A Deep Collocation Method for the Bending Analysis of Kirchhoff Plate

In this paper,a deep collocation method(DCM)for thin plate bending problems is proposed.This method takes advantage of computational graphs and backpropagation algorithms involved in deep learning.Besides,the proposed DCM is based on a feedforward deep neural network(DNN)and differs from most previous applications of deep learning for mechanical problems.First,batches of randomly distributed collocation points are initially generated inside the domain and along the boundaries.A loss function is built with the aim that the governing partial differential equations(PDEs)of Kirchhoff plate bending problems,and the boundary/initial conditions are minimised at those collocation points.A combination of optimizers is adopted in the backpropagation process to minimize the loss function so as to obtain the optimal hyperparameters.In Kirchhoff plate bending problems,the C^1 continuity requirement poses significant difficulties in traditional mesh-based methods.This can be solved by the proposed DCM,which uses a deep neural network to approximate the continuous transversal deflection,and is proved to be suitable to the bending analysis of Kirchhoff plate of various geometries.

A Nonlocal Operator Method for Partial Differential Equations with Application to Electromagnetic Waveguide Problem

A novel nonlocal operator theory based on the variational principle is proposed for the solution of partial differential equations.Common differential operators as well as the variational forms are defined within the context of nonlocal operators.The present nonlocal formulation allows the assembling of the tangent stiffness matrix with ease and simplicity,which is necessary for the eigenvalue analysis such as the waveguide problem.The present formulation is applied to solve the differential electromagnetic vector wave equations based on electric fields.The governing equations are converted into nonlocal integral form.An hourglass energy functional is introduced for the elimination of zeroenergy modes.Finally,the proposed method is validated by testing three classical benchmark problems.

The Prediction of Self-Healing Capacity of Bacteria-Based Concrete Using Machine Learning Approaches

Advances in machine learning(ML)methods are important in industrial engineering and attract great attention in recent years.However,a comprehensive comparative study of the most advanced ML algorithms is lacking.Six integrated ML approaches for the crack repairing capacity of the bacteria-based self-healing concrete are proposed and compared.Six ML algorithms,including the Support Vector Regression(SVR),Decision Tree Regression(DTR),Gradient Boosting Regression(GBR),Artificial Neural Network(ANN),Bayesian Ridge Regression(BRR)and Kernel Ridge Regression(KRR),are adopted for the relationship modeling to predict crack closure percentage(CCP).Particle Swarm Optimization(PSO)is used for the hyper-parameters tuning.The importance of parameters is analyzed.It is demonstrated that integrated ML approaches have great potential to predict the CCP,and PSO is efficient in the hyperparameter tuning.This research provides useful information for the design of the bacteria-based self-healing concrete and can contribute to the design in the rest of industrial engineering.

Computational Machine Learning Representation for the Flexoelectricity Effect in Truncated Pyramid Structures

In this study,machine learning representation is introduced to evaluate the flexoelectricity effect in truncated pyramid nanostructure under compression.A Non-Uniform Rational B-spline(NURBS)based IGA formulation is employed to model the flexoelectricity.We investigate 2D system with an isotropic linear elastic material under plane strain conditions discretized by 45×30 grid of B-spline elements.Six input parameters are selected to construct a deep neural network(DNN)model.They are the Young's modulus,two dielectric permittivity constants,the longitudinal and transversal flexoelectric coefficients and the order of the shape function.The outputs of interest are the strain in the stress direction and the electric potential due flexoelectricity.The dataset are generated from the forward analysis of the flexoelectric model.80%of the dataset is used for training purpose while the remaining is used for validation by checking the mean squared error.In addition to the input and output layers,the developed DNN model is composed of four hidden layers.The results showed high predictions capabilities of the proposed method with much lower computational time in comparison to the numerical model.

Three-Dimensional Isogeometric Analysis of Flexoelectricity with MATLAB Implementation

Flexoelectricity is a general electromechanical phenomenon where the electric polarization exhibits a linear dependency to the gradient of mechanical strain and vice versa.The truncated pyramid compression test is among the most common setups to estimate the flexoelectric effect.We present a three-dimensional isogeometric formulation of flexoelectricity with its MATLAB implementation for a truncated pyramid setup.Besides educational purposes,this paper presents a precise computational model to illustrate how the localization of strain gradients around pyramidal boundary shapes contributes in generation of electrical energy.The MATLAB code is supposed to help learners in the Isogeometric Analysis and Finite Elements Methods community to learn how to solve a fully coupled problem,which requires higher order approximations,numerically.The complete MATLAB code which is available as source code distributed under a BSD-style license,is provided in the part of Supplementary Materials of the paper.

Characterization of Loading Rate Effects on the Interactions Between Crack Growth and Inclusions in Cementitious Material

The microcapsule-enabled cementitious material is an appealing building material and it has been attracting increasing research interest.By considering microcapsules as dissimilar inclusions in the material,this paper employs the discrete element method(DEM)to study the effects of loading rates on the fracturing behavior of cementitious specimens containing the inclusion and the crack.The numerical model was first developed and validated based on experimental results.It is then used to systematically study the initiation,the propagation and the coalescence of cracks in inclusion-enabled cementitious materials.The study reveals that the crack propagation speed,the first crack initiation stress,the coalescence stress,the compressive strength and the ultimate strain increase with the loading rate.The initiation position,the propagation direction,the cracking length and the type of the initiated cracks are influenced by the loading rates.Two new crack coalescence patterns are observed.It is easier to cause the coalescence between the circular void and a propagating crack at a slow loading rate than at a fast loading rate.

A Dual-Support Smoothed Particle Hydrodynamics for Weakly Compressible Fluid Inspired By the Dual-Horizon Peridynamics

A dual-support smoothed particle hydrodynamics(DS-SPH)that allows variable smoothing lengths while satisfying the conservations of linear momentum,angular momentum and energy is developed.The present DS-SPH is inspired by the dual-support,a concept introduced from dual-horizon peridynamics from the authors and applied here to SPH so that the unbalanced interactions between the particles with different smoothing lengths can be correctly considered and computed.Conventionally,the SPH formulation employs either the influence domain or the support domain.The concept of dual-support identifies that the influence domain and the support domain involves the duality and should be simultaneously in the SPH formulation when variable smoothing lengths are used.The DS-SPH formulation can be implemented into conventional SPH codes with minimal changes and also without compromising the computational efficiency.A number of numerical examples involving weakly compressible.fluid are presented to demonstrate the capability of the method.

The Interaction between Microcapsules with Different Sizes and Propagating Cracks

The microcapsule-contained self-healing materials are appealing since they can heal the cracks automatically and be effective for a long time.Although many experiments have been carried out,the influence of the size of microcapsules on the self-healing effect is still not well investigated.This study uses the two-dimensional discrete element method(DEM)to investigate the interaction between one microcapsule and one microcrack.The influence of the size of microcapsules is considered.The potential healing time and the influence of the initial damage are studied.The results indicate that the coalescence crack is affected by the size of holes.The elastic modulus,the compressive strength and the coalescence stress decrease with the rising radius of holes.The initial damage in experiments should be greater than 95%of the compressive strength to enhance the self-healing effect.The large microcapsules require slight initial damage.Both a new type of displacement field near the crack and a new category of coalescence crack are observed.The influence of sizes of holes on the cracking behavior of concrete with a circular hole and a pre-existing crack is clarified.

Effect of graph generation on slope stability analysis based on graph theory

Limit equilibrium method （LEM） and strength reduction method （SRM） are the most widely used methods for slope stability analysis. However, it can be noted that they both have some limitations in practical application. In the LEM, the constitutive model cannot be considered and many assumptions are needed between slices of soil/rock. The SRM requires iterative calculations and does not give the slip surface directly. A method for slope stability analysis based on the graph theory is recently developed to directly calculate the minimum safety factor and potential critical slip surface according to the stress results of numerical simulation. The method is based on current stress state and can overcome the disadvantages mentioned above in the two traditional methods. The influences of edge generation and mesh geometry on the position of slip surface and the safety factor of slope are studied, in which a new method for edge generation is proposed, and reasonable mesh size is suggested. The results of benchmark examples and a rock slope show good accuracy and efficiency of the presented method.

A Systematic Molecular Dynamics Investigation on the Graphene Polymer Nanocomposites for Bulletproofing

In modern physics and fabrication technology,simulation of projectile and target collision is vital to improve design in some critical applications,like;bulletproofing and medical applications.Graphene,the most prominent member of two dimensional materials presents ultrahigh tensile strength and stiffness.Moreover,polydimethylsiloxane(PDMS)is one of the most important elastomeric materials with a high extensive application area,ranging from medical,fabric,and interface material.In this work we considered graphene/PDMS structures to explore the bullet resistance of resulting nanocomposites.To this aim,extensive molecular dynamic simulations were carried out to identify the penetration of bullet through the graphene and PDMS composite structures.In this paper,we simulate the impact of a diamond bullet with different velocities on the composites made of single-or bi-layer graphene placed in different positions of PDMS polymers.The underlying mechanism concerning how the PDMS improves the resistance of graphene against impact loading is discussed.We discuss that with the same content of graphene,placing the graphene in between the PDMS result in enhanced bullet resistance.This work comparatively examines the enhancement in design of polymer nanocomposites to improve their bulletproofing response and the obtained results may serve as valuable guide for future experimental and theoretical studies.

Introduction to the Special Issue on Recent Developments of Peridynamics

Peridynamics is a nonlocal continuum mechanics theory.Peridynamics overcomes the computational challenges in classical continuum mechanics and enables the solution of complex mechanical and physical equations in the presence of jump discontinuities or singularities with ease and simplicity,while preserving a length scale to capture nonlocal behavior.Peridynamics has been recently extended and further developed to solve mass and heat transfer and fluid dynamics.Therefore,peridynamics can now be used for analyzing multiphysics and multiscale problems involving damage and cracks.As a rapidly rising topic in computational mechanics,peridynamics has gained intensive and wide interests in the community.

Multi-source data integration and multi-scale modeling framework for progressive prediction of complex geological interfaces in tunneling

A reliable geological model plays a fundamental role in the efficiency and safety of mountain tunnel construction.However,regional models based on limited survey data represent macroscopic geological environments but not detailed internal geological characteristics,especially at tunnel portals with complex geological conditions.This paper presents a comprehensive methodological framework for refined modeling of the tunnel surrounding rock and subsequent mechanics analysis,with a particular focus on natural space distortion of hard-soft rock interfaces at tunnel portals.The progressive prediction of geological structures is developed considering multi-source data derived from the tunnel survey and excavation stages.To improve the accuracy of the models,a novel modeling method is proposed to integrate multi-source and multi-scale data based on data extraction and potential field interpolation.Finally,a regional-scale model and an engineering-scale model are built,providing a clear insight into geological phenomena and supporting numerical calculation.In addition,the proposed framework is applied to a case study,the Long-tou mountain tunnel project in Guangzhou,China,where the dominant rock type is granite.The results show that the data integration and modeling methods effectively improve model structure refinement.The improved model’s calculation deviation is reduced by about 10%to 20%in the mechanical analysis.This study contributes to revealing the complex geological environment with singular interfaces and promoting the safety and performance of mountain tunneling.

Investigation of crack segmentation and fast evaluation of crack propagation, based on deep learning

Identifying crack and predicting crack propagation are critical processes for the risk assessment of engineering structures.Most traditional approaches to crack modeling are faced with issues of high computational costs and excessive computing time.To address this issue,we explore the potential of deep learning(DL)to increase the efficiency of crack detection and forecasting crack growth.However,there is no single algorithm that can fit all data sets well or can apply in all cases since specific tasks vary.In the paper,we present DL models for identifying cracks,especially on concrete surface images,and for predicting crack propagation.Firstly,SegNet and U-Net networks are used to identify concrete cracks.Stochastic gradient descent(SGD)and adaptive moment estimation(Adam)algorithms are applied to minimize loss function during iterations.Secondly,time series algorithms including gated recurrent unit(GRU)and long short-term memory(LSTM)are used to predict crack propagation.The experimental findings indicate that the U-Net is more robust and efficient than the SegNet for identifying crack segmentation and achieves the most outstanding results.For evaluation of crack propagation,GRU and LSTM are used as DL models and results show good agreement with the experimental data.

Surrounding rock classification from onsite images with deep transfer learning based on EfficientNet

This paper proposes an accurate,efficient and explainable method for the classification of the surrounding rock based on a convolutional neural network(CNN).The state-of-the-art robust CNN model(EfficientNet)is applied to tunnel wall image recognition.Gaussian filtering,data augmentation and other data pre-processing techniques are used to improve the data quality and quantity.Combined with transfer learning,the generality,accuracy and efficiency of the deep learning(DL)model are further improved,and finally we achieve 89.96%accuracy.Compared with other state-of-the-art CNN architectures,such as ResNet and Inception-ResNet-V2(IRV2),the presented deep transfer learning model is more stable,accurate and efficient.To reveal the rock classification mechanism of the proposed model,Gradient-weight Class Activation Map(Grad-CAM)visualizations are integrated into the model to enable its explainability and accountability.The developed deep transfer learning model has been applied to support the tunneling of the Xingyi City Bypass in the high mountain area of Guizhou,China,with great results.

A continuous/discontinuous deformation analysis(CDDA)method based on deformable blocks for fracture modeling

In the framework of finite element meshes,a novel continuous/discontinuous deformation analysis(CDDA)method is proposed in this paper for modeling of crack problems.In the present CDDA,simple polynomial interpolations are defined at the deformable block elements,and a link element is employed to connect the adjacent block elements.The CDDA is particularly suitable for modeling the fracture propagation because the switch from continuous deformation analysis to discontinuous deformation analysis is natural and convenient without additional procedures.The SIFs(stress intensity factors)for various types of cracks,such as kinked cracks or curved cracks,can be easily computed in the CDDA by using the virtual crack extension technique(VCET).Both the formulation and implementation of the VCET in CDDA are simple and straightforward.Numerical examples indicate that the present CDDA can obtain high accuracy in SIF results with simple polynomial interpolations and insensitive to mesh sizes,and can automatically simulate the crack propagation without degrading accuracy.

On the seismic stability analysis of reinforced rock slope and optimization of prestressed cables

The evaluation of the seismic stability of high rock slopes is of vital importance to ensure the safe operation of the hydropower stations.In this paper,an equivalent pseudo-static force analysis based on the finite element method is developed to evaluate the seismic stability of reinforced rock slopes where the prestressed cables are modeled by the bar elements applied with nodal forces and bounded only at the anchored parts.The method is applied to analyze a high rock slope in south-west China and the optimization of cables.The stabilization effects of prestressed cables on the seismic stability of the slope are studied,the simulations of the concrete heading are discussed and the potential failure modes of the shear concrete plug are compared.Based on this,the optimization of cables is studied including the anchor spacing and inclined angles.

Machine-learning-driven on-demand design of phononic beams

The development of phononic crystals, especially their interaction with topological insulators, allows exploration of the anomalous properties of acoustic/elastic waves for various applications. However, rapidly and inversely exploring the geometry of specific targets remains a major challenge. In this work, we show how machine learning can address this challenge by studying phononic crystal beams using two different inverse design schemes. We first develop the theory of phononic beams using the transfer matrix method. Then, we use the reinforcement learning algorithm to effectively and inversely design the structural parameters to maximize the bandgap width. Furthermore, we employ the tandem-architecture neural network to solve the training-difficulty problem caused by inconsistent data and complete the task of inverse structure design with the targeted topological properties. The two inverse-design schemes have different adaptabilities, and both are characterized by high efficiency and stability. This work provides deep insights into the combination of machine learning, topological property,and phononic crystals and offers a reliable platform for rapidly and inversely designing complex material and structure properties.

Isogeometric cohesive zone model for thin shell delamination analysis based on Kirchhoff-Love shell model

We present a cohesive zone model for delamination in thin shells and composite structures.The isogeometric(IGA)thin shell model is based on Kirchhoff-Love theory.Non-Uniform Rational B-Splines(NURBS)are used to discretize the exact mid-surface of the shell geometry exploiting their C 1-continuity property which avoids rotational degrees of freedom.The fracture process zone is modeled by interface elements with a cohesive law.Two numerical examples are presented to test and validate the proposed formulation in predicting the delamination behavior of composite structures.

A deep neural network-based algorithm for solving structural optimization

We propose the deep Lagrange method(DLM),which is a new optimization method,in this study.It is based on a deep neural network to solve optimization problems.The method takes the advantage of deep learning artificial neural networks to find the optimal values of the optimization function instead of solving optimization problems by calculating sensitivity analysis.The DLM method is non-linear and could potentially deal with nonlinear optimization problems.Several test cases on sizing optimization and shape optimization are performed,and their results are then compared with analytical and numerical solutions.

Micromechanical study of loading rate effects between a hole and a crack

The interactions between defects are important in rocks.The micromechanical interactions between a circular hole and a pre-existing crack under uniaxial compression with different loading rates are investigated by the discrete element method(DEM).The crack initiation,crack propagation,and crack coalescence at different loading rates are studied.The loading rates influence the primary as well as secondary cracks.Both the primary and secondary cracks disturb the stress field and displacement field.The DEM simulation explains the initiation position of the primary and secondary cracks.The evolution of the displacement field and the stress field at different loading rates is analyzed.A new displacement field type is observed.The hole is easier to be broken by compression at higher loading rates while it tends to be broken by the coalescence crack at lower loading rates.The high loading rates lead to shielding effects of the hole on the pre-existing crack.