waves. A novel, fully coupled mathematical model that describes the plasma thermoelastic behavior of semiconductor materials is derived. Our new model is applied to obtain the solution to Danilovskaya’s problem, which is formed from an isotropic homogeneous semiconductor material. The Laplace transform is utilized to get the solution in the frequency domain using a direct approach. Numerical methods are employed to calculate the inverse Laplace transform, enabling the determination of the solution in the physical domain. Graphical representations are utilized to depict the numerical outcomes of many physical fields, including temperature, stress, displacement, chemical potential, carrier density, and current carrier distributions. These representations are generated for different values of time and depth of the semiconductor material. Ultimately, we receive a comparison between our model and several earlier fundamental models, which is then graphically represented.

The Behavior of Long Thin Rectangular Plates under Normal Pressure-A Thorough Investigation.

Thin rectangular plates are considered basic structures in various sectors like aerospace, civil, and mechanical engineering. Moreover, isotropic and laminated composite plates subjected to transverse normal loading and undergoing small and large deflections have been extensively studied and published in the literature. Yet, it seems that the particular case of long thin plates having a high aspect ratio appears to be almost ignored by various scholars despite its engineering importance. The present study tries to fill this gap, yielding novel findings regarding the structural behavior of long thin plates in the small- and large-deflection regimes. In contrast to what is normally assumed in the literature, namely that a long plate with a high aspect ratio can be considered an infinitely long plate, the present results clearly show that the structural effects of the ends continue to exist near the remote ends of the long plate. An innovative finding is that long plates would (only on movable boundary conditions for the large-deflection regime) exhibit a larger mid-width displacement in comparison with deflections of infinitely long plates. This innovative higher deflection appears for both small and large-deflection regimes for both all-around simply supported and all-around clamped boundary conditions. This new finding was shown to be valid for both isotropic and orthotropic materials and presents a novel engineering approach for the old assumption well quoted in the literature that a relatively long plate on any boundary condition can be considered an infinite plate. Based on the present research, it is recommended that this assumption should be used carefully as the largest plate mid-deflection might occur at finite aspect ratios.

Topological design of microstructured materials using energy-based homogenization theory and proportional topology optimization with the level-set method

In this study, we propose a novel approach to designing microstructures of porous material with extreme mechanical properties to maximize the bulk or shear modulus. The approach integrates energy-based homogenization theory and proportional topology optimization with the level-set method (HPTO-LSM). A level-set function (LSF) evolution strategy based on the nodal element mutual energies (EME) proportion is proposed and drives the LSF’s evolution. An EME proportion filtering technique is proposed and reduces the redundant branch structure. And a linear scaling strategy is applied to the HPTO-LSM to enhance the topological change ability. The effectiveness of the HPTO-LSM for designing microstructures of cellular materials to maximize the bulk or shear modulus is demonstrated using several 2D and 3D cases. The effects (changes in objective function values or topologies) of the EME proportion filtering scheme and scaling strategy on the HPTO-LSM are discussed. In addition, we compared the HPTO-LSM method with the solid isotropic material with penalization (SIMP) and bi-directional evolutionary structural optimization (BESO) methods through numerical examples. As shown by the results, effective objective function values and 2D and 3D microstructural topologies with clear interfaces and smooth boundaries can be acquired using the new approach. Applying the EME proportion filtering scheme and scaling strategy in the HPTO-LSM not only enhanced the topological variation of microstructures but also facilitated the acquisition of microstructures conducive to engineering applications. Compared to the SIMP and BESO methods, the HPTO-LSM method has significant advantages in obtaining better objective function values and better microstructural topologies.

Topology optimization of fiber-reinforced concrete structures using membrane-embedded model

Fiber-reinforced concrete is a typical unidirectional fiber-reinforced composite. For practicality and efficiency, fiber-reinforced concrete usually has the fiber and matrix modeled separately and then the fiber is embedded into the matrix. Therefore, this paper proposes a novel method to realize the topology and fiber orientation optimization for fiber-reinforced concrete structures. The optimization formulation considers two types of discrete variables, i.e., topology and fiber orientation, which are optimized by using the solid isotropic material with penalization method and bi-value coding parameterization method, respectively. To reduce the computational complexity, the topology and fiber orientation are independently updated at each iteration during the optimization process. Numerical examples verify the validity of the proposed method, which provides new ideas for the design of fiber-reinforced concrete structures.

Effect of quadratically varying electric potential on the multiple cracks in piezoelectric materials

A basic solution to the problem of three collinear equal cracks in a transversely isotropic piezoelectric material plate is obtained under the influence of electromechanical forces. Stroh formalism and complex variable methods are used to derive the mathematical expressions for SIF (stress intensity factor), COD (crack opening displacement), and COP (crack opening potential). The length of the saturation zones is investigated at each crack tip under the influence of quadratically varying electric displacement. Furthermore, a numerical study is carried out to discuss the effect of quadratically varying electrical potential on the saturation zone, COD, and COP. The results obtained numerically are reported graphically.

Spatiotemporally distinct responses to mechanical forces shape the developing seed of Arabidopsis.

Organ morphogenesis depends on mechanical interactions between cells and tissues. These interactions generate forces that can be sensed by cells and affect key cellular processes. However, how mechanical forces, together with biochemical signals, contribute to the shaping of complex organs is still largely unclear. We address this question using the seed of Arabidopsis as a model system. We show that seeds first experience a phase of rapid anisotropic growth that is dependent on the response of cortical microtubule (CMT) to forces, which guide cellulose deposition according to shape-driven stresses in the outermost layer of the seed coat. However, at later stages of development, we show that seed growth is isotropic and depends on the properties of an inner layer of the seed coat that stiffens its walls in response to tension but has isotropic material properties. Finally, we show that the transition from anisotropic to isotropic growth is due to the dampening of cortical microtubule responses to shape-driven stresses. Altogether, our work supports a model in which spatiotemporally distinct mechanical responses control the shape of developing seeds in Arabidopsis.