Principle Of Minimum Energy Research Articles

Deep learning of buckling instability in geometrically symmetry-breaking kirigami

Kirigami, subjected to escalating strain, frequently exhibits pronounced instability, coupled with remarkable flexibility and extraordinary extensibility. This behavior holds significant relevance for domains associated with malleable and reconfigurable surfaces, including stretchable electronics and modifiable functional devices. Nonetheless, conventional design methodologies, anchored in geometric symmetry and governed by minimum energy principles, tend to manifest buckling instabilities restricted to symmetric and anti-symmetric modes. To scrutinize the mechanisms of buckling behavior that disrupt geometric symmetry and comprehend the influence of geometry on programmability during reconfiguration, we propose an innovative strategy for kirigami’s design. This strategy capitalizes on advanced deep learning methodologies, employing convolutional neural networks (CNNs) for categorizing buckling modes and recurrent neural networks (RNNs) for prognosticating constitutive relationships. Our approach furnishes a programmable design solution adept at identifying optimal kirigami patterns, characterized by their superior tensile strength and distinct buckling conformations, thereby fulfilling a diverse array of functional necessities. Our results illustrate that the proposed method displays a high level of precision in distinguishing between buckling modes of geometric symmetry and patterns that deviate from such symmetry. The buckling mode space has been extended and rediscovered, allowing unique modes to have the potential to be adopted into functional devices. Additionally, it demonstrates minimal losses in predicting constitutive relationships. Intriguingly, we discovered that tensile responses are geometry-centric and adjustable. Buckling modes showcase a dependency on geometry, with certain geometric parameters either significantly augmenting the sensitivity of buckling modalities or causing the buckling instability modes to become apathetic and unresponsive. Guided by the principle of target-led pattern parameter design, we proffer prospective tactics for the design of kirigami capable of delivering the desired mechanical performance. Moreover, we explore the feasibility of employing alternative biological materials in these designs.

Improved energy method and agglomeration influence of carbon nanotubes on polymer composites

In this paper, the geometric analysis of carbon nanotubes (CNTs) without external loading is carried out by energy method. Based on the theory of molecular mechanics, an improved mechanical model is proposed to predict the energy of armchair carbon nanotubes under stress-free conditions, and the diameter of CNTs is estimated according to the principle of minimum energy. The results show that the diameter obtained by the improved model is larger, but basically consistent with that obtained by conformal mapping. The inversion energy term is added to the modified model, and the inversion energy term related to atomic curvature is characterized by the conization angle. It can be seen from the error that the inversion energy of carbon nanotubes can not be neglected in the stress-free state, especially in the case of small diameter. The agglomeration of nanotubes is one of the important factors, which affects the effective elastic modulus of nanocomposites. Here, a new micro-mechanics model consisting of both agglomeration of CNTs and pure matrix is also presented to analyze its effect on the effective elastic modulus. It is noted from the results that the stiffness of nanocomposites is very sensitive to the CNTs agglomeration.

Numerical method for predicting the nucleation and propagation of multiple cracks based on the modified extended finite element method

In practical engineering, structures will inevitably suffer from multiple cracks and require accurate numerical methods to calculate the structural behavior. Regarding the multi-crack problems, the nucleation of new cracks and the development of existing cracks will affect the subsequent structural responses. Therefore, the criterion for calculating crack nucleation and development is a critical factor influencing the numerical results. This paper presents a modified Extended Finite Element Method (XFEM) to predict the nucleation and development of multiple cracks in plane members focusing on the interaction of multiple cracks. In the proposed method, the crack competition criterion is based on the minimum total energy principle, which can ensure that the nucleation and development of cracks can achieve a maximum energy dissipation per unit length. The effectiveness and robustness of the presented method are verified by comparing the numerical results with experimental and/or other numerical simulations. The result shows that the proposed competition criterion can accurately judge the sequence of new-crack nucleation and existing-crack propagation.

First-principles calculation of the effect of V content on the properties of NbMoTaWVx refractory high-entropy alloys

This work focused on the influence of V content on NbMoTaWVx (x = 0.00, 0.25, 0.50, 0.75, 1.00, 1.25, 1.50, 1.75, 2.00) refractory high-entropy alloys (RHEAs). The influence of V content with structure stability, electronic properties, elastic properties, and thermodynamic properties was systematically studied by first-principles calculations and the Gibbs2 program. All alloys prefer to form body centered cubic (BCC) structure according to the minimum energy principle. The electronic properties show that the V element can strengthen the metallicity of NbMoTaWVx RHEAs. The results of elastic properties show that NbMoTaWV0.75 owns the highest ductility and lowest hardness at the same time. Moreover, according to the results of thermodynamic properties, the V element can reinforce the abilities of resistance for thermal softening and thermal expansion at high temperatures. This study can provide guidance for the design and practical preparation of RHEAs.

Adaptive machining of damaged blades repaired by additive manufacturing: a novel double-constrained method for model reconstruction

This article introduces a novel model reconstruction method for machining turbine blades damaged in service and repaired via additive manufacturing (AM). Addressing the lack of a model for damaged parts crucial for precise adaptive machining, the method involves model registration and construction. Initially, the AM-repaired blade is aligned with a theoretical CAD model through rough registration using Principal Component Analysis (PCA), followed by precise alignment within the blade profile’s tolerance zone. The model construction employs the minimum curve energy principle to ensure seamless integration with undamaged areas and adherence to profile tolerance constraints. The interfacial profile curve between the undamaged and AM-repaired areas is used as the original curve to construct the curves in the AM-repaired area. The reconstructed curves are modified with a double constraint of being smooth and minimum occupation of the theoretical model tolerance zone. The efficacy of this method is validated through a case study. The repaired blade showed deviations from −0.101 mm to 0.115 mm, within profile tolerances, and a surface smoothness difference of less than 6.41 μm between the damaged and undamaged sections. This method significantly improves the precision and efficiency of turbine blade repair, offering substantial benefits for the turbomachinery manufacturing industry.

Buckling and vibration analysis of axially functionally graded nanobeam based on local stress- and strain-driven two-phase local/nonlocal integral models

This paper presented an efficient finite element formulation for analysis of the buckling and free vibration of the axial functionally graded (AFG) Euler-Bernoulli nanobeam based on minimum total potential energy principle with linear constraints. The stress- and strain-driven two-phase local/nonlocal integral models are utilized to address small scale effects. The material properties of the AFG nanobeam vary exponentially along the axial direction. The nonlocal integral constitutive equation can be equivalently transformed into a differential equation with two constitutive boundary conditions. The governing equation and standard boundary conditions are derived via Hamilton's principle. The weak form associated with total potential energy is derived and the constitutive boundary conditions can be converted to external forces at the boundaries. By employing a numerical solution methodology on the basis of the finite element method (FEM) together with Lagrangian multiplier method (LMM), a unified finite element formulation based on stress- and strain-driven two-phase local/nonlocal elasticity is constructed to obtain the critical buckling load and vibration frequency. Meanwhile, the numerical results obtained through generalized differential quadrature method (GDQM) validate the efficiency and accuracy of the present results. The influence of gradient index, nonlocal parameter and local phase parameter on buckling and free vibration of AFG Euler-Bernoulli nanobeam is investigated in detail under different nonlocal models and boundary conditions. It is demonstrated that the gradient index has more effect on mode shapes than the buckling load and vibration frequency between the local stress- and strain-driven two-phase local/nonlocal models.

Research on the Optimal Design of Retaining Piles of a Wide Metro Tunnel Foundation Pit Based on Deformation Control

Engineers pay more and more attention to the economic benefits of foundation pit engineering. At present, the optimal design of the foundation pit supporting structure mainly focuses on strength and functional design, and there is no mature theoretical design method for deformation control. In this paper, a method for calculating the overall deformation of a foundation pit supporting structure based on the principle of minimum potential energy is proposed. Based on this method, the optimal design of the foundation pit of Guangzhou Baiyun District Comprehensive Transportation Hub Metro Station is realized. The deformation calculation results and optimization design scheme are validated by finite element numerical simulation and field monitoring data. The results show that the proposed theoretical algorithm predicts the pile deformation curves better than the finite element method, suggesting the proposed theoretical method is reasonable and the optimization scheme of the retaining pile is feasible. In the optimized design, the deformation of the foundation pit retaining pile is controlled by its push-back effect. The proposed deformation calculation method can realize the overall deformation calculation of the foundation pit supporting structure.

A single-axis force sensor based on a 3D-printed elastic ring

Force measurement is indispensable in vast engineering applications but conventional force sensors usually encounter large measurement errors or high costs. To address this problem, we develop a force sensor based on a 3D-printed elastic ring structure, which measures the external force by utilizing the displacement variation of the elastic ring. The nonlinear theory based on the minimum potential energy principle is proposed to describe the nonlinear relationship between the external force and the ring top displacement. The feasibility of the proposed force sensor scheme is validated through FEM simulations and experiments. The range of the force sensor can be adjusted by tuning the geometric parameters and the material parameters of the elastic ring, while the force sensor shows good measurement error at different measurement ranges. This force sensor possesses simple fabrication and low cost, showing good potential for various applications such as industrial automation, mechanical testing, and medical devices.

Thermodynamic Model for Hydrogen Production from Rice Straw Supercritical Water Gasification.

Supercritical water gasification (SCWG) technology is highly promising for its ability to cleanly and efficiently convert biomass to hydrogen. This paper developed a model for the gasification of rice straw in supercritical water (SCW) to predict the direction and limit of the reaction based on the Gibbs free energy minimization principle. The equilibrium distribution of rice straw gasification products was analyzed under a wide range of parameters including temperatures of 400-1200 °C, pressures of 20-50 MPa, and rice straw concentrations of 5-40 wt%. Coke may not be produced due to the excellent properties of supercritical water under thermodynamic constraints. Higher temperatures, lower pressures, and biomass concentrations facilitated the movement of the chemical equilibrium towards hydrogen production. The hydrogen yield was 47.17 mol/kg at a temperature of 650 °C, a pressure of 25 MPa, and a rice straw concentration of 5 wt%. Meanwhile, there is an absorptive process in the rice straw SCWG process for high-calorific value hydrogen production. Energy self-sufficiency of the SCWG process can be maintained by adding small amounts of oxygen (ER < 0.2). This work would be of great value in guiding rice straw SCWG experiments.

Multi-scale pore model construction and damage behavior analysis of SiCf/SiC composite tubes

SiCf/SiC composite materials are essential for spacecraft thermal protection, determining the safety of spacecraft. However, their complex structures and intricate fabrication processes have led to an unclear understanding of their failure mechanisms, limiting their application. In this study, circumferential compression experiments were conducted, and X-ray computed tomography (X-CT) was used to analyze the distribution characteristics of pore spaces. The experimental results indicate that damage manifests as secondary fracture phenomena based on temporal evolution characteristics. Specifically, after experiencing performance degradation of 24.73–60.96%, the material still maintained basic stability, exhibiting a performance recovery of 31.55–36.1% under the applied load until failure. To predict the dynamic damage behavior of materials at multiple scales, a multi-scale method combining statistical and microscopic approaches was proposed. A micro representative volume element (RVE) random fiber pore distribution model was established based on random processes and random medium theory. Finally, considering the CT data and the principle of minimum potential energy, a macroscopic finite element model of the micro-pores' structural characteristics in a three-dimensional wound tube was reconstructed. The results indicate that cracks initiate around pore defects and gradually propagate to form crack bands. The model closely matches the macroscopic damage and microscopic characteristics of the material. This work provides a new approach for the numerical simulation of pore defects in such materials.

Material optimization of reinforced concrete structures in multiple limit states

AbstractA common limitation in current material optimization methods for reinforced concrete structures is that they often concentrate solely on either the serviceability limit state (SLS) or the ultimate limit state (ULS). In response, this paper introduces a novel approach to optimize the material layout in planar reinforced concrete structures in plane stress, accounting for both limit states simultaneously. The proposed method employs an iterative strategy, integrating criteria for serviceability and ultimate limit states while approximating the elastoplastic behavior of cracked reinforced concrete. Here, the criteria for the limit states are incorporated as limits on the strains. The methodology initiates with a finite element limit analysis for the preliminary layout. The minimum potential energy principle is utilized to determine the strains for the nonlinear material response, and subsequently, an iterative linearized method is applied for material optimization. The research showcases the successful application of this approach to simple examples and presents improved and optimized solutions that adhere to the limit criteria for more complex structural scenarios.

A method for predicting deformation field of deep foundation pit considering spatial effect

Urban underground spaces have experienced significant development and utilization due to the rapid progress of urban construction and continuous advancements in construction technology. The number of foundation-pit projects immediately adjacent to buildings, structures, and pipelines has been increasing. Ensuring the safety of construction and surrounding facilities, it is essential to predict deformation caused by foundation pit excavations. In this study, a simple calculation method was proposed for predicting deformation of an envelope structure and surface settlement caused by deep foundation excavation with spatial effects. Firstly, the principle of minimum potential energy was applied and the lateral displacement equation of the envelope structure was derived, considering spatial deformation effects. Secondly, based on linear elasticity theory, a surface settlement expression was formulated utilizing the plane strain boundary. Finally, the stratigraphic loss method was used to establish a connection between horizontal envelope deformation and surface settlement, allowing for calculations of surface settlement at any position behind the envelope structure. The effectiveness and practicability of the proposed method were demonstrated by comparison of two existing foundation-pit engineering examples.

Conglomerate rock interface debonding characteristics and damage evolution based on cohesive phase-field method

Rock failure often occurs due to uneven mechanical strength and discontinuous strain at the interface. However, due to the complex interaction mechanism between different phases of conglomerate, it is necessary to improve the crack growth model at the conglomerates' interface. In view of the physical structure and mechanical properties of conglomerate materials, this paper innovatively adopts the cohesive phase field model to study the material deformation and crack growth of conglomerate materials. Different from the traditional phase field model, this model characterises the real structure of the interface by adding an interface phase field, which is used to simulate the debonding of the interface during crack propagation and damage evolution. The regularization of the phase field is carried out to ensure the smoothness of the interface. The transition state of the interface region is determined by the element and the additional phase field. The energy equation is coupled with the crack propagation process using the crack surface density function. The evolution of the damaged phase field and displacement field is driven by the principle of energy minimization. The innovative assumption is that there is a virtual crack at the crack tip, and the interface related elements show a certain cohesive softening form during the damage evolution, which is the main way to realize the particularity of interface mechanics. By controlling the crack dispersion state and stiffness degradation of the material, several ideal softening models are innovatively assumed according to the cohesive force change law to satisfy the mechanical properties and stress function constraints. When cutting blocks n=2.5×104, the errors of the linear model, exponential model, and compound inverse model are 1.76%, 7.48%, and 5.19%, respectively. The results of the exponential model agree well with the stress strength (the error is 2%) and interface crack kinking angle (68.89°). The simulation results indicate that the deformation process of the conglomerate can be divided into three stages: elastic deformation stage, crack propagation stage, and stable load stage. The tensile strength of conglomerate is positively correlated with interface's fracture toughness and proportion of gravel area, respectively.

Three-dimensional calculation method on local slurry wall stability of diaphragm wall trench based on minimum potential energy principle

Because the soft weak soil layer rich in confined groundwater is prone to local instability and failure in the construction of diaphragm wall trenches, in order to check the local slurry wall stability in the construction of diaphragm wall trenches, a new three-dimensional (3D) calculation method on the local stability safety factor (LSF) of slurry walls is proposed based on the minimum potential energy principle. After the new method is applied to two engineering cases, the value of the LSF solved is 0.82 for engineering case 1, and the values of the LSF solved are 0.84 and 1.05 when the phreatic water levels are 2 and 4.5 m, respectively, for engineering case 2. These results are very close to the calculation results in the existing references, so the rationality of the new method is verified. Then the sensitivity of the LSFs obtained from the new method to various parameters has been analyzed and clarified on the basis of ten design examples. Finally, the new method is used to check the local slurry wall stability in the construction of diaphragm wall trenches for a practical project, and the obtained values of the LSF for three concerned weak soil layers are 1.37, 1.19, and 0.82, respectively. These results are in agreement with the actual situation in the construction site. This reveals that both the 3D model established and the 3D calculation method proposed in this paper are suitable for application in practical projects.

Formation Mechanism and Morphology Evolution of β-NaYF4 Single Microcrystals in Hydrothermal Process

Lanthanide-doped upconversion (Ln-doped UC) materials with predicable phase and geometry are attractive for their promising application in optics and biological. Herein, we report a facile strategy for deterministic synthesis of β-NaYF4 microcrystals by an ethylenediaminetetraacetic acid (EDTA) assisted hydrothermal process. The nucleation and growth process of the β-NaYF4 microcrystals have been experimentally revealed with different hydrothermal times. The phase and geometry of as-obtained crystals can be well manipulated by the experimental parameters such as pH values, precursors’ ratio, and reactant concentrations. The formation and morphology evolution mechanism of β-NaYF4 single microcrystals can be qualitatively analyzed using energy minimization principles under the thermodynamic and kinetic control. In addition, we presented the colour-changing up-conversion of Tm3+ and Yb3+ doped single β-NaYF4 microrod. Our work could help the understanding on crystal growth and design of rare earth fluoride mateirals at micro and nanoscale.

Static response of vertically loaded pile in inhomogeneous soil

In this study, an analytical model is developed to obtain the static response of the vertically loaded pile in the inhomogeneous soil with arbitrary properties varying along the depth. The soil displacement is expressed by the product of the axial displacement function and the shape function attenuating with the distance from the pile periphery. Through the minimum potential energy principle, the governing equations are established for the axial displacement function and the shape function. The governing equation for the shape function is independent of soil properties and it can be explicitly solved. The governing equation for the axial displacement function contains variable coefficients due to the inhomogeneity of soil and it is solved using the weighted residual method. An iterative procedure is introduced to implement the solution. The proposed model is validated by comparing the present solutions with those obtained by the available methods. The parametric study shows that the pile head stiffness is affected by the distribution of soil shear modulus heavily, in which the average shear moduli are the same for these distributions. Moreover, the relationship between the pile head stiffness and the pile slenderness ratio for a floating pile is different from that for an end-bearing pile.

Design Optimization of Flexural and Eigenvalue Characteristics of Perforated and Skewed Bio-Composite Functionally Graded Panels

The development of novel materials is of prime importance in the biomedical areas, especially for bone replacements and dental implants. This study uses finite element modeling of skewed functionally graded bio-composite structures with perforations to examine flexural and eigenfrequency responses. Here, the bio-composite structure comprises Titanium (Ti) and Hydroxyapatite (HAp). Voigt’s micromechanical material model via power-law distribution and Representative volume element (RVE) method is utilized to compute the in-homogenous material properties in the thickness direction. The strain field is based on the equivalent single-layer first-order shear deformation theory with five degrees of freedom, and the governing equations are obtained using principle of minimum potential energy. A computer algorithm is developed in a 2D finite element platform using eight-noded quadrilateral elements. The mesh stability of the skewed and perforated structure is confirmed through the smart mesh technique, and the present model’s accuracy is demonstrated by comparing it with the available reported results. Numerous examples reveal the significance of material gradation, skewness, aspect ratios, perforations, and support conditions on bio-composite functionally graded structures’ flexural and eigenfrequency responses. Furthermore, parametric optimization is conducted to minimize the flexural response and maximize the fundamental frequency by employing the response surface methodology (RSM), followed by determining optimal process parameters and valuable findings.

New insights into folding tape-spring

The tape-spring is widely used in aerospace, mechanical, and civil engineering due to its unique mechanical properties and compact size. This paper aims to establish a new analytical model to more accurately predict the folding behavior of the tape-spring, including the geometric configuration, folding moment versus longitudinal curvature curve, peak moment, and propagation moment. This model comprehensively considers the influence of stretching strain energy and bending strain energy on the total strain energy, and determines the folding behavior of the tape-spring through the minimum energy principle. The proposed analytical model was compared with Wuest’s model, Yee’s model, and Yao’s model. Experiments of tape-springs made from two different materials were utilized for validation. The study shows that the proposed model has the highest prediction accuracy compared with the classical models, with the error of approximately 10%. The reason for the significant difference in the prediction results between the proposed model and Yao’s model was given, and the relationship between stretching strain energy and bending strain energy during the folding process of the tape-spring was analyzed. The proposed model has broader applicability than classical models and provides new insights and solutions for accurate prediction of the folding behavior of the tape-spring.

Analyze the temperature-dependent elastic properties of single-walled boron nitride nanotubes by a modified energy method

The elastic properties of boron nitride nanotubes (BNNTs) were investigated utilizing an enhanced energy method. By considering small deformations and applying the principle of minimum potential energy, the variations in atomic bonds and bond angles within the nanotube structure were determined. The modified model incorporated the contribution of inversion energy to the overall potential energy of the system, leading to the derivation of analytical expressions for the Young's modulus, shear modulus, and strain energy of both armchair and zigzag BNNTs under varying temperatures. The results indicate that compared to zigzag BNNTs, the impact of inversion energy on the elastic constants of armchair BNNTs is more significant, especially at small diameters (<1 nm). In thermal environment, this study demonstrates that the change in Young's modulus of BNNTs is lower than that of carbon nanotubes (CNTs), confirming the superior thermal stability of BNNTs over CNTs. Furthermore, molecular structure mechanics (MSM) and continuum mechanics models were employed to analyze the strain energy of BNNTs. The effects of different bonds, bond angles, and inversion angles on strain energy were analyzed in a thermal environment, revealing distinct differences between the two types of BNNTs. These findings provide more accurate theoretical guidance for thermal applications based on the stretching of BNNTs.

Ispitivanje poprečne unutarnje sile sandučastog nosača primjenom principa varijacije energije

This study investigated the transverse internal force of a box girder with a trapezoidal cross-section under eccentric loading. The effects of the box girder distortion and frame shear difference on the transverse internal force were considered. An energy variation method based on the minimum potential energy principle was adopted for transverse internal force analysis of the frames. The variable shear difference of the top slab was considered an unknown quantity, and a fourth-order governing differential equation was established. The transverse bending moment of the frame was obtained by solving for the shear difference. Two examples were used to verify the proposed method and analyse the differences between the transverse internal force results calculated using different methods. The effect of the distribution of the box-girder distorted transverse bending moment on each slab was investigated for various stiffness ratios. The results showed that the transverse internal force of the box girder calculated using the proposed method agreed well with the finite element results, with a maximum error of less than 9.68 %. When the stiffness ratio of the box girder increased, the distribution of the distorted transverse bending moment on the top slab increased, whereas that on the bottom slab decreased.