Planar Structure Research Articles

Homogenization of non-rigid origami metamaterials as Kirchhoff–Love plates

Origami metamaterials have gained considerable attention for their ability to control mechanical properties through folding. Consequently, there is a need to develop systematic methods for determining their effective elastic properties. This study presents an energy-based homogenization framework for non-rigid origami metamaterials, effectively linking their mechanical treatment with that of traditional materials. To account for the unique mechanics of origami systems, our framework incorporates out-of-plane curvature fields alongside the usual in-plane strain fields used for homogenizing planar lattice structures. This approach leads to a couple-stress continuum, resembling a Kirchhoff–Love plate model, to represent the homogeneous response of these lattices. We use the bar-and-hinge method to assess lattice stiffness, and validate our framework through analytical results and numerical simulations of finite lattices. Initially, we apply the framework to homogenize the well-known Miura-ori pattern. The results demonstrate the framework’s ability to capture the unconventional relationship between stretching and bending Poisson’s ratios in origami metamaterials. Subsequently, we extend the framework to origami lattices lacking centrosymmetry, revealing two distinct neutral surfaces corresponding to bending along two lattice directions, unlike in the Miura-ori pattern. Our framework enables the inverse design of metamaterials that can mimic the unique mechanics of origami tessellations using techniques like topology optimization.

Experimental and numerical investigation of the fracture behavior in granite specimens with two co-planar side flaws under biaxial loading

It is well known that the structural plane plays a decisive role in the mechanical properties of rock mass. To better understand the cracking mechanism and stress characteristics of co-planar intermittent double-flawed granite specimens with various dip angles (Abbreviated as flawed specimens), two co-planar flaws were prefabricated on both sides of the granite, and biaxial compression tests were conducted. The failure characteristics and local microstrain were recorded by the camera and strain acquisition instrument. The evolution law of mechanical parameters of flawed specimens was analyzed. Simultaneously, a two-dimensional particle flow code (PFC2D) was used to establish a biaxial compression model of flawed specimens. The crack initiation and propagation of the specimens were explained by the crack hot spot, the evolution law of crack, and the evolution law of the number of microcracks. It is found that (a) as flaw dip angle (α) increases, peak strength and elastic modulus initially decrease and then increase, with reductions ranging from 17.6% to 46.1% and 15.6% to 48.2%, respectively. (b) Increasing lateral stress (σ2) triggers a shift in failure mode from a tensile-shear mixed failure to a shear failure. The cohesion (c) and friction angle (φ) of flawed specimens were notably smaller compared to those of intact specimens, with reductions correlating with the α. (c) Flawed specimens exhibit pronounced contact force concentration and stress concentration at the flaw tip. The analysis of the microstrain confirms stress concentration at the flaw tip, leading to failure. However, various σ2 induces the differences in the magnitude and extent of tip stress.

A Skin-Inspired High-Performance Tactile Sensor for Accurate Recognition of Object Softness.

High-performance tactile sensors with skin-sensing properties are crucial for intelligent perception in next-generation smart devices. However, previous studies have mainly focused on the sensitivity and response range of tactile sensation while neglecting the ability to recognize object softness. Therefore, achieving a precise perception of the softness remains a challenge. Here, we report an integrated tactile sensor consisting of a central hole gradient structure pressure sensor and a planar structure strain sensor. The recognition of softness and tactile perception is achieved through the synergistic effect of pressure sensors that sense the applied pressure and strain sensors that recognize the strain of the target object. The results indicate that the softness evaluation parameter (SC) of the integrated structural tactile sensor increases from 0.14 to 0.47 along with Young's modulus of the object decreasing from 2.74 to 0.45 MPa, demonstrating accurate softness recognition. It also exhibits a high sensitivity of 10.55 kPa-1 and an ultrawide linear range of 0-1000 kPa, showing an excellent tactile sensing capability. Further, an intelligent robotic hand system based on integrated structural tactile sensors was developed, which can identify the softness of soft foam and glass and grasp them accurately, indicating human skin-like sensing and grasping capabilities.

Analysis of physical characteristics and mechanism of retarder to stratified cemented backfill

The stratified structural plane caused by stratified backfill will reduce the strength of backfill, and the introduction of retarder will make up for the defect. Three retarders, sodium tripoly-phosphate, citric acid and sucrose, were introduced. After determining the optimal dosage of retarder, they were added into the filling slurry with a ratio of lime to sand of 1:6 and a mass concentration of 75%. Based on the hydration reaction mechanism and damage mechanics theory of cement, the setting time test and uniaxial compressive strength test were carried out. With the help of scanning electron microscopy and X-ray diffraction, the influence mechanism of retarder on the physical characteristics of stratified cemented filling was investigated.The main research contents and achievements are as follows:. The results showed that the three retarding agents can delay the setting time of the cement filling slurry, and the retarding effect is sucrose > citric acid > sodium tripolyphosphate. The addition of retarder can improve the uniaxial compressive strength and integrity of stratified consolidated backfill, and the best filling interval time (FIT) is 12 h. Appropriate addition of retarder will increase the amount of cement hydration products, make the structure of hydration products more dense, reduce the formation of stratified structural plane, and help to improve the strength of stratified cemented backfill.

BaCu, a Two-Dimensional Electride with Cu Anions.

The electron-rich characteristic and low work function endow electrides with excellent performance in (opto)electronics and catalytic applications; these two features are closely related to the structural topology, constituents, and valence electron concentration of electrides. However, the synthesized electrides, especially two-dimensional (2D) electrides, are limited to specific structural prototypes and anionic p-block elements. Here we synthesize and identify a distinct 2D electride of BaCu with delocalized anionic electrons confined to the interlayer spaces of the BaCu framework. The bonding between Cu and Ba atoms exhibits ionic characteristics, and the adjacent Cu anions form a planar honeycomb structure with metallic Cu-Cu bonding. The negatively charged Cu ions are revealed by the theoretical calculations and experimental X-ray absorption near-edge structure. Physical property measurements reveal that BaCu electride has a high electronic conductivity (ρ = 3.20 μΩ cm) and a low work function (2.5 eV), attributed to the metallic Cu-Cu bonding and delocalized anionic electrons. In contrast to typical ionic 2D electrides with p-block anions, density functional theory calculations find that the orbital hybridization between the delocalized anionic electrons and BaCu framework leads to unique isotropic physical properties, such as mechanical properties, and work function. The freestanding BaCu monolayer with half-metal conductivity exhibits low exfoliation energy (0.84 J/m2) and high mechanical/thermal stability, suggesting the potential to achieve low-dimensional BaCu from the bulk. Our results expand the space for the structure and attributes of 2D electrides, facilitating the discovery and potential application of novel 2D electrides with transition metal anions.

Microwave metamaterial microstrip line with enhanced refractive index and its application to compact a Wilkinson power divider

A new microwave metamaterial microstrip line (meta-MSL) is studied by integrating planar mushroom metamaterial structures into a conventional MSL. The meta-MSL is featured with an enhanced effective refractive index than the conventional, extracted from numerical demonstrations using the S-parameter method. The extraordinarily increased refractive index is found to be associated with weak dispersion and low dissipation loss, making the meta-MSL particularly beneficial to compact a microwave Wilkinson power divider (WPD). One metamaterial WPD (meta-WPD) is built using new meta-MSLs. Full-wave numerical calculations reveal that the new meta-WPD has low insertion losses, low reflections, and high isolations between the output ports, working as a good substitute for the conventional WPD. However, the new meta-WPD is exceptional in its small size, which is particularly useful in mobile and wireless applications where compact microwave components are in critical demand.

Analysis of local strain fields around individual threading dislocations in GaN substrates by nanobeam x-ray diffraction

Position-dependent three-dimensional reciprocal space mapping (RSM) by nanobeam x-ray diffraction (nanoXRD) was performed to reveal the strain fields produced around individual threading dislocations (TDs) in GaN substrates. The distribution and Burgers vector of TDs for the nanoXRD measurements were confirmed by prerequisite analysis of multi-photon excited photoluminescence and etch pit methods. The present results demonstrated that the nanoXRD can identify change in the lattice plane structure for all types of TDs, i.e., edge-, screw-, and mixed TDs with the Burgers vector of b = 1a, 1c and 1m + 1c. Strain tensor components related to edge and/or screw components of the TDs analyzed from the three-dimensional RSM data showed a nearly symmetrical strained region centered on the TD positions, which were in good agreements with simulation results based on the isotropic elastic theory using a particular Burgers vector. The present method is beneficial in that it allows non-destructive analysis of screw components of TDs that tend to contribute to leakage characteristics and are not routinely accessible by conventional structural analysis. These results indicate that nanoXRD could be a powerful way to reveal three-dimensional strain fields associated with arbitrary types of TDs in semiconductor materials, such as GaN and SiC.

New polyketides and cytotoxic alkaloids from the mangrove endophytic fungus Talaromyces sp. SAF14

Investigation of secondary metabolites from the mangrove endophytic fungus Talaromyces sp. SAF14 led to the isolation of two new polyketides, methyl (R)-3-(6,8-dihydroxy-7-methoxy-1-oxoisochroman-3-yl)propanoate (1), (R)-3-(5,8- dihydroxy-1-oxoisochroman-3-yl)propanoic acid (2), together with four known alkaloids (3–6). The planar structures of new compounds were elucidated by comprehensive analysis of HR-ESI-MS and NMR data. The absolute configurations were determined by comparison of the calculated ECD spectrum with the measured one. All the isolated compounds were tested for cytotoxic activities against three human cancer cell lines. The known beauvericin (3) exhibited strong cytotoxic activity against A549, MCF-7, and KB cell lines with IC50 values of 5.36 ± 2.49, 1.96 ± 1.09 and 4.46 ± 0.68 μM, respectively.

Controlling structural, electronic and optical properties of cubic FASnI3 perovskites using biaxial strains in the presence of spin orbit coupling: A DFT analysis

There is a significant research focus on the utilization of organic-inorganic hybrid perovskite materials in the field of photovoltaics. The remarkable electronic and optical characteristics of organic-inorganic hybrid perovskites are prevalent in solar applications. In this study, the first-principles density functional theory (DFT) was used to investigate how strains affect the structural, electronic, and optical properties of the formamidinium tin tri-iodide (hereafter FASnI3) perovskite structure. The band structure analysis revealed that FASnI3 possesses semiconductor properties. A direct bandgap of 0.96 eV was found at the R-point for unstrained planar FASnI3 structure. The bandgap was reduced when compressive strains were applied. In contrast, the bandgap attained a higher value due to the increased tensile strains. Moreover, the optical properties, such as absorption coefficient, dielectric function and electron loss function, showed that FASnI3 structures have good photo-absorption ability. The dielectric constant exhibited a redshift in its peaks as the compressive strains were increased. However, the dielectric peaks exhibited a blueshift when subjected to the tensile strains. Additionally, for a deeper understanding of the band structure, the effect of spin-orbit coupling (SOC) was considered. The band gap of the FASnI3 perovskite structure was 0.75 eV when the SOC effect was considered. The strain is a crucial factor to consider for optimizing the performance of FASnI3 perovskite structure for their applications in optoelectronic devices.

Tetrathiafulvalene Carboxylate-Based Anode Material for High-Performance Sodium-Ion Batteries.

Organic electrode materials are promising to be applied in sodium ion batteries (SIBs) due to their low cost and easily modified molecular structures. Nevertheless, low conductivity and high solubility in electrolytes still limit the development of organic electrodes. In this work, a carboxylate small molecule (BDTTS) based on tetrathiafulvalene is developed as anode material for SIBs. BDTTS has a large rigid π-conjugated planar structure, which may reduce solubility in the electrolyte, meanwhile facilitating charge transporting. Experimental results and theoretical calculations both support that apart from the four carbonyl groups, the sulfur atoms on tetrathiafulvalene also provide additional active sites during the discharge/charge process. Therefore, the additional active sites can well compensate for the capacity loss caused by the large molecular weight. The as-synthesized BDTTS electrode renders an excellent capacity of 230 mAh g-1 at a current density of 50 mA g-1 and an excellent long-life performance of 128 mAh g-1 at 2 C after 500 cycles. This work enriches the study on organic electrodes for high-performance SIBs and paves the way for further development and utilization of organic electrodes.

Thermal radiation forces on planar structures with asymmetric optical response

Abstract Light carries momentum and, upon interaction with material structures, can exert forces on them. Here, we show that a planar structure with asymmetric optical response is spontaneously accelerated when placed in an environment at a different temperature. This phenomenon originates from the imbalance in the exchange rates of photons between both sides of the structure and the environment. Using a simple theoretical model, we calculate the force acting on the planar structure and its terminal velocity in vacuum, and analyze their dependence on the initial temperature and the geometrical properties of the system for different realistic materials. Our results unravel an alternative approach to manipulating objects in the nano and microscale that does not require an external source of radiation.

Structure-optoelectronic properties correlation of fluorene-based blue fluorescence emitters with different pendant moieties

Fluorene is a blue luminous moiety attracting wide attention due to its all kinds of high technology applications, and the rigid biphenyl planar structure of fluorene makes it prone to crystalize and form intermolecular aggregation, which means that emitting colors and carrier mobilities of fluorene-based fluorescence emitters are highly adjustable by the modification of 9,9-position of fluorene with different pendant moieties. In this regard, fluorene (F) is used as a model blue emitter, and different pendant groups of n-butyl, p-hexyloxy phenyl and 2,4,6-triphenyl-1,3,5-triazine are introduced into the 9-position of fluorene to produce four topology-varied organic light-emitting emitters, namely 9,9-dibutyl-fluorene (DBF), 9,9-bis-(4-butoxy-phenyl)-fluorene (BOPF), 2-{4-[9-(4-hexyloxy-phenyl)-fluoren-9-yl]-phenyl}-4,6-diphenyl- (Chan et al., 2017; Wex and Kaafarani, 2017; Liang et al., 2019) [1,3,5]triazine (FTRZ) and 2,4,6-tris-{4-[9-(4-hexyloxy-phenyl) -fluoren-9-yl]-phenyl}- (Chan et al., 2017; Wex and Kaafarani, 2017; Liang et al., 2019) [1,3,5]triazine (pTFTRZ). The general differences in thermal stability, photoluminescence quantum efficiency, emission wavelength, electrochemical energy levels, crystal structure, carrier mobility and film morphology of the emitters are experimentally and theoretically studied to correlate their structures with optoelectronic properties. FTRZ and pTFTRZ solid powder show higher melting points of 186 °C and 122 °C. The highest occupied molecular orbit energy levels are −5.95 eV for F, −6.02 eV for DBF, −6.11 eV for BOPF and −6.23 eV for FTRZ, and the corresponding lowest unoccupied molecular orbits energy levels are −2.03 eV for F, −2.19 eV for DBF, −2.25 eV for BOPF and −2.55 eV for FTRZ. When compared with the other three emitters, due to the enhanced intramolecular charge transfer caused by the electron-deficient 2,4,6-triphenyl-1,3,5-triazine group, FTRZ showed significant redshifts of 75 nm in their emission spectrum of solution, and the photoluminescence quantum efficiencies of FTRZ and pTFTRZ solid powder were also decreased to less than 1%. The single crystal of F is an orthorhombic system while those of DBF, BOPF and FTRZ are all monoclinic system. The electron and hole mobilities of the thin solid films were decreased in the order of FTRZ, BOPF and pTFTRZ, and thin solid film of FTRZ showed the highest electron mobility of 10−4cm2/V • s at an electric field of 4 × 104 V/cm. The RMS values corresponding to root-mean-square averages of the height deviations of film measured by atomic force microscopy are 4.32 nm for BOPF, 1.11 nm for FTRZ, 11.8 nm for pTFTRZ. The FTRZ films exhibited smaller RMS and smooth surface morphology beneficial for the carrier mobility relative to those of BOPF and pTFTRZ. The pendant groups of n-butyl, p-hexyloxy phenyl and 2,4,6-triphenyl-1,3,5-triazine in the 9-position of fluorene adjust the general optoelectronic properties of the obtained emitters in a wide range.

Magneto-plasmonic “switch” device for magnetic field detection

Abstract This paper introduces a novel class of low-loss and cost-effective optical planar structures tailored for magnetic detection applications. These structures represent unconventional magneto-plasmonic devices specifically optimized for an ‘optical switch’ configuration. The structure consists of a 1D deep sinusoidal gold grating covered by a thin cobalt layer. In this unique arrangement, the excited plasmon induces a high-contrast switching phenomenon between the reflected free space intensity of specular (0th) and −1st diffracted orders, sensitive to any transverse magnetic fields applied to the cobalt layer. The use of these two distinct diffracted orders induces differential measurements, effectively mitigating common drift and perturbations. This innovative approach results in an enhanced detection sensitivity, showcasing the potential of these structures for advanced magnetic field sensing applications.

Mirror Plane Effect of Magnetoplumbite-Type Oxide Restraining Long-Chain Polysulfides Disproportionation for High Loading Lithium Sulfur Batteries.

A facile solid-state approach is employed to synthesize a novel magnetoplumbite-type oxide of NdMgAl11O19, which integrates spinel-stacking layers (MgAl2O4) with Nd-O6 mirror plane structures. The resulting NdMgAl11O19 exhibits remarkable catalytic activity and conversion efficiency during the sulfur reduction reaction (SRR) in lithium-sulfur batteries. By employing the 2D projection mapping technique of in situ confocal Raman spectroscopy and electrochemical technique, it is discovered that the exposed mirror plane structure of Nd-O6 can effectively suppress the undesiring disproportionation reaction (S8 2-→S6 2-+1/4 S8) of long-chain lithium polysulfides at the initial stages of sulfur reduction, thereby promoting the positive process of sulfur to lithium sulfide. This not only mitigates the issue of sulfur shuttle loss but also significantly improve the kinetics of the conversion process. Leveraging these advantages, the NdMgAl11O19/S cathode delivered an impressive initial capacity of up to 1398 mAh g-1 at an electrolyte/sulfur (E/S) ratio of 5.1µL mg-1 and a sulfur loading of 2.3mg cm-2. Even when the sulfur loading is increased to 10.02mg cm-2, the cathode retained a reversible areal capacity of 10.01 mAh cm-2 after 200 cycles. This mirror engineering strategy provides valuable and universal insights into enhancing the efficiency of cathodes in Li-S battery.

The Kavaratamides: Discovery of Linear Lipodepsipeptides from the Marine Cyanobacterium Moorena bouillonii Using a Comparative Chemogeographic Analysis.

Kavaratamide A (1), a new linear lipodepsipeptide possessing an unusual isopropyl-O-methylpyrrolinone moiety, was discovered from the tropical marine filamentous cyanobacterium Moorena bouillonii collected from Kavaratti, India. A comparative chemogeographic analysis of M. bouillonii collected from six different geographical regions led to the prioritized isolation of this metabolite from India as distinctive among our data sets. AI-based structure annotation tools, including SMART 2.1 and DeepSAT, accelerated the structure elucidation by providing useful structural clues, and the full planar structure was elucidated based on comprehensive HRMS, MS/MS fragmentation, and NMR data interpretation. Subsequently, the absolute configuration of 1 was determined using advanced Marfey's analysis, modified Mosher's ester derivatization, and chiral-phase HPLC. The structures of kavaratamides B (2) and C (3) are proposed based on a detailed analysis of their MS/MS fragmentations. The biological activity of kavaratamide A was also investigated and found to show moderate cytotoxicity to the D283-medullablastoma cell line.

Tailored Metal-Porphyrin Based Molecular Electrocatalysts for Enhanced Artificial Nitrogen Fixation to Green Ammonia.

Electrochemical nitrogen reduction (E-NRR) is one of the most promising approaches to generate green NH3. However, scarce ammonia yields and Faradaic efficiencies (FE) still limit their use on a large scale. Thus, efforts are focusing on different E-NRR catalyst structures and formulations. Among present strategies, molecular electrocatalysts such as metal-porphyrins emerge as an encouraging option due to their planar structures which favor the interaction involving the metal center, responsible for adsorption and activation of nitrogen. Nevertheless, the high hydrophobicity of porphyrins limits the aqueous electrolyte-catalyst interaction lowering yields. This work introduces a new class of metal-porphyrin based catalysts, bearing hydrophilic tris(ethyleneglycol) monomethyl ether chains (metal = Cu(II) and CoII)). Experimental results show that the presence of hydrophilic chains significantly increases ammonia yields and FE, supporting the relevance of fruitful catalyst-electrolyte interactions. This study also investigates the use of hydrophobic branched alkyl chains for comparison, resulting in similar performances with respect to the unsubstituted metal-porphyrin, taken as a reference, further confirming that the appropriate design of electrocatalysts carrying peripheral hydrophilic substituents is able to improve device performances in the generation of green ammonia.

Highly Planar Oligomeric Acceptor Enables Efficiency over 18% with Synergistically Enhanced VOC and Light Absorption

AbstractThe highly planar molecular structure is conducive to electron delocalization, thus facilitating efficient charge transport. A new thiophene terminal‐linked dimerized small‐molecular acceptor (DSMA), DTY‐2Cl, is synthesized, which achieves high planarity with a bithiophene linkage. The results of theoretical calculation and single crystal analysis of regional configuration demonstrate that the twisting angle between the bithiophene binding unit of DTY‐2Cl is almost zero. Devices based on DTY‐2Cl:D18 show an outstanding photoelectric performance with a power conversion efficiency (PCE) of 18.06% and excellent device stability. It is worth noting that DTY‐2Cl exhibits a redshifted absorption of up to 840 nm, which is rare among DSMAs, and DTY‐2Cl‐based devices obtain a VOC of 0.913 V, thus achieving a win‐win situation of redshifted absorption and high VOC. These results indicate that using bithiophene instead of biphenyl to optimize the planarity of oligomer acceptors is an effective strategy and provide a new idea for the improvement of subsequent materials.

Discrete Structural Design Synthesis: A Hierarchical-Inspired Deep Reinforcement Learning Approach Considering Topological and Parametric Actions

Abstract Structural design synthesis considering discrete elements can be formulated as a sequential decision process solved using deep reinforcement learning, as shown in prior work. By modeling structural design synthesis as a Markov decision process (MDP), the states correspond to specific structural designs, the discrete actions correspond to specific design alterations, and the rewards are related to the improvement in the altered design’s performance with respect to the design objective and specified constraints. Here, the MDP action definition is extended by integrating parametric design grammars that further enable the design agent to not only alter a given structural design’s topology, but also its element parameters. In considering topological and parametric actions, both the dimensionality of the state and action space and the diversity of the action types available to the agent in each state significantly increase, making the overall MDP learning task more challenging. Hence, this paper also addresses discrete design synthesis problems with large state and action spaces by significantly extending the network architecture. Specifically, a hierarchical-inspired deep neural network architecture is developed to allow the agent to learn the type of action, topological or parametric, to apply, thus reducing the complexity of possible action choices in a given state. This extended framework is applied to the design synthesis of planar structures considering both discrete elements and cross-sectional areas, and it is observed to adeptly learn policies that synthesize high performing design solutions.

A dual-directional metamaterial perfect absorber base on Al2O3 etched cross cavity in the visible and near-infrared ranges

Due to their unique properties, metamaterial perfect absorbers have been widely used in such fields as solar energy absorption, seawater desalination, sensing and so on. Recently, ultra-wide band perfect absorbers and multi-narrow band perfect absorbers are studied and reported. However, there are a few researches on metamaterial perfect absorbers with both narrow-band and wide-band absorption properties. In this paper, we propose a dual-directional perfect absorber which can switch between wide band absorption and narrow band absorption. It consists of a multi-layer planar structure topped by a pattern layer being arranged periodically. In the wavelength range of 600 nm to 2000 nm, when the incident light is vertically incident from the upper surface of the structure, there will be three resonance absorption peaks, locating at 863 nm, 875 nm and 1135 nm, and the absorption rates will reach to 99.51 %, 99.61 % and 99.58 %, respectively. The analysis demonstrates that the structure has good sensing performance in the environment of different refractive index. When the incident light is incident from the lower surface of the structure, the absorber exhibits broadband absorption with an average absorption rate of 98.04 % (600 ∼ 2000 nm). When the temperature reaches 1000 K, the total photothermal conversion efficiency of the absorber can still reach more than 92 %. In addition, our research shows that the structure is independent of polarization. All these features promise for our proposed dual-function perfect absorber to realize diverse applications in the fields of sensing, detection, sunlight acquisition, optical conversion devices, and so on.

True triaxial unloading test on the mechanical behaviors of sandstone: Effects of the intermediate principal stress and structural plane

A series of true triaxial unloading tests are conducted on sandstone specimens with a single structural plane to investigate their mechanical behaviors and failure characteristics under different in situ stress states. The experimental results indicate that the dip angle of structural plane (θ) and the intermediate principal stress (σ2) have an important influence on the peak strength, cracking mode, and rockburst severity. The peak strength exhibits a first increase and then decrease as a function of σ2 for a constant θ. However, when σ2 is constant, the maximum peak strength is obtained at θ of 90°, and the minimum peak strength is obtained at θ of 30° or 45°. For the case of an inclined structural plane, the crack type at the tips of structural plane transforms from a mix of wing and anti-wing cracks to wing cracks with an increase in σ2, while the crack type around the tips of structural plane is always anti-wing cracks for the vertical structural plane, accompanied by a series of tensile cracks besides. The specimens with structural plane do not undergo slabbing failure regardless of θ, and always exhibit composite tensile-shear failure whatever the σ2 value is. With an increase in σ2 and θ, the intensity of the rockburst is consistent with the tendency of the peak strength. By analyzing the relationship between the cohesion (c), internal friction angle (φ), and θ in sandstone specimens, we incorporate θ into the true triaxial unloading strength criterion, and propose a modified linear Mogi-Coulomb criterion. Moreover, the crack propagation mechanism at the tips of structural plane, and closure degree of the structural plane under true triaxial unloading conditions are also discussed and summarized. This study provides theoretical guidance for stability assessment of surrounding rocks containing geological structures in deep complex stress environments.