Homogenization is a promising approach to capture the behavior of complex structures like corrugated panels. It enables us to replace high-cost shell models with stiffness-equivalent orthotropic plate alternatives. Many homogenization models for corrugated panels of different shapes have been proposed. However, there is a lack of investigations for verifying their accuracy and reliability. In addition, in the recent trend of development of smoothed finite element methods, the cell-based smoothed three-node Mindlin plate element (CS-MIN3) based on the first-order shear deformation theory (FSDT) has been proposed and successfully applied to many analyses of plate and shell structures. Thus, this paper further extends the CS-MIN3 by integrating itself with homogenization models to give homogenization methods. In these methods, the equivalent extensional, bending, and transverse shear stiffness components which constitute the equivalent orthotropic plate models are represented in explicit analytical expressions. Using the results of ANSYS and ABAQUS shell simulations as references, some numerical examples are conducted to verify the accuracy and reliability of the homogenization methods for static analyses of trapezoidally and sinusoidally corrugated panels.

We present an overview of the most popular state-of-the-art computational methods available for modelling fracture in rock. The summarized numerical methods can be classified into three categories: Continuum Based Methods, Discrete Crack Approaches, and Block-Based Methods. We will not only provide an extensive review of those methods which can be found elsewhere but particularly address their potential in modelling fracture in rock mechanics and geotechnical engineering. In this context, we will discuss their key applications, assumptions, and limitations. Furthermore, we also address ‘general’ difficulties that may arise for simulating fracture in rock and fractured rock. This review will conclude with some final remarks and future challenges.

The most common experimental methods of measuring material strength are the uniaxial compressive and tensile tests. Generally, shearing fracture model occurs in both the tests. Compressive strength is higher than tensile strength for a material. Shearing fracture angle is smaller than 45° under uniaxial compression and greater than 45° under uniaxial tension. In this work, a unified relation of material strength under uniaxial compression and tension is developed by correlating the shearing fracture angle in theory. This constitutive relation is quantitatively illustrated by a function for analyzing the material strength from shear fracture angle. A computational simulation is conducted to validate this theoretical function. It is full of interest to give a scientific illustration for designing the high-strength materials and engineering structures.

The stress evolution, total charging time and capacity utilization of pulse charging (PC) method are investigated in this paper. It is found that compared to the conventional constant current (CC) charging method, the PC method can accelerate the charging process but will inevitably cause an increase in stress and a decrease in capacity. The charging speed for PC method can be estimated by the mean current. By introducing stress control, a modified PC method called the PCCC method, which starts with a PC operation followed by a CC operation, is proposed. The PCCC method not only can accelerate charging process but also can avoid the stress raising and capacity loss occurring in the PC method. Furthermore, the optimal pulsed current density and switch time in the PCCC method is also discussed.

In this paper, models of the global system of the Koyna dam have been created using ABAQUS software considering the dam-reservoir-foundation interaction. Non coupled models and the coupled models were compared regarding the horizontal displacement of the dam crest and the differential settlement of the dam base in clay foundation. Meta models were constructed and uncertainty quantification process was adopted by the support of Sobol’s sensitivity indices considering five uncertain parameters by exploiting Box-Behnken experimental method. The non coupled models results determined overestimated predicted stability and damage detection in the dam. The rational effects of the reservoir height were very sensitive in the variation of the horizontal displacement of the dam crest with a small interaction effect with the beta viscous damping coefficient of the clay foundation. The modulus of elasticity of the clay foundation was the decisive parameter regarding the variation of the differential settlement of the dam base. The XFEM approach has been used for damage detection in relation with both minimum and maximum values of each uncertain parameter. Finally the effects of clay and rock foundations were determined regarding the resistance against the propagation of cracks in the dam, where the rock foundation was the best.

In the present study, the free vibration of laminated functionally graded carbon nanotube reinforced composite beams is analyzed. The laminated beam is made of perfectly bonded carbon nanotubes reinforced composite (CNTRC) layers. In each layer, single-walled carbon nanotubes are assumed to be uniformly distributed (UD) or functionally graded (FG) distributed along the thickness direction. Effective material properties of the two-phase composites, a mixture of carbon nanotubes (CNTs) and an isotropic polymer, are calculated using the extended rule of mixture. The first-order shear deformation theory is used to formulate a governing equation for predicting free vibration of laminated functionally graded carbon nanotubes reinforced composite (FG-CNTRC) beams. The governing equation is solved by the finite element method with various boundary conditions. Several numerical tests are performed to investigate the influence of the CNTs volume fractions, CNTs distributions, CNTs orientation angles, boundary conditions, length-to-thickness ratios and the numbers of layers on the frequencies of the laminated FG-CNTRC beams. Moreover, a laminated composite beam combined by various distribution types of CNTs is also studied.

A three-dimensional two-level gradient smoothing meshfree method is presented for rainfall induced landslide simulations. The two-level gradient smoothing for meshfree shape function is elaborated in the three-dimensional Lagrangian setting with detailed implementation procedure. It is shown that due to the successive gradient smoothing operation without the requirement of derivative computation in the present formulation, the two-level smoothed gradient of meshfree shape function is capable of achieving a given influence domain more efficiently than the standard gradient of meshfree shape function. Subsequently, the two-level smoothed gradient of meshfree shape function is employed to discretize the weak form of coupled rainfall seepage and soil motion equations in a nodal integration format, as provides an efficient three-dimensional regularized meshfree formulation for large deformation rainfall induced landslide simulations. The exponential damage and pressure dependent plasticity relationships are utilized to describe the failure evolution in landslides. The plastic response of soil is characterized by the true effective stress measure, which is updated according to the rotationally neutralized objective integration algorithm. The effectiveness of the present three-dimensional two-level gradient smoothing meshfree method is demonstrated through numerical examples.

The effects of interfacial strength on fractured microcapsule are investigated numerically. The interaction between crack and microcapsule embedded in mortar matrix is modeled based on cohesive approach. The microcapsules are modelled with variation of core-shell thickness ratio and potential cracks are represented by pre-inserted cohesive elements along the element boundaries of the mortar matrix, microcapsules core, microcapsule shell, and at the interfaces between these phases. Special attention is given to the effects of cohesive fracture on the microcapsule interface, namely fracture strength, on the load carrying capacity and fracture probability of the microcapsule. The effect of fracture properties on microcapsule is found to be significant factor on the load carrying capacity and crack propagation characteristics. Regardless of core-shell thickness ratio of microcapsule, the load carrying capacity of self-healing material under tension increases as interfacial strength of microcapsule shell increases. In addition, given the fixed fracture strength of the interface of microcapsule shell, the higher the ratio core-shell thickness, the higher the probability of microcapsules being fractured.

The maximum entropy theory has been used in a wide variety of physical, mathematical and engineering applications in the past few years. However, its application in numerical methods, especially in developing new shape functions, has attracted much interest in recent years. These shape functions possess the potential for performing better than the conventional basis functions in problems with randomly generated coarse meshes. In this paper, the maximum entropy theory is adopted to spatially discretize the deformation variable of the governing coupled equations of porous media. This is in line with the well-known fact that higher-order shape functions can provide more stable solutions in porous problems. Some of the benchmark problems in deformable porous media are solved with the developed approach and the results are compared with available references.

In the recent years, the phase field method for simulating fracture problems has received considerable attention. This is due to the salient features of the method: 1) it can be incorporated into any conventional finite element software; 2) has a scalar damage variable is used to represent the discontinuous surface implicitly and 3) the crack initiation and subsequent propagation and branching are treated with less complexity. Within this framework, the linear momentum equations are coupled with the diffusion type equation, which describes the evolution of the damage variable. The coupled nonlinear system of partial differential equations are solved in a ‘staggered’ approach. The present work discusses the implementation of the phase field method for brittle fracture within the open-source finite element software, FEniCS. The FEniCS provides a framework for the automated solutions of the partial differential equations. The details of the implementation which forms the core of the analysis are presented. The implementation is validated by solving a few benchmark problems and comparing the results with the open literature.

The isogeometric analysis (IGA) method was extended for the solution of the coupled thermo-elastodynamic equations. The dimensionless formulation was accepted in discretization of the uncoupled and coupled thermoelasticity equations and the Generalized Newmark method was used in the time integration procedure. First, the performance of the proposed method was verified against a two-dimensional benchmark example subjected to constant thermal shock with available exact analytical solutions. Then a two-dimensional half-space benchmark example under thermal shock was solved. Finally, cyclic thermal shock (CTS) loading was applied on the half-space problem. The results dedicated that IGA can be used as a suitable approach in the analysis of the general thermomechanical problems.

We approximate the fracture surface energy functional based on phase-field method with smooth local maximum entropy (LME) and second-order maximum entropy (SME) approximants. The higher-order continuity of the meshfree methods such as LME and SME approximants allows to directly solve the fourth-order phase-field equations without splitting the fourth-order differential equation into two second-order differential equations. We will first show that the crack surface functional can be captured more accurately in the fourth-order model with smooth approximants such as LME, SME and B-spline. Furthermore, smaller length scale parameter is needed for the fourth-order model to approximate the energy functional. We also study SME approximants and drive the formulations. The proposed meshfree fourth-order phase-field formulation show more stable results for SME compared to LME meshfree methods.

This paper provides a comprehensive overview of a phase-field model of fracture in solid mechanics setting. We start reviewing the potential energy governing the whole process of fracture including crack initiation, branching or merging. Then, a discretization of system of equation is derived, in which the key aspect is that for the correctness of fracture phenomena, a split into tensile and compressive terms of the strain energy is performed, which allows crack to occur in tension, not in compression. For numerical analysis, standard finite element shape functions are used for both primary fields including displacements and phase field. A staggered scheme which solves the two fields of the problem separately is utilized for solution step and illustrated with a segment of Python code.

In this study, average-interpolating radial basis functions (RBFs) are successfully integrated with central high-resolution schemes to achieve a higher-order central method. This proposed method is used for simulation of generalized coupled thermoelasticity problems including shock (singular) waves in their solutions. The thermoelasticity problems include the LS (systems with one relaxation parameter) and GN (systems without energy dissipation) theories with constant and variable coefficients. In the central high resolution formulation, RBFs lead to a reconstruction with the optimum recovery with minimized roughness on each cell: this is essential for oscillation-free reconstructions. To guarantee monotonic reconstructions at cell-edges, the nonlinear scaling limiters are used. Such reconstructions, finally, lead to the total variation bounded (TVB) feature. As RBFs work satisfactory on non-uniform cells/grids, the proposed central scheme can handle adapted cells/grids. To have cost effective and accurate simulations, the multiresolution–based grid adaptation approach is then integrated with the RBF-based central scheme. Effects of condition numbers of RBFs, computational complexity and cost of the proposed scheme are studied. Finally, different 1-D coupled thermoelasticity benchmarks are presented. There, performance of the adaptive RBF-based formulation is compared with that of the adaptive Kurganov-Tadmor (KT) second-order central high-resolution scheme with the total variation diminishing (TVD) property.

The smoothed finite element method (S-FEM) was originated by G R Liu by combining some meshfree techniques with the well-established standard finite element method (FEM). It has a family of models carefully designed with innovative types of smoothing domains. These models are found having a number of important and theoretically profound properties. This article first provides a concise and easy-to-follow presentation of key formulations used in the S-FEM. A number of important properties and unique features of S-FEM models are discussed in detail, including 1) theoretically proven softening effects; 2) upper-bound solutions; 3) accurate solutions and higher convergence rates; 4) insensitivity to mesh distortion; 5) Jacobian-free; 6) volumetric-locking-free; and most importantly 7) working well with triangular and tetrahedral meshes that can be automatically generated. The S-FEM is thus ideal for automation in computations and adaptive analyses, and hence has profound impact on AI-assisted modeling and simulation. Most importantly, one can now purposely design an S-FEM model to obtain solutions with special properties as wish, meaning that S-FEM offers a framework for design numerical models with desired properties. This novel concept of numerical model on-demand may drastically change the landscape of modeling and simulation. Future directions of research are also provided.

A concise review of recent studies about the fracture assessments of elastic brittle solid materials containing V-notches is presented. In this preliminary and brief survey, elastic stress distributions in V-notched solids are discussed first. The concept of notch stress intensity factor is introduced. Combine the digital image correlation method with numerical computation techniques to analyze the stress distribution near the notches. Fracture criteria such as strain energy density, J-integral, theory of critical distance are used.

However, various new materials are developed in different engineering fields, thus, the establishment of reliable and accurate material strength theory or failure criterion is imperative. Therefore, predicting fracture for various modern materials would require more experiments to infer material dependent parameters in the local fracture model.

During the last decade, numerous high-quality two-dimensional (2D) materials with semiconducting electronic character have been synthesized. Recent experimental study (Sci. Adv. 2017;3: e1700481) nevertheless confirmed that 2D ZrSe₂ and HfSe₂ are among the best candidates to replace the silicon in nanoelectronics owing to their moderate band-gap. We accordingly conducted first-principles calculations to explore the mechanical and electronic responses of not only ZrSe₂ and HfSe₂, but also ZrS₂ and HfS₂ in their single-layer and free-standing form. We particularly studied the possibility of engineering of the electronic properties of these attractive 2D materials using the biaxial or uniaxial tensile loadings. The comprehensive insight provided concerning the intrinsic properties of HfS₂, HfSe₂, ZrS₂, and ZrSe₂ can be useful for their future applications in nanodevices.

Phagraphene is a very attractive two-dimensional (2D) full carbon allotrope with very interesting mechanical, electronic, optical, and thermal properties. The objective of this study is to investigate the mechanical properties of this new graphene like 2D material. In this work, mechanical properties of phagraphene have been studied not only in the defect-free form, but also with the critical defect of line cracks, using the classical molecular dynamics simulations. Our study shows that the pristine phagraphene in zigzag direction experience a ductile behavior under uniaxial tensile loading and the nanosheet in this direction are less sensitive to temperature changes as compared to the armchair direction. We studied different crack lengths to explore the influence of defects on the mechanical properties of phagraphene. We also investigated the temperature effect on the mechanical properties of pristine and defective phagraphene. Our classical atomistic simulation results confirm that larger cracks can reduce the strength of the phagraphene. Moreover, it was shown the temperature has a considerable weakening effect on the tensile strength of phagraphene. The results of this study may be useful for the design of nano-devices using the phagraphene.