Modulus Ratio Research Articles

A method for predicting thermal expansion coefficients of carbon fiber/epoxy composites with void defects

AbstractTo predict the coefficient of thermal expansion (CTE) of carbon fiber/epoxy resin composites with void defects comprehensively and accurately, a comprehensive study is carried out by integrating experiment, analytical model (ANM), and finite element model (FEM). The experiments on composites are conducted combining with Micro‐CT to provide geometric parameters and verification for ANM and FEM. An ANM considering void defects is established based on the Chamis model to investigate the influence of porosity, temperature and the ratio of modulus of the constituents of composites. A FEM is established to verify the ANM and reveal the mechanisms of the influence of void defects. The results show that the proposed ANM has high agreement with FEM and experiment. The longitudinal CTE decreases by 61.94% as the porosity increases from 0% to 20% at 60°C, and the same change of porosity results in a 15.62% decrease at 180°C. The transverse CTE is less susceptible to changes in porosity, showing reductions of 2.32% at 60°C and 3.33% at 180°C.Highlights An innovative model is proposed to predict CTE considering void defects. The glass transition temperature Tg of the resin has a significant effect on CTE. Void defects change the homogeneity of the original stress field of the matrix. The reduction of the longitudinal CTE caused by void defects is more significant.

Machine Learning Enabled High‐Throughput Screening of 2D Ultrawide Bandgap Semiconductors for Flexible Resistive Materials

AbstractThe 2D ultrawide bandgap (UWBG) semiconductors have attracted great attentions for the next generation of electronics and optoelectronics, owing to their superiority on material flexibility, device stability, and power consumption. However, few 2D UWBG semiconductors have been discovered, impeding their prosperous developments and widespread applications. Here, a high‐throughput workflow is constructed to screen 2D UWBG semiconductors assisted by machine learning, and 507 potential candidates are obtained. Moreover, by learning, predicting, and screening Young's modulus and Poisson's ratio, 31 flexible 2D UWBG semiconductors are identified. Then the generation and the diffusion of anion vacancies, as well as the corresponding electronic properties are investigated by using the first‐principles calculations, and 3 of them are demonstrated as the most promising candidates for the flexible resistive materials. The facile interface tunneling and the increased material conductance caused by the anion vacancies will contribute to the transition from high resistive state to low resistive state. This work provides an efficient high‐throughput screening protocol to enrich the family of 2D UWBG semiconductors and is expected to foster their practical applications.

Linear viscoelasticity of anisotropic carbon fibers reinforced thermoplastics: From micromechanics to dynamic torsion experiments

The link between experimental characterization and the constitutive behavior of an anisotropic linear viscoelastic unidirectional carbon fiber-reinforced thermoplastic composite is explored using micromechanics modeling. Dynamic torsion tests were conducted at 1 Hz over a wide temperature range, from the glassy to the rubbery states of the polymeric matrix, on both the pure matrix and the composite, for various cutting angles relative to the fibers. A two-step modeling procedure in the frequency domain is presented to predict and validate the effective behavior of the composite. The first step involves FFT-based homogenization, which maps the microstructure and constituent behaviors to effective transversely isotropic viscoelastic properties. The second step consists of finite element simulations using the effective behavior calculated from homogenization as input to replicate the experiments. A comparison between experimental results and model predictions across the entire temperature range is performed. The modeling predictions show good accuracy at low temperatures, where the matrix is in the glassy state. At high temperatures, where the matrix is in the rubbery state, the predicted behavior becomes too soft. As the phase contrast increases and the ratio of matrix bulk modulus to shear modulus rises significantly, the impact of fiber arrangement on the effective properties becomes more pronounced.

Experimental study on the deformation behavior of soils under one-dimensional unloading

Soils are usually subjected to one-dimensional unloading due to the excavation, groundwater recharge, and other activities. This paper investigates the deformation behavior of soils under one-dimensional unloading. A series of oedometer tests with loading–unloading cycles were conducted on silty sand, silt, silty clay, and muddy silty clay samples extracted from southern Jiangsu, China. The influence of effective vertical stress before unloading on rebound deformation of soils was investigated. Test results show that the unloading deformation of soils increases nonlinearly with the increasing unloading ratio. When the unloading ratio reaches 0.8, only 30% of the total rebound deformation occurs. The rebound ratio increases with the increasing effective vertical stress before unloading. A power function was proposed to describe the relationship between one-dimensional unloading modulus and unloading ratio with two parameters named initial one-dimensional unloading modulus and decrease rate of the one-dimensional unloading modulus. The initial unloading modulus increased linearly with the increase of effective vertical stress before unloading, and a power function could be used to describe the relationship between the decrease rate and effective vertical stress. Formulas were also proposed to predict the initial unloading modulus and decrease rate of the one-dimensional unloading modulus based on piezocone test measurements.

Forced vibration assessment of moderately thick carbon nanotube-reinforced composite plates

Carbon nanotubes, distributed in composite sheets with various arrangements, can lead to the development of materials with functionally graded properties. In the present study, the method of spectral components was used to investigate the free vibration frequencies and dynamic responses of single-layer sheets reinforced with carbon nanotubes. The spectral component method offers significant advantages for high-frequency dynamic problems, as it requires fewer fine elements to solve boundary conditions. Based on the first-order shear theory, the governing equations of sheet vibration are derived. The discrete Fourier transform is applied to convert the differential equations from the time domain to the frequency domain. Using dynamic shape functions obtained from the exact solutions, the stiffness matrix of the spectral element is constructed. Dynamic frequency responses are then derived, and time-domain responses are obtained using the inverse Fourier transform. The study extracted the exact natural frequencies of functionally graded sheets and verified them with results from the literature, showing high accuracy with a minimal number of elements. The spectral finite element method of fundamental natural frequencies for different ratios of modulus of elasticity and width-to-thickness ratios obtained were investigated and compared with the results of research. The forced vibration was addressed, demonstrating that the method efficiently captures dynamic responses under different carbon nanotube distributions, with spectral displacements verified through numerical comparison. These findings demonstrate the capability and efficiency of the spectral finite element method for analyzing carbon nanotube-reinforced composite plates.

Effects of Interfacial Imperfections on Nanoscale Adhesive Contact for Layered Medium

Depending on processing technologies and working conditions, imperfect bonding at the layer-substrate interface may occur, resulting in diverse mechanical responses compared to a perfectly bonded layer-substrate system. This study focuses on an imperfect interface under force-like conditions and incorporates it into a nanoscale adhesive contact model to explore the influences of interfacial imperfection on the adhesive contact behaviors of the layered medium. The adhesive contact model is formulated based on the Lennard-Jones (LJ) potential and the Hammaker summation method. The adhesive contact problem is addressed by solving the nonlinear surface gap equations between the contact bodies. The deformation within the gap equations, accounting for the influence of imperfections, is computed using the fast Fourier transform (FFT) algorithm. This study explores the influence of three stress jumping coefficients t1,t2 and t3, which quantitatively characterize the interfacial imperfection, and their coeffects with material parameters, including imperfection depth (layer thickness), adhesion work, and elastic modulus, on the adhesive contact behaviors of the layered medium. The findings underscore that the normal stress jumping coefficient t3 exerts the most significant impact, wherein a higher t3 value corresponds to a smaller adhesive force and a larger absolute contact approach, while tangential stress jumping coefficients t1 and t2 exhibit negligible influence. Decreasing t3 values correspond to varying interaction force-contact approach responses and contribute to alleviating contact stability in cases with large Tabor parameters. Interfacial imperfections manifest their influence by modifying the pressure-displacement response, with noticeable effects only within a specific imperfection depth range h¯<40. While the introduction of interfacial imperfections does not alter the fundamental impact of material parameters—such as imperfection depth, adhesion work ratios, and elastic modulus ratios—on adhesive force and contact approach, it does modify the magnitude of these effects. Furthermore, imperfections alter stress distribution, increasing maximal von Mises stress and causing stress concentration within the layer and at the interface. In summary, force-like imperfections reduce surface displacement, resulting in a smaller region of positive pressure and ultimately contributing to a larger adhesive force. However, this effect is accompanied by increased stress concentration at the imperfect interface. This heightened stress level poses a potential risk to the system's reliability.

Thermal Expansion of Römerite under Low-Temperature Conditions Revision 2

Abstract Römerite, a triclinic hydrous sulfate in the P1 space group with the chemical formula Fe2+Fe3+2 (SO4)4 × 14(H2O), is of potential interest in studies of planetary environments, with particular relevance to Mars and the icy Jovian satellites. Past work has indicated the presence of hydrous sulfates on said bodies and the mixed-valence iron in the structure of römerite makes the mineral a worthwhile end-member composition in thermodynamic models. Such models should be constrained with measurements at the low temperatures relevant to the planetary environments in question. We characterized single crystals of römerite with time-domain Mössbauer spectroscopy, Raman spectroscopy, and X-ray diffraction methods. Through our X-ray diffraction experiment, we refined the unit–cell parameters of the crystal between 100 and 300 K. The resulting temperature-variant lattice parameters and volumes are reported and are fit by physical and empirical models of the thermal expansion coefficient. The physical model considered, a Debye model of thermal expansion, provides estimates of additional thermodynamic parameters: the ratio of the bulk modulus at 0 K and 1 bar to the thermodynamic Grüneisen parameter (K0,0K/γth), the volume at 0 K and 1 bar (V0,0K), and the Debye temperature (θD).

Evaluation of elastic constants of M23C6 and M7C3 embedded in Fe-Cr-C alloys using in-situ XRD tensile test and self-consistent model

This paper investigates the elastic properties of the model Fe-Cr-C alloys, specifically focusing on M23C6 and M7C3. The study uses in-situ synchrotron X-ray data during tensile deformation to determine the individual elastic characteristics of the matrix and iron/chromium carbides. The experimental results obtained from in-situ X-ray diffraction (XRD) are compared to the elastic constants of carbides that were reported in previous studies and derived using density function theory (DFT). The appropriate elastic constants for M23C6 and M7C3 were selected based on the self-consistent code executing with reported elastic constants. The directional elastic modulus and Poisson's ratio of iron/chromium carbides are calculated, and the anisotropy of the elastic constants is evaluated using the XRD lattice deformations under loading. The elastic modulus of carbide varies with the volume fraction of carbide in the effective medium. The study finds that the hexagonal structure is more probable than orthorhombic structure for M7C3 due to well-matched estimations of the directional elastic modulus and Poisson's ratio obtained from in-situ XRD data and the self-consistent calculations. In-situ XRD analysis of elastic behavior of each diffraction can be used to demonstrate the elastic constants of carbides and shows potential for obtaining precise elastic constants by integrating with self-consistent modeling and DFT.

Model Test on Acoustic Emission Monitoring of Loess Slope Failure.

The three stages of loess collapse are characterized by notable concealment and sudden onset due to the sudden nature of loess collapse and the prolonged duration of the peristaltic deformation stage. Traditional displacement monitoring methods struggle to detect early signals of instability and failure, leading to poor timeliness in disaster warnings. This project begins by examining non-force field information related to the loess collapse process. It focuses on acoustic emission monitoring and employs model tests to identify effective waveguide rods for monitoring loess collapse. Additionally, the project investigates the evolution anomalies of acoustic emission parameters before and after loess collapse failure, aiming to establish early warning criteria for loess collapse based on acoustic emission. This work provides a theoretical basis for monitoring and early warning of loess collapses. This study evaluates five parameters of the active waveguide system: sensor installation method, filling material, waveguide rod wall thickness, outer wrapping material, and outer wrapping wall thickness. The densities of the filler materials were tested using the optimal parameters derived from the tests to identify the best configurations for active acoustic emission (AE) waveguide systems suitable for monitoring loess collapse. Subsequently, a one-sided connected loess collapse model was employed for indoor tests, integrating real-time AE monitoring with the active waveguide method. This model facilitates the exploration of AE response characteristics during loess collapse and the analysis of destructive forms of loess collapse and time-sequence evolution of AE ringing counts throughout the deformation and destruction process. Results indicate that using filler materials with high elasticity modulus, high compactness, and low Poisson's ratio, along with thin outer wrapping and waveguide rod walls, leads to strong AE signals. As deformation damage of loess collapse intensifies, the number of AE ringing counts notably increases. A rapid rise in cumulative ringing counts can indicate a "sudden increase", or the b-value may stabilize, providing precursor information for loess collapse.

Mechanisms of hardness enhancement in CrB2 thin films with varying VB2 concentrations

Transition metal borides are well-known for their high hardness, excellent wear resistance, chemical inertness, and electrical conductivity, making them promising for a wide range of applications. Understanding the interconnections between material structure, composition, and mechanical properties is essential for designing and synthesizing effective coatings. This study systematically investigates the structural and mechanical properties of CrB₂ thin films with varying concentrations of VB₂ (0–10 wt%), focusing on structure, hardness, elastic behavior and deformation characteristics mechanisms through atomic force microscopy and nanoindentation measurements. The results show that increasing VB₂ content leads to the formation of island cluster structures, which significantly strengthens atomic bonds and, in turn, enhances the hardness of the thin films. As particle size decreases, the higher proportion of surface atoms and increased surface energy have a more pronounced effect on the mechanical properties. In particular, the addition of VB₂ up to 10 wt% in CrB₂ thin films results in a marked improvement in superhard properties. 26 % increase in hardness value is also influenced directly by the changes in Young's modulus and Poisson's ratio that depend on the VB₂ concentration.

Structural, elastic and gamma-ray attenuation properties of potassium borate glasses doped with BaO, Bi2O3, or Pb3O4: A comparative assessment

This study investigates the effect of substituting boron oxide (B2O3) with heavy metal oxides (HEMOs) on the structural, mechanical, and gamma-ray shielding properties of potassium borate (KB) glass systems. The glass compositions analyzed include 80B2O3–20K2O and 65B2O3–20K2O-15HEMO (where, HEMO = BaO, Bi2O3, or Pb3O4). All samples were prepared using the melt-quenching method, and their amorphous nature was confirmed through X-ray diffraction (XRD). Fourier-transform infrared spectroscopy (FTIR) had revealed BO3, BO4, and BiO6 groups beside the B–O–B linkages. The density increased with the addition of HEMOs, following the order: Pb3O4 (KB4) > Bi2O3 (KB3) > BaO (KB2) > and pure KB (KB1). This trend was also observed in the molar volume (Vₘ) and oxygen molar volume (Vₒ), while the oxygen packing density (Pρ) decreased. Mechanical properties assessed using the Makishima-Mackenzie model indicated that KB3 exhibited the highest elastic modulus (Yₘ) and Poisson's ratio (μ). The microhardness (Hₘ) followed the sequence KB2 > KB3 > KB4 > KB1, attributed to the higher bonding energy in KB2. Gamma-ray shielding parameters, including mass attenuation coefficients (MAC), were calculated using Phy-X and XCOM software for photon energies between 0.2835 MeV and 1.333 MeV. KB4 (Pb3O4) showed superior shielding performance with the highest linear attenuation coefficient (LAC) and the lowest half-value layer (HVL) and mean free path (MFP). Despite KB4's high density, KB3 (Bi2O3) is suggested as a more suitable candidate for radiation shielding applications due to its balanced combination of mechanical strength and γ-ray attenuation efficiency.

A Modified Reentrant Metamaterial with Equal and Enhanced Orthogonal Elastic Properties

Herein, an improved mechanical metamaterial is proposed, which is derived from the decomposition, rotation, and reassembly of reentrant structures. The structure is parametric, allowing for rapid redesign. The study focuses on the variations in equivalent stiffness and Poisson's ratio of the structure within the linear elastic range when internal rib angle θ changes. First, based on homogenization simulation analyses, it has been verified that this design achieves the tailorable equivalent elastic modulus and Poisson's ratio over a wide range, meanwhile, maintaining equal elastic properties in the orthogonal direction at all times. Second, to reduce future repetitive experiments, an interpolation model is established to expand the design domain. The fitting formula indicates that by modifying θ and relative wall thickness t/L0, the elastic performance of the structures can be tailored. Additionally, the impact of boundary conditions is discussed to minimize experimental costs. Finally, the accuracy of the simulations is validated through uniaxial compression tests.

Improving energy absorption of rotating triangle auxetic metamaterials through multistage perforations

This article described the new rotating triangle auxetic metamaterials with multistage perforations which can achieve both lightweight design and higher energy absorption. Primary star shaped perforations can induce rotating triangle deformation behavior in the structure, and secondary circular or triangular perforations can enable lightweight design of metamaterials. Two kinds of lightweight structures, the rotating triangle-circle auxetic (RTCA) structure and the rotating triangle-truss auxetic (RTTA) structure, were established based on the above method. Experimental and numerical results showed that the elastic modulus, strength and Poisson's ratio of the RTCA and RTTA structures did not decrease compared to the secondary unperforated structures, but the specific energy absorption was greatly improved. There were the energy absorption thresholds for both RTCA and RTTA structures, and RTCA structure had better specific energy absorption characteristics at the same densities. Furthermore, the influence of star shaped perforation geometrical parameters on the mechanical properties of the RTCA structure was revealed. Considering the stability and energy absorption of metamaterials, the optimal geometric parameters for the RTCA structure were determined. The designed RTCA structure was approximately 28.2 % lighter and 103.2 % higher in the energy absorption capacity compared to the secondary unperforated structures. The lightweight design strategy proposed in this paper can be applied to aerospace, automotive manufacturing, and other engineering fields to enhance the performance of metamaterials and reduce structural loads.

Analytical Solutions for Consolidation of Soft Ground With Impervious Columns Considering Non‐Darcian Flow

ABSTRACTCohesive material columns have been extensively used in foundation improvement projects to enhance the bearing capacity of composite foundations and mitigate post‐construction settlement. However, the low permeability of cohesive material columns restricts the dissipation of pore water primarily through the top surface of the foundation, potentially resulting in longer drainage paths compared to foundations treated with granular material columns or vertical drains. Moreover, the impact of non‐Darcian flow within soils on consolidation behavior becomes increasingly pronounced as the drainage path increases. Consequently, a novel analytical model for the consolidation of impervious column‐assisted foundations is established, which can incorporate the seepage model accounting for the initial hydraulic gradient. The accuracy and reasonableness of the obtained solution are then validated by conducting a comparative analysis with existing models and through a detailed case study. Furthermore, a parametric analysis is conducted to delve into the influence of several crucial factors on the consolidation performance. The findings demonstrate that non‐Darcian flow has a greater influence on composite foundations compared to natural foundations. Additionally, the threshold value of the well‐diameter ratio decreases with the increase in the initial hydraulic gradient. Finally, the final seepage front remains at a shallower position when the column–soil modulus ratio becomes larger, and the influence of non‐Darcian flow on the consolidation rate becomes more pronounced.

Optimal design of vibration resistance of fiber-reinforced composite sandwich plates embedded in a viscoelastic square honeycomb core

This work focuses on investigating the optimal design of composite sandwich plates (FCSPs) with a viscoelastic square honeycomb core (VSHC). Firstly, using the cross-fill theory, the complex modulus technique, the first-order shear deformation theory, the minimum strain energy principle, and the Newmark-β method, a theoretical model of the VSHC-FCSPs under half-sine pulse excitation is formulated to calculate the inherent frequencies, the peak and vibration decay time of the transient response in time domain. The peak and vibration decay time are taken as the indexes of the anti-vibration performance. Considering an index of structural stiffness performance, the average value of the inherent frequencies is adopted to calculate the overall stiffness. After a set of literature validations and optimization validations, the multi-objective genetic algorithm is employed to study the optimization issue of VSHC-FCSPs. The optimization objectives are to minimize the three design variables of the transient response peak, vibration decay time, and reciprocal of overall stiffness. Then, the fiber laying angle of each layer, the core thickness ratio and the modulus ratio are assumed as optimization variables. Finally, the results with good vibration resistance and structural stiffness in the Pareto front are chosen as references, and these corresponding variations of the design variables and optimization objectives are obtained. The optimization results have revealed that the optimization variables corresponding to the intermediate points should be selected as references to improve the anti-vibration capacity and ensure the structural stiffness performance.

Ultrahigh carrier mobility and anisotropy of the layered semiconductor ATiN2 (A = Ca, Sr and Ba)

Semiconductors with a suitable band gap and high carrier mobility are highly desirable in the electronics, optoelectronic and photovoltaic applications. The mechanical, electronic, optical and transport properties of the layered nitrides ATiN2 (A = Ca, Sr, and Ba) have been systematically studied by theoretical calculations. These nitrides show good ductility with moderate moduli, larger Poisson's ratio than 0.26 and Pugh's modulus ratio exceeding 1.75. CaTiN2 and SrTiN2 are direct bandgap semiconductors, while BaTiN2 is an indirect bandgap semiconductor, showing suitable band gaps (1.54–1.78 eV) and band edge positions for optoelectronic and photocatalytic water-splitting applications. More intriguingly, they possess superhigh carrier mobility with remarkable anisotropy. Particularly, the in-plane electron mobility reaches an ultrahigh order of 104 cm2V−1s−1, whereas those along the out-of-plane direction are almost zero. In addition, the hole mobilities are also very large along the in-plane direction and the anisotropic ratios are as high as about 30 for all these nitrides. Furthermore, these ATiN2 nitrides exhibit high optical absorption coefficients (∼105 cm−1) and lower exciton binding energies. Due to the suitable band gaps and band alignments, ultrahigh carrier mobility and huge anisotropy, excellent visible light absorption performance, the ATiN2 nitrides will be promising candidate semiconductors in electronics, optoelectronic, photovoltaic and photocatalytic applications.

Predicting the properties of metamaterials consisting of curved-wall triangles using ensemble neural networks with interpretability

Machine learning has emerged as a promising tool for predicting the properties of metamaterials, owing to its substantially faster prediction speed compared to conventional methods. However, the lack of interpretability of black-box machine learning models has impeded their adoption in this field. In this work, we develop an ensemble of neural networks (NNE) for predicting the mechanical properties of metamaterials consisting of curved-wall triangles. Our method achieves high prediction accuracy for the effective Young's modulus and Poisson's ratio for most samples. The average relative errors of the NNE are less than 5% for predicting the dimensionless Young's modulus and less than 10% for predicting Poisson's ratios. Additionally, our method is orders of magnitude faster than finite element simulations. More importantly, by explaining the predictions of NNE using SHapley Additive exPlanations (SHAP), we are able to quantify the relationships between geometric features and metamaterial properties. This reveals insights into parameter couplings and nonlinear effects. New physical insights can thus be obtained and new design rules discovered through this machine learning interpretability approach. Overall, our interpretable machine learning model can accelerate the design and discovery of metamaterials while providing physical insights into the inner workings of the models.

Effect of order-disorder transition and lattice distortion on the mechanical properties of W-X (X = V, Nb, Ta) solid solutions

With the prosperity of high entropy alloys, short-range ordering is getting more and more attentions and regarded as the deciding role in the hardening or softening of solid solutions. In this work, the phase stability and mechanical properties of short-range ordered and disordered body-centered cubic (BCC) structures of W-X solid solutions (X = V, Nb, and Ta) are systematically investigated through a combination of first-principles calculation, cluster expansion and quasi-harmonic Debye formula. Based on the calculated heat of formation (ΔHf), W-X solid solutions show a strong short-range ordering tendency, as those ordered structures have a lower ΔHf than the disordered ones. Generally, short-range ordering results in the decrease of the shear modulus to bulk modulus ratio (G/B) and hardness for W-V and W-Ta systems, while an increase for W-Nb system, manifesting solid-solution softening and hardening effect, respectively. The short-ranged ordered C11b W2X phase exhibits a singularity in mechanical properties characterized by a higher G/B than solid solution phases compared to other ordered phases. The lattice distortion breaks the symmetric W-W bonds and leads to partial covalency in the W2X phases. Besides the increased brittleness, this distortion also causes the increase of ideal strength and the reduction of maximum tensile elongation of W2X. The effect of short-range ordering and lattice distortion on the hardening or softening of the W-X systems disappears after the order-disorder transition. The W-V and W-Ta phases have higher order-disorder transition temperature than W-Nb phase. Nevertheless, the transition temperature is relatively low in comparison to their melting points, signifying the important role in controlling the solute concentration at lower temperature.

Wrinkling of differentially growing bilayers with similar film and substrate moduli

Growth-induced surface wrinkling in constrained bilayers comprising a thin film attached to a thick substrate is a canonical model for understanding pattern formation in many biological systems. While the bilayer model has received much prior attention, the nonlinear behaviour for arrangements with similar film and substrate properties, or substrate growth that outpaces film growth, remains poorly understood. This paper therefore focuses on these cases in which the substrate’s elasticity dominates surface wrinkling. By combining analytical modelling and finite element simulations incorporating advanced path-following techniques, we characterise critical wrinkling states and explore the initial and advanced post-buckling behaviour for a wide range of film-to-substrate modulus and growth rate ratios. It is shown that the classical leading-order asymptotic expression for the critical strain is not of sufficient accuracy for film-to-substrate modulus ratios below 50, and higher order correction terms are presented. Leveraging a weakly nonlinear analytical model, we introduce a phase diagram categorising stable and unstable post-buckling regimes. Advanced path-following simulations are employed to unveil the evolution of wrinkling patterns, from initial sinusoidal instabilities to complex formations involving period doubling, quadrupling, and eventual surface creasing. These comprehensive phase diagrams, parameterised by film-to-substrate modulus and growth rate ratios, provide new insights into the rich dynamics of surface wrinkling. Finally, we demonstrate the existence of multi-stability in the advanced post-buckling regimes for bilayers experiencing substrate-dominated growth. This work contributes to the understanding of the mechanics underlying pattern formation in growing bilayers over the entire parameter regime, with potential implications for explaining biological morphogenesis and informing the development of novel diagnostic tools and artificial flexible electronic skins.

Bed strength in sheared beds of mono- and bi-disperse particles: Dependence on geometrical and mechanical properties of constituent particles

Temporary plugging zones are low-permeability fracture-scale plugs ‘assembled’ in situ by injecting polymer particles into petroleum reservoirs. We applied the rolling resistance linear model to simulate the shear strength of a rectangular packed bed, our model for a temporary plugging zone, comprising either uniform-sized particles or a binary mixture of larger bridging particles and smaller filling particles. Simulation results show that the strength of uniform beds increases with the size, the aspect ratio, the friction coefficient, and the Young’s modulus of the particles. The strength of binary packed beds first increased and then decreased as the fractional volume of the domain occupied by filling particles increased. Maximum strength was achieved when bridging particles have uniform Young’s modulus and aspect ratio but a range of friction coefficients, and their friction coefficient, Young’s modulus and aspect ratio are 21%, 17% and 18% larger than those of filling particles.