Search

Based on the minimum potential energy principle, a novel method is proposed to determine the global sliding direction (GSD), the critical slip surface and the corresponding safety factor (SF) of three-dimensional (3D) slopes with arbitrary-shaped slip surface. The resistance direction at one point on the failure surface is determined based on the relationship between the mobilized shear strength and the virtual displacement which minimizes the total potential energy of failure mass system. The GSD is considered to be the opposite to the composition of resistance on failure surface. Meanwhile, the critical slip surface of 3D slope is generated by two random curves with 8 parameters. Three benchmark slopes and a slope from practice engineering are analyzed to test the validity and accuracy of the present model. The results from the developed method match well with the classical solutions, and the obtained SFs demonstrate that some factors (e.g., local surcharge, composite failure surface, slope geometry and so on) can cause slope instability and failure. The location of critical slip surface and the SF provided by the present method are in good agreement with other solutions. Finally, the influence of failure body volume, shear strength parameters, unit weight, slope angle, surcharge and slope height on the GSD is revealed. This study provides a useful guideline for landslide prediction and reinforcement management in slope engineering. • 3D slope stability analysis is conducted based on the minimum potential energy principle. • The safety factor of 3D slope can be directly evaluated. • A method is proposed to determine the direction of shear stress on failure surface. • A method is developed to determine the critical slip surface of 3D slope. • Effects of some factors on the global sliding direction are investigated. [ABSTRACT FROM AUTHOR]

Shakedown analysis plays a substantial role in safety assessment, especially in nuclear plant industry, chemical industry and civil engineering. This paper presents numerical investigations of shakedown problems with holes using the adaptive extended isogeometric analysis (XIGA). An adaptive strategy performed in the discretized framework of a kinematic approach and second-order cone programming (SOCP) is presented. The main idea is to integrate XIGA based on locally refined non-uniform rational B-splines (LR NURBS) into the SOCP to form an efficient approach for shakedown analysis. A SOCP form based on the von Mises yield criterion is established. By means of an effective SOCP solver, the arising optimization problem is then solved. In addition, the level set function is adopted to detect the position of holes. The L 2 -norm of plastic strain rates is used to guide local mesh refinement. The merits of the developed approach are its easy implementation and high computational efficiency. We consider several benchmark examples to illustrate the accuracy, reliability and efficiency of the developed method. • We propose an adaptive XIGA strategy for shakedown analysis of hole problems. • The large-scale optimization problems are solved with second-order cone programming. • The adaptive local refinement is guided by L2-norm of plastic strain rates. • The present method achieves high accuracy with low computational cost. [ABSTRACT FROM AUTHOR]

In recent years, the phase-field method (PFM) has gained considerable attention to model fracture process. This is because, in a single framework, the method allows to model crack nucleation, growth, coalescence and branching. In addition, existing FE codes can be used with minimal modifications. However, one of the major limitations of the PFM is that, it requires extremely fine mesh to accurately capture the fracture process. An adaptive phase-field method within the framework of isogeometric analysis is presented in this work to model tensile and compressive-shear crack propagation in rock-like materials. Locally refined NURBS are adopted for describing both the geometry and the field variables. The local refinement is performed by structured mesh refinement strategy based on an error indicator that depends on the user-defined threshold value for the phase-field variable. Two phase-field models are adopted for simulating tensile and compressive-shear fractures in rock-like materials. For numerical implementation, a hybrid formulation combined with a staggered solution scheme is adopted. Several two-dimensional benchmark problems are investigated to demonstrated the robustness of the proposed framework. From the numerical study, it can be found that the developed adaptive framework achieves results comparable to a uniformly refined mesh with higher degrees of freedom. • Adaptive isogeometric phase field method is developed for modeling brittle fracture in rock-like materials. • Local refinement is done according to a threshold value of the phase field variable. • Two phase field models are adopted for simulating tensile and compressive-shear fractures in rock-like materials. • Local mesh refinement technique reduces computational time without compromising the accuracy. [ABSTRACT FROM AUTHOR]

This paper aims at presenting a hybrid computational strategy and its detailed implementation for simulation of crack propagation problems in three-dimensional (3D) solids. The key idea of the hybrid approach lies in the combination of extended finite element method (XFEM) and bond-based peridynamics (PD), which takes excellent features of the high computation efficiency by the XFEM and the flexibility by the PD in dealing with crack growth problems. The PD theory is restricted to the region where crack tips are located and cracks grow, while the XFEM theory is applied in the rest of the specimen. One of the merits of this integrated approach allows cracks to grow naturally without any fracture criteria, and it thus enhances the computation efficiency as compared to the pure PD. It additionally removes most of the problems due to the surface effects typical of nonlocal methods. Explicit integration scheme and implicit solving scheme are used for crack propagation problems under dynamic and quasi-static loading conditions. Numerical examples with 3D dynamic and quasi-static crack propagation cases are considered to show the accuracy and performance of the developed method. Reproducing the shape of the experimentally observed crack is demonstrated. For dynamic crack propagation, we additionally explore the change of the crack propagation speed during the cracking process, and the crack propagation speeds from the present method match well with the reference solutions. • A hybrid XFEM - PD approach for three-dimensional fracture problems is presented. • Simulation of three-dimensional crack propagation under static and dynamic loadings in solids is studied. • The present method provides much higher computational efficiency than the traditional PD. • The developed hybrid framework alleviates the need for fracture criteria for crack propagation. [ABSTRACT FROM AUTHOR]

Plate structures suffering thermal environments are often encountered in practice. In this paper, thermal buckling behavior of complex-shaped plates by an adaptive multi-patch isogeometric analysis (IGA) based on locally refined NURBS and Nitsche's method is studied. Kinematic equations are derived using Reissner–Mindlin plate theory, while complex geometries of plates are represented with multiple patches, where the connection between two adjacent patches is constructed through Nitsche's method. To conduct adaptive local refinement, structural mesh refinement strategy is combined with a posterior error estimator, which is defined according to the recovered stresses of the first thermal buckling mode. Numerical examples of plates with simple and complex geometries are considered. The accuracy of critical buckling temperature rise obtained from this study is verified against reference solutions. • Thermal buckling of arbitrary shaped plates is studied by an adaptive multi-patch IGA. • Nitsche's method is used to link two adjacent patches. • A posterior error estimator is defined based on the first thermal buckling mode. • Effects of some factors on thermal buckling behavior of plates are investigated. • High accuracy and computational efficiency are obtained. [ABSTRACT FROM AUTHOR]

In this paper, the computational performance of alternate minimization (AM) and Broyden–Fletcher–Goldfarb–Shanno (BFGS) to solve the coupled partial differential equations arising within the framework of the phase field method is numerically studied. Both the numerical approaches are employed on an adaptive phase field method. In the case of BFGS, a double-loop recursive algorithm in combination with a line search is implemented. The local refinement is based on a pre-defined threshold on the damage variable and element size. The incompatible nodes due to adaptive refinement are handled by variable-node elements. The performance of the solution algorithm is numerically studied for a few problems with different loading conditions, viz., pure mechanical, pure thermal and combined thermo-mechanical. From the study, it is opined that the BFGS algorithm is 2 ∼ 5 times faster than the AM approach, which is typically used for adaptive phase field framework. In addition, the detailed numerical implementation is presented. • BFGS algorithm is incorporated into the adaptive hybrid PFM. • Divergence of iterations is treated by a line search method. • Detailed numerical implementation is presented. • Comparison study on BFGS and AM algorithms in adaptive phase-field method is conducted. [ABSTRACT FROM AUTHOR]

The anchor cable is a widely used reinforcement device in geotechnical engineering. However, conservative assessment results are provided by existing methods due to neglecting the strength reserve of anchor cables. To address this issue, this work establishes a model considering the safety reserve of anchor cables by incorporating the influence of the axial force increment of anchor cables on slope stability within the framework of the minimum potential energy method. The potential sliding mass is regarded as an ellipsoid controlled by six parameters, and the failure surface corresponding to the maximum sliding direction of slopes is considered as the critical slip surface. The reasonableness of the proposed method is tested with three benchmark cases and an engineering example. These outcomes indicate that safety factor obtained by considering the axial force increment of anchor cables is higher than that predicted by the traditional theory, and the growth rate of SF decreases with an increase in the foundation coefficient. The optimal anchor angle is strongly influenced by the vertical spacing of anchor cables as well as the installation height of the first row of anchor cables, while the shear parameters of soil have almost no effect on it. • A new perspective for assessing the stability of 3D reinforced slopes is introduced. • A model that considers the strength reserve of anchor cables is developed. • Effects of foundation coefficient on the axial force of anchor cables are explored. • Range of optimal anchor angle is suggested. [ABSTRACT FROM AUTHOR]

A size-dependent post buckling analysis of functionally graded (FG) microbeams is conducted by using an analytical solution based on a reformulated strain gradient elasticity theory (RSGET). The nonlinear behavior of post buckling is considered by employing the von-Karman nonlinear strain–displacement relation. The microstructure-dependent behavior of the microbeam is captured by the RSGET which incorporated both couple stress and strain gradient effects using one size-dependent parameter for each. The material properties of the FG microbeam changed along the thickness direction, which are described using a power law relation. Based on the principle of minimum potential energy, the equations of equilibrium and boundary conditions of the Euler–Bernoulli microbeam are obtained. The post buckling response of FG mcirobeams with different boundary conditions are analytically derived. Moreover, the effects of the length scale parameter, material gradient index, length-thickness ratio and Poisson's ratio on the post buckling responses are studied. In addition, the total critical pressure for the FG array structures is estimated. These results are helpful for designing FG-MEMS devices. [ABSTRACT FROM AUTHOR]

The objective of this article is to simulate crack growth of complex Mindlin–Reissner plates by developing an adaptive multi-patch extended isogeometric analysis (XIGA). Nitsche's method is used to treat continuity between multi-patches or the coupling of non-conforming meshes, exactly describing the geometry of complex plates. The computational meshes in XIGA are independent of the cracks by introducing some enrichment functions into the displacement approximation based on the partition of unity, thus it is convenient in modeling evolution of crack. The locally refined non-uniform rational B-splines (LR NURBS), which have the properties of local refinement and exact description of geometry, are used to construct geometric model and taken as the shape functions in XIGA. To implement the adaptive local refinement, a method based on recovery technique by Zienkiewicz and Zhu is proposed. Based on the Mindlin–Reissner plate theory, interaction integral method is employed to calculate stress intensity factors (SIFs) and the maximum circumferential stress criterion is used to determine the crack propagation direction. Several numerical examples are carried out to demonstrate the performance of the adaptive multi-patch XIGA for simulating crack growth in complex plates. • Multi-patch local mesh refinement XIGA based on LR NURBS for complex cracked Mindlin–Reissner plate is proposed. • Nitsche's method is used to treat continuity between multiple patches. • Higher order continuity and local refinement property are guaranteed by LR NURBS. • Adaptive process is controlled by a stress recovery-based posteriori error estimator technique. • Results demonstrate the efficiency and accuracy of the method for simulating cracked complex plates. [ABSTRACT FROM AUTHOR]

Concrete structures in cold regions are exposed to harsh environmental conditions, including freeze–thaw cycles, which lead to frost damage and degradation. Accurate simulation of the freeze–thaw damage process is essential for assessing concrete structures' performance and service life. This paper presents a novel approach for simulating microcracks propagation in concrete during freeze–thaw cycles based on a fatigue phase-field model, in which a fatigue degradation function is introduced in the energy functional. The commercial software COMSOL is employed to implement the proposed model using a segregated scheme. The proposed model is validated against experimental results presented in the literature. Additionally, three cases are studied to get insight into the freeze–thaw damage. The results demonstrate the effectiveness of the fatigue phase-field model in capturing crack propagation in concrete under freeze–thaw cycles. The developed model offers valuable insights for assessing and designing concrete structures in cold regions. • A fatigue phase-field model is proposed to model freeze–thaw damage in concrete. • A fatigue degradation function is introduced in the energy functional. • The developed model is successfully implemented using the commercial software COMSOL. • Numerical examples show the accuracy and availability of the proposed method. [ABSTRACT FROM AUTHOR]

Fatigue fracture is one of the main causes of structural failure under cyclic loading, so accurate evaluation of fatigue fracture is very important for the design of structures subjected to cyclic loading. In this work, we propose an adaptive fatigue phase-field model within the framework of multi-patch isogeometric analysis to simulate crack nucleation and propagation in brittle materials under cyclic loading. Multiple non-uniform rational B-splines (NURBS) patches are used to exactly represent complex structures, and the Nitsche's method is adopted to enforce the compatibility of the displacements, stresses and phase-field variables between two patches. The coupled governing equations of fatigue phase-field model are established based on the Nitsche's method, and the selection of Nitsche's parameters are determined from numerical experiments. A refinement-correction adaptive approach based on locally refined non-uniform rational B-splines (LR NURBS) structured mesh refinement strategy is developed to alleviate the computational burden caused by the requirement of small element size around crack surface and the large number of fatigue loading. The proposed multi-patch isogeometric phase-field model can deal with the coupling between equal/unequal length interfaces, thus the fatigue crack propagation simulation in arbitrary complex structure can be implemented. Several numerical examples are investigated to verify the practicality of the multi-patch isogeometric phase-field model and the effectiveness of the adaptive scheme. [Display omitted] • An adaptive isogeometric fatigue phase-field model is developed. • Complex geometry is exactly represented with multi-patch technology. • Nitsche's method is used to couple two patches. • Two interfaces with equal/unequal length can be coupled. • A refinement-correction adaptive strategy is proposed. [ABSTRACT FROM AUTHOR]

This work presents an adaptive phase field framework for the simulation of crack nucleation and propagation in brittle materials subject to low-cycle loading. We introduce a fatigue history strain parameter within the phase-field framework to capture the fatigue effect. The resulting coupled differential equations are solved using a staggered iteration scheme. In order to improve the computational efficiency of the phase-field model, an adaptive refinement scheme is introduced. This scheme utilizes an artificial threshold that takes into consideration of both phase-field variables and cumulative fatigue history field variables to determine the elements to be refined. The handling of the hanging nodes resulting from mesh refinement is accomplished through the application of the variable-node element technique, offering a flexible and efficient mesh integration technique. We validate our proposed numerical scheme through five representative numerical examples: single-edge cracked specimen, compact tension specimen, double-edge cracked panel, plate with a hole and plate with multi-cracks and hole. The results demonstrate that the adaptive mesh refinement scheme significantly reduces computational costs without compromising the accuracy of the numerical predictions. • Fracture due to low cyclic loading is simulated by an adaptive phase-field method. • Variable-node elements for handling the mismatching meshes are adopted. • An artificial threshold is employed to perform adaptive local refinement. • Adaptive mesh refinement scheme retains accuracy at a low cost. • Simulated results demonstrate the robustness of the proposed method. [ABSTRACT FROM AUTHOR]

Many achievements for soft grippers are made in the structure design and grasping of target objects. However, there are limited studies on grasping objects with different attributes by soft grippers with omnidirectional bending capabilities within environments containing obstacles. In this paper, drawing inspiration from the multi-segment structure of the biological finger, a 3D-multi-segment soft pneumatic actuator (3D-MSSPA) with a strong envelope and omnidirectional independent bending is designed and manufactured. Additionally, we developed a novel prototype for a soft gripper prototype. A quasi-static model is proposed to effectively describe the bending deformation of 3D-MSSPA. The experimental results show that, for an applied pressure of 40 kPa, the single segment SPA achieves a maximum bending angle of 175.2°, aligning closely with the theoretical prediction. Furthermore, the omnidirectional bending ability of multi-segments is analyzed through the finite element method, and a position compensation method for gravity deviation is presented. Through experiments, the pressure fore and lifting force of the soft gripper are investigated, yielding maximum values of 11 N and 4.08 N, respectively. These results serve as a benchmark for the mass grasping range of the target objects. Finally, the experiments are conducted to demonstrate the soft gripper's adaptive and flexible grasping capabilities for objects with varying attributes, in both free space and complex space with obstacles. These experiments showcase their ability to avoid obstacles, adaptively grasp objects, and their good envelope ability. The proposed 3D-MSSPA can provide good inspiration and reference for flexible applications, particularly in fields such as post-disaster rescue and rehabilitation medicine. [Display omitted] • A novel multi-segment soft gripper with omnidirectional bending is designed. • The soft gripper has strong adaptive envelope ability. • Experiments verify the theoretical model of soft pneumatic actuator. • The pressure and lifting force of the actuator are tested through experiments. • Object grasping is carried out in free and obstacle spaces. [ABSTRACT FROM AUTHOR]

In rock-like materials, mode I and II fracture toughness are distinctive while the compressive strength is much greater than the tensile strength. Besides, mixed-mode fractures instead of pure mode I or II fractures occur under complicated load cases in those materials. Therefore, to capture the mixed-mode cracking process, we developed a mixed-mode phase-field cohesive zone model based on the unified phase-field theory proposed by Wu. The model was built based on a strain energy decomposition scheme and the softening behavior of each mode is controlled by an independent degradation function. Thus, independent values of strength and toughness can be given for different failure modes simultaneously. A simple mixture rule of fracture toughness was introduced to describe the transition between different failure modes. The model can keep variational consistency perfectly and governing equations for displacement- and phase-field, which was never reported in other works. Several numerical examples verified the effectiveness and flexibility of this work. The present work showed a simple but effective way to simulate mixed-mode fracture. • A modified phase-field cohesive zone model is developed for mixed-mode fracture. • A simple mixture rule is utilized to describe the transition between each fracture mode. • The present model can keep the variational consistency perfectly. • Several numerical cases verify the present model. [ABSTRACT FROM AUTHOR]

Within the isogeometric analysis framework, industrial products or complex shapes are represented using multiple NURBS patches, resulting in non-matching interfaces and introducing additional numerical challenges, particularly in scenarios involving nonlinear behavior. This paper introduces the application of Nitsche's method to address interface coupling challenges presented in non-matching multi-patch configurations. A detailed formulation addressing geometric non-linearity in multiple Reissner–Mindlin plates is developed, and the resulting nonlinear equations are solved using the Newton–Raphson approach. The proposed formulation's effectiveness is demonstrated by a series of numerical examples involving complex geometries represented by multi-patches with non-matching interfaces. These examples are validated against the analytical solutions and results obtained using the commercial finite element package, Abaqus. • Formulations of multi-patch geometrically nonlinear behavior are derived. • Nitsche's method is employed to couple non-conforming patches. • Geometrically nonlinear behavior of complex multi-patch IGA plate is investigated. • High accuracy and computational efficiency are obtained. [ABSTRACT FROM AUTHOR]

This work proposes a phase-field framework for hydrogen-assisted failures of brittle materials using multi-patch isogeometric modeling, considering the effects of hydrogen concentration field evolution and concentration accumulation on material fracture behavior. A phase-field fracture formulation for stress-assisted hydrogen diffusion is derived within the framework of multi-patch IGA and applied to the simulation of hydrogen embrittlement fracture phenomenons in complex structural metallic materials. Nitsche's method imposes continuous conditions to handle the coupling between interfaces, ensuring compatibility between patches and continuity of variables on the coupling edges. In response to the excessive computational burden of the phase-field method, a refinement-correction loop adaptive strategy based on combined refinement indicators is proposed to improve computational efficiency. Several numerical examples are compared with reference cases to verify the proposed model's effectiveness, and the adaptive strategy's performance is tested in simulating hydrogen embrittlement failure. • A multi-patch isogeometric phase-field fracture model for stress-assisted hydrogen diffusion is devised. • Nitsche's method is applied to ensure the compatibility of all variables between two adjacent patches. • Complex geometric structures are constructed with multi-patch modeling. • A refinement-correction loop adaptive strategy based on a combined refinement indicator is proposed. [ABSTRACT FROM AUTHOR]

The inflation of hyperelastic thin shells is a highly nonlinear problem that arises in multiple important engineering applications. It is characterised by severe kinematic and constitutive nonlinearities and is subject to various forms of instabilities. To accurately simulate this challenging problem, we present an isogeometric approach to compute the inflation and associated large deformation of hyperelastic thin shells following the Kirchhoff–Love hypothesis. Both the geometry and the deformation field are discretized using Catmull–Clark subdivision bases which provide the required C 1 -continuous finite element approximation. To follow the complex nonlinear response exhibited by hyperelastic thin shells, inflation is simulated incrementally, and each incremental step is solved using the Newton–Raphson method enriched with arc-length control. An eigenvalue analysis of the linear system after each incremental step assesses the possibility of bifurcation to a lower energy mode upon loss of stability. The proposed method is first validated using benchmark problems and then applied to engineering applications, where the ability to simulate large deformation and associated complex instabilities is clearly demonstrated. [ABSTRACT FROM AUTHOR]

This work presents an adaptive phase-field method incorporated into a finite element framework combined with variable-node elements to investigate the cohesive dynamic fracture. The proposed framework builds upon the regularized phase-field cohesive-zone model as its foundation utilizes a hybrid form of the history field to drive the crack evolution. A staggered iteration scheme is utilized to compute the displacement and phase-field variables for the coupled elastic-phase field system. The error indicator, utilizing the phase-field as well as the history strain variables, is employed to control the adaptive refinement process. The variable-node element technique facilitates adaptive mesh refinement, which is simple and flexible to act as a transition element between coarse and refined elements. In addition, an implicit HHT time integration scheme is employed for temporal discretization. Several standard problems are presented to showcase the efficiency and accuracy of the proposed method, highlighting its superiority when compared to the results documented in the literature. The results show that the proposed framework can significantly improve computational efficiency without affecting the accuracy of numerical results. • An adaptive dynamic phase-field method for cohesive fracture is developed. • Variable-node element effectively treats local refinement-induced incompatibility. • Error indicator is based on phase-field and history strain field values. • Adaptive mesh refinement strategy significantly reduces the computational cost. • Results manifest the performance of the proposed method. [ABSTRACT FROM AUTHOR]

Although robust in handling different fracture processes such as nucleation, branching and coalescence, the phase-field method (PFM) is computationally very expensive because it requires extremely fine meshes to resolve the necessary physics. This paper presents a hybrid adaptive PFM discretized by using finite element method to model quasi-static fracture of thermoelastic solids and quenching. Based on a user-defined threshold on the phase field variable, the computational domain is local refined. The incompatibility between the meshes due to local refinement is directly handled by the variable-node elements, without the special handling of hanging-nodes. The coupled phase-field thermo-elastic equations are solved using the hybrid approach combined with a staggered solution scheme, and the robustness of the proposed framework in terms of capturing the crack morphology is demonstrated with several standard benchmark problems. • Simulation of thermoelastic fracture by an effective adaptive phase-field method is presented. • Variable-node elements for capturing the mismatching meshes are adopted. • A threshold value of the phase-field variable is used to perform local refinement. • Adaptive local mesh refinement technique enhances the accuracy at a low cost. • Simulated results manifest the performance of the proposed method. [ABSTRACT FROM AUTHOR]

Rainfall infiltration is a key factor to induce landslides, and it is important to study the rule of rainfall infiltration on slopes for the prediction and prevention of landslides. This paper combines the minimum potential energy method with the existing analytical solution of seepage field, and proposes a new method for unsaturated soil slopes under rainfall conditions. Specifically, the total potential energy function of the unsaturated soil slope is established by considering the real-time changes in system potential energy caused by rainfall infiltration. Additionally, the effects of rainfall infiltration on the shear strength of the soil, the self-weight of sliding mass and the seepage force are considered. The ratio of the slip resistance moment to the sliding moment is defined as the safety factor (SF) of the slope. The real-time evaluation of the stability of unsaturated soil slopes is realized during rainfall. The research results show that the results obtained by the proposed method are closer to the reference solutions. Meanwhile, the rules of rainfall intensity as well as slope angle on slope stability are conducted. Finally, the relationship between the sliding depth of failure surface and rainfall is also studied. [ABSTRACT FROM AUTHOR]

Nano-structures always show size effects. In the paper, a new FEM framework is developed to analyze the mechanical responses of nanobeams made of axially functionally-graded material (FGM) under different boundary conditions. The stress-driven two-phase nonlocal integral model is utilized to introduce the size effect into the model. The present work is based on the nonlocal constitution in a differential form and the corresponding constitutive boundary conditions are converted to external loads equivalently. A series of numerical examples, including static bending, buckling, and free vibration are carried out for the beams with different boundary conditions and various nonlocal and FGM parameters. The present framework shows a promising way for its flexibility in handling complex FGM distribution patterns, boundary conditions, and loads. [ABSTRACT FROM AUTHOR]

Multiscale piezoelectric materials and structures have shown their promising potential of applications in sensor, energy harvester, actuator and so on. However, the large complexity of such materials and structures poses a significant challenge to the accurate and efficient prediction of their piezoelectric behavior which is significant for guiding and optimizing their applications. In this paper, a Direct FE 2 method was proposed for concurrent multilevel modeling of the coupled electromechanical behavior of multiscale piezoelectric materials and structures. The energy equilibrium and kinematic constraints between macro- and meso-scales were satisfied by prescribing periodic boundary conditions for both displacement and electric potential, which were derived from the governing equation of FEM. Another boundary condition was prescribed to the center node of each RVE, to prevent rigid motion and shifting of electric potential of meso-scale RVEs. All these boundary conditions can be easily prescribed to the Direct FE 2 using multiple points constraints (MPCs), a commonly used feature in most commercial software. The accuracy, computational efficiency and ease of numerical implementation of the proposed Direct FE 2 method were validated using a series of multiscale simulations, including the quasi-static response of homogeneous piezoelectric panels, an arc honeycomb structure, a regular honeycomb structure and a piezoelectric composite panel, as well as the dynamic response of the piezoelectric composite panel. It shows that the proposed Direct FE 2 method will be valuable for large-scale simulations of complicated multiscale piezoelectric materials and structures. • A Direct FE 2 method is proposed for concurrent multilevel modeling of multiscale piezoelectric materials and structures. • The proposed methods can accurately capture the coupled electromechanical response of piezoelectric materials and structures. • The computational efficiency of the proposed method is 9 times higher than traditional FE simulations. [ABSTRACT FROM AUTHOR]

The pile is a widely used reinforcement device in geotechnical engineering. For the present paper, we propose a new solution for calculating the safety factor (SF) of the 3D slope reinforced with piles and determining the critical slip surface (CSS) in the framework of minimum potential energy method. In particular, the mobilized shear stress on failure surface is determined by the equilibrium equation of forces operating on slip body. Meanwhile, the moving direction of 3D slope is equivalent to the direction of combined force acting on slip body. Additionally, the present method is combined with the genetic algorithm to identify CSS, and a novel criterion is proposed to locate the shape and position of CSS of a 3D slope using the total potential energy of landslide system as the objective function. The validation and comparison of results indicate that the SF obtained by the introduced method are close to reference solutions, and SF shows an obvious negative correlation with sliding direction (SD). It is also found that the support effect of pile is related to the pile location and the pile density. Meanwhile, the optimal pile position depends on the shape of failure surface and shear strength parameter of soil. Moreover, the effects of some parameters on SD of 3D slopes reinforced with piles are also studied. • A stability analysis model of 3D slopes reinforced with stabilizing piles is established. • An improved method of determining the elastic potential energy is introduced. • A unique insight into identifying critical slip surface is presented. • An analytical solution for calculating the moving direction of 3D landslide is given. • Influencing factors of reinforcement effect are revealed. [ABSTRACT FROM AUTHOR]

Interfacial debonding affects the mechanical behaviors of composite structures. In the present work, we developed a new phase-field-based cohesive zone model for modeling debonding at interfaces. The traction-separation law and evolution of phase-field considering the mixed-mode scheme of fracture toughness are given in a variational form. Besides, the present interfacial model can work with the phase-field cohesive zone model for the bulk region, in which a common phase-field value ϕ is shared for both regions. The interaction between the bulk region and interfacial cracking in both displacement, as well as phase-field, are taken into account directly to avoid the over-estimation of the free surface energy. The framework is implemented with the finite element method and validated with several numerical examples. The present work provides a unified approach for modeling quasi-brittle fracture in the bulk region and interfaces and shows its advantage in describing interactions between bulk and interfacial cracking. • A phase-field-based cohesive element is proposed for interfacial failure. • Srength and fracture toughness can be defined independently in different directions. • Closure effect of the interfacial crack can be modeled with given penalty stiffness. • Governing equation is given in a variational form. • Mixed-mode behaviors of interfacial fracture is also considered. • The interaction between interface and matrix is considered by a driving force term. [ABSTRACT FROM AUTHOR]

The piezoelectric semiconductor combines the characteristics of both piezoelectric and semiconducting materials, making it highly promising for a variety of engineering applications. The present work adopts a Galerkin approach to derive a general weak form of the coupled governing equations for the analysis of piezoelectric semiconductors. The coupling effect between the strain, the electric field, and the gradients of the concentrations of holes and electrons has been considered. Piezoelectric semiconductors are often deployed in the shape of rods and beams and therefore commonly experience axial and transverse load. Thus, the Euler–Bernoulli beam theory is employed to formulate a numerical approach to analyse the coupling behaviour of such piezoelectric semiconductor beams. In order to satisfy the C 1 continuity requirement of Euler–Bernoulli beam theory without introducing additional degrees of freedom, a discretisation with B-Splines is used. Non-mechanical variables, including electrical potential, holes and electrons concentrations, are decomposed into constant, linear and quadratic terms through series expansion along the thickness, which ensures compatibility with beam formulation. To validate the proposed method, an N-type piezoelectric semiconducting beam under a sinusoidal distributed load, for which an analytical solution is available, is initially examined. Subsequently, complex examples including a cantilever beam with generalised loading conditions and a beam with PN-junction are analysed to demonstrate the capabilities of the proposed method in handling more challenging scenarios. • A finite element framework has been established to analyse the response of the piezoelectric semiconducting structures. • The multi-physics coupling effects in piezoelectric semiconducting beams have been well studied through numerical simulations. • The proposed method provides valuable insights into the performance of piezoelectric semiconductors containing PN-junctions. • It offers a powerful tool for predicting and understanding the behaviour of piezoelectric semiconducting beams. [ABSTRACT FROM AUTHOR]

This paper presents an isogeometric shape optimization methodology to widen the band gap of periodic composite plates by smoothly optimizing its thickness profile. To save the computational cost, two NURBS surfaces are used in the isogeometric optimization method. While a fine NURBS surface (analysis mesh) is used for modeling the band gap of periodic composite plates within the isogeometric analysis (IGA) framework, a coarser NURBS design surface, i.e., the design mesh, is employed to describe the periodic plate thickness profile exactly and the position of control points are taken as optimal thickness variables. The particle swarm optimization (PSO) algorithm is adopted to solve the constrained dynamic maximization problems. On the other hand, the level set method and triangular domain integration technique are employed to describe the two-phase material interface of periodic composite plates. Numerical examples are provided to validate the accuracy and reliability of the present method. The numerical results showed that the present method can provide an accurate analysis and smooth plate thickness profile in the optimization process. The band gap of periodic composite plates is maximized effectively by the design of the plate thickness profile using the present optimization approach. • We develop an IGA shape optimization method to widen the band gap of periodic composite plates by optimize its thickness profile smoothly. • The thickness, i.e., z-component of control point is defined as optimal design variable and the smooth thickness profile can be obtained with few control points. • Band gap of phononic composite plates is maximized by design of the thickness profile using the present optimization approach. • Band gap and central frequency are increased with increasing the plate thickness. [ABSTRACT FROM AUTHOR]

• We present a theoretical model of flexoelectric layerwise nanobeams based on the classical couple stresss. • We established the isogeometric formulation for solution of flexoelectric nanobeams. • We derived analytical solutions for static bending and free vibration of layerwise simply supported nanobeams. • The derived analytical solutions are compared with the isogeometric numerical results. • Microstructural effects and flexoelectric effect on mechanical behavior of layerwise nanobeams are analyzed. The theory of layerwise beam, which considers both microstructure and flexoelectric effects, is used in the curvature-based flexoelectricity theory. The displacement field function of the layerwise beam model is given. The governing equations and boundary conditions are obtained using a variational formulation based on Hamilton's principle. Analytical solutions for static bending and free vibration of a simply supported layerwise beam are derived. Isogeometric analysis (IGA) with higher-order continuity considering the flexoelectric effect is presented to numerically solve the static bending and free vibration problems. The results obtained from the analytical and IGA approaches are compared through several examples in which the microstructure and flexoelectric effects on the mechanical responses of layerwise nanobeams are analyzed. [ABSTRACT FROM AUTHOR]

• Different eigenvectors are tested respectively. Combined with different kinds of BP neural network and ELM classifiers, two motion decoders are constructed for lying and sitting postures, respectively. • The experimental platform of this study is a novel multi-posture lower limb rehabilitation robot, which has three postures: lying, reclining and sitting. • A simple and effective connection method based on label number retrieval is designed, and two different motion decoders based on lying and sitting are constructed. • Through real-time experiments, the effectiveness of active control based on sEMG signals is verified. The construction of motion decoder based on surface Electromyography (sEMG) signals is an important part in the clinical trial of rehabilitation robot. Its performance directly determines the success of clinical trial. However, feature extraction is essential in motion decoder. A single feature such as time domain and frequency domain can achieve good classification results, but it is only suitable for a single posture. Hence, for the lying and sitting postures, different feature analysis and their combination are used in this study to improve the sEMG-based lower limb motion classification performance. Nine participants in the clinical trial performed four different movements respectively. Through feature extraction and pattern recognition of sEMG, the trained motion decoders were obtained. The control commands are sent to the robot through labels retrieval to drive the lower limbs for corresponding rehabilitation training. The effectiveness of the based on sEMG signals control method is verified through real-time experimental analysis. [Display omitted] [ABSTRACT FROM AUTHOR]

• The variable-node multiscale extended finite element method (V-XFEM) is elaborated for the dynamic crack analysis of the linearly uncoupled and coupled physical phenomena in a compact formula. • The numerical results of the linearly elastic and piezoelectric problems considered as illustrated examples show that the V-XFEM has a higher accuracy and more and efficiency than standard XFEM. • For piezoelectric structures, numerical results show that the normalized dynamic intensity factors have a significant dependence on the poling direction and electrical impact loading. • Because of a unified way for all single and coupled linear phenomena, the proposed V-XFEM has the potential to simulate all the linearly physical phenomena. This paper aims to develop a variable-node multiscale extended finite element method (V-XFEM) for dynamic fracture analysis of the linearly uncoupled and coupled physical phenomena in a compact formula. The general governing equations for the linearly uncoupled and coupled physical phenomena are presented in a compact form. The local mesh refinement technique for modeling cracks is used to improve the accuracy and efficiency, in which variable-node elements without modifying the system matrix or impose additional boundary conditions are taken to connect/link different scale elements. In addition, the time-dependent equations are solved by the unconditionally stable implicit Newmark time integration method, and the dynamic intensity factors (DIFs) are derived from the domain forms of the interaction integrals. Numerical results of the linearly elastic and piezoelectric problems show that V-XFEM is an efficient numerical approach to simulate the dynamic fracture problems of the linearly uncoupled and coupled physical phenomena. [ABSTRACT FROM AUTHOR]