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The purpose of this paper is to establish a peridynamic method in predicting viscoelastic creep behaviour with recovery stage and to find the suitable numerical parameters of peridynamic method.

A rheological viscoelastic creep constitutive equation including recovery and an elastic peridynamic equation (with integral basis) are examined and used. The elasticity equation within the peridynamic equation is replaced by the viscoelastic equation. A new peridynamic method with two time parameters, i.e. numerical time and viscoelastic real time is designed. The two parameters of peridynamic method, horizon radius and number of nodes per unit volume are studied to get their optimal values. In validating this peridynamic method, comparisons are made between numerical and analytical result and between numerical and experimental data.

The new peridynamic method for viscoelastic creep behaviour is approved by the good matching in numerical-analytical data comparison with difference of < 0.1 per cent and in numerical-experimental data comparison with difference of 4-6 per cent. It can be used for further creep test which may include non-linear viscoelastic behaviour and creep rupture. From this paper, the variation of constants in Burger’s viscoelastic model is also studied and groups of constants values that can simulate solid, fluid and solid-fluid viscoelastic behaviours were obtained. In addition, the numerical peridynamic parameters were also manipulated and examined to achieve the optimal values of the parameters.

The peridynamic model of viscoelastic creep behaviour preferably should have only one time parameter. This can only be done by solving the unstable fluctuation of dynamic results, which is not discussed in this paper. Another limitation is the tertiary region and creep rupture are not included in this paper.

The viscoelastic peridynamic model in this paper can serve as an alternative for conventional numerical simulations in viscoelastic area. This model also is the initial step of developing peridynamic model of viscoelastic creep rupture properties (crack initiation, crack propagation, crack branching, etc.), where this future model has high potential in predicting failure behaviours of any components, tools or structures, and hence increase safety and reduce loss.

The application of viscoelastic creep constitutive model on peridynamic formulation, effect of peridynamic parameters manipulation on numerical result, and optimization of constants of viscoelastic model in simulating three types of viscoelastic creep behaviours.

The paper aims to use a switching technique which allows to couple a nonlocal bond-based Peridynamic approach to the Meshless Local Exponential Basis Functions (MLEBF) method, based on classical continuum mechanics, to solve planar problems.

The coupling has been achieved in a completely meshless scheme. The domain is divided in three zones: one in which only Peridynamics is applied, one in which only the meshless method is applied and a transition zone where a gradual transition between the two approaches takes place.

The new coupling technique generates overall grids that are not affected by ghost forces. Moreover, the use of the meshless approach can be limited to a narrow boundary region of the domain, and in this way, it can be used to remove the “surface effect” from the Peridynamic solution applied to all internal points.

The current study paves the road for future studies on dynamic and static crack propagation problems.

In this paper, the standard Peridynamic Timoshenko beam model accounting for the shear deformation is chosen to describe the thick beam kinematics. Unfortunately, when applied to very thin beam structures, the standard Peridynamics (PD) encounters the shear locking phenomenon, leading to incorrect solutions.

PD differs from classical continuum mechanics and other nonlocal theories that do not involve spatial derivatives of the displacement field. PD is based on the integral equation instead of differential equations to handle discontinuities and other singularities.

The shear locking can be successfully alleviated using the developed selective integration method. In particular, this technique has been implemented in the standard PD, which allows an accurate result for a wide range of slenderness from very thin to thick (10 < L/t < 10³) structures. It can also accelerate the computational time for particular dynamic problems using fewer neighboring integration particles. Several numerical examples are solved to demonstrate the effectiveness of the proposed method for modeling beam structures.

The paper highlights the severe shear locking phenomenon in the Peridynamic Timoshenko beam available in the literature, especially for very thin structures. A new alternative for the alleviation of shear locking in the Peridynamic Timoshenko beam, using selective integration. Hence the developed Peridynamic Timoshenko beam model is effective for thin and thick structures. A new peridynamic formulation for the low-velocity impact beam models is presented and validated.

1. The paper highlights the severe shear locking phenomenon in the Peridynamic Timoshenko beam proposed in the literature, especially for very thin structures.

2. The developed Peridynamic Timoshenko beam model based on selective integration is effective for thin and thick structures.

3. A new peridynamic formulation for the low-velocity impact beam models is presented and validated.

The paper highlights the severe shear locking phenomenon in the Peridynamic Timoshenko beam proposed in the literature, especially for very thin structures.

The developed Peridynamic Timoshenko beam model based on selective integration is effective for thin and thick structures.

A new peridynamic formulation for the low-velocity impact beam models is presented and validated.

The purpose of this paper is to propose a novel quasi-nonlocal coupling of the bond-based peridynamic model with the classical continuum mechanics model to fully take advantage of their merits and be free of ghost forces.

This study reconstructs a total energy functional by introducing a coupling parameter that alters only the nonlocal interactions in the coupling region rather than the whole region and a modified elasticity tensor that affects the local interactions. Then, the consistency of force patch test is enforced in the coupling region to completely eliminate the ghost force in a general energy-based coupling scheme. For a one-dimensional problem, these coupling parameters are further determined through an energy patch test to preserve the energy equivalence or through an l¹-regularization. And, for a two- or three-dimensional problem, depending on the existence of a solution to the discretized force patch test, they are determined through an l¹-minimization or l¹-regularization.

One- and two-dimensional numerical examples under affine deformation have been conducted to verify the accuracy of the quasi-nonlocal coupling method, which exhibits no ghost force. Moreover, the coupling model can reproduce almost the same deformation behaviors of points near the crack for a cracked plate under tension as that from a pure peridynamic model, the former with a rather low computational cost and an easier application of boundary conditions.

This work is aiming at getting over long-standing ghost force issues in the energy-based coupling scheme. The numerical results from the cracked plate problem are exhibited promising extension to dynamic problems.

This paper aims to review the existing bond-based peridynamic (PD) and state-based PD heat conduction models, and further propose a refined bond-based PD thermal conduction model by using the PD differential operator.

The general refined bond-based PD is established by replacing the local spatial derivatives in the classical heat conduction equations with their corresponding nonlocal integral forms obtained by the PD differential operator. This modeling approach is representative of the state-based PD models, whereas the resulting governing equations appear as the bond-based PD models.

The refined model can be reduced to the existing bond-based PD heat conduction models by specifying particular influence functions. Also, the refined model does not require any calibration procedure unlike the bond-based PD. A systematic explicit dynamic solver is introduced to validate 1 D, 2 D and 3 D heat conduction in domains with and without a crack subjected to a combination of Dirichlet, Neumann and convection boundary conditions. All of the PD predictions are in excellent agreement with the classical solutions and demonstrate the nonlocal feature and advantage of PD in dealing with heat conduction in discontinuous domains.

The existing PD heat conduction models are reviewed. A refined bond-based PD thermal conduction model by using PD differential operator is proposed and 3 D thermal conduction in intact or cracked structures is simulated.

The purpose of this paper is to apply the Peridynamic differential operator (PDDO) to incompressible inviscid fluid flow with moving boundaries. Based on the potential flow theory, a Lagrangian formulation is used to cope with non-linear free-surface waves of sloshing water in 2D and 3D rectangular and square tanks.

In fact, PDDO recasts the local differentiation operator through a nonlocal integration scheme. This makes the method capable of determining the derivatives of a field variable, more precisely than direct differentiation, when jump discontinuities or gradient singularities come into the picture. The issue of gradient singularity can be found in tanks containing vertical/horizontal baffles.

The application of PDDO helps to obtain the velocity field with a high accuracy at each time step that leads to a suitable geometry updating for the procedure. Domain/boundary nodes are updated by using a second-order finite difference time algorithm. The method is applied to the solution of different examples including tanks with baffles. The accuracy of the method is scrutinized by comparing the numerical results with analytical, numerical and experimental results available in the literature.

Based on the investigations, PDDO can be considered a reliable and suitable approach to cope with sloshing problems in tanks. The paper paves the way to apply the method for a wider range of problems such as compressible fluid flow.

The purpose of this paper is to describe a novel implementation of a multispatial method, multitime-scheme subdomain differential algebraic equation (DAE) framework allowing a mix of different space discretization methods and different time schemes by a robust generalized single step single solve (GS4) family of linear multistep (LMS) algorithms on a single body analysis for the first-order nonlinear transient systems.

This proposed method allows the coupling of different numerical methods, such as the finite element method and particle methods, and different implicit and/or explicit algorithms in each subdomain into a single analysis with the GS4 framework. The DAE, which constrains both space and time in multi-subdomain analysis, combined with the GS4 framework ensures the second-order time accuracy in all primary variables and Lagrange multiplier. With the appropriate GS4 parameters, the algorithmic temperature rate variable shift can be matched for all time steps using the DAE. The proposed method is used to solve various combinations of spatial methods and time schemes between subdomains in a single analysis of nonlinear first-order system problems.

The proposed method is capable of coupling different spatial methods for multiple subdomains and different implicit/explicit time integration schemes in the GS4 framework while sustaining second-order time accuracy.

Traditional approaches do not permit such robust and flexible coupling features. The proposed framework encompasses most of the LMS methods that are second-order time accurate and unconditionally stable.

The purpose of this paper is to develop an efficient numerical method to study the complex crack initiation and propagation in linear elastic multiphase composites.

A phase field method is developed to study the complex fracture behavior in multiphase composites. A damage threshold is introduced for referring crack initiation in the proposed method. The damage threshold is assigned as a material property so that different composite components possess different thresholds. In this manner, smooth transition from crack initiation to propagation is revealed.

The proposed method is used to investigate complex crack evolution in mesoscale cementitious composite, which consists of aggregates, matrix and void pores. From a mesoscale point of view, it is found that cracks prefer to evolve within the matrix phase. As a crack encounters an aggregate, it tends to bypass the aggregate and evolve along the interface. Cracks tend to avoid to penetrate through aggregates. Also, cracks tend to be attracted by void pores. From a mesoscale point of view, it is revealed that the elastic modulus and strength of concrete models are closely related to porosity.

A criterion with a damage threshold is introduced to the proposed method. The criterions with and without a damage threshold are compared with each other in details. The proposed method is proven to be a useful tool to study mechanical behavior and crack evolution of brittle multiphase composites.

The interaction between hydraulic fracture (HF) and natural fracture (NF) in naturally fractured rocks is critical for hydraulic fracturing. This paper aims to focus on investigating the development of tensile and shear debonding zone on the NF caused by the stresses produced by HF, and the influence of NF’s debonding behavior on the interaction between HF and NF.

Theoretically, tensile and shear debonding modes of NF are considered, two dimensionless parameters are proposed to characterize the difficulty of tensile and shear failure of NF, respectively. Numerically, a finite element model combining the extended finite element method and cohesive zone method (CZM) is proposed to study NF’s debonding behavior and its influence on the interaction between HF and NF.

Both theoretical analysis and numerical simulation show the existence of two debonding modes. The numerical results also show that the HF can cross, offset or propagate along the NFs depending on the parameters’ value, resulting in different fracture network and stimulated reservoir volume. When they are large, the NF’s debonding area is small, HF tends to cross the NF and the fracture network is simple; when they are small, the NF’s debonding area is large, HF will propagate along the NF. In addition, HF is easier to propagate along with NF under tensile debonding mode while it is easier to pass through NF under shear debonding mode.

The theoretical and numerical considerations are taken into account in the influence of the debonding of NFs on the interaction between HFs and NFs and the influence on the formation of the fracture network.

This paper aims to investigate the equivalent relationship between accelerated corrosion tests and real environmental spectrum of suspenders in long-span suspension bridge considering multiple factors action.

Based on Faraday's law, corrosion current was used as a measure of metal corrosion, and the equivalent conversion relationship between laboratory environment and real service environment was established. The equivalent conversion method for bridge structural steel had been determined under different temperature, humidity, pH value and NaCl concentration conditions. The compilation of environmental spectra for large span bridges considering multiple factors and the principle of equivalent conversion have been proposed.

Environmental factors, including temperature, humidity, pH value and NaCl concentration, have significant impact on the corrosion degree of suspension steel wires, and only considering these two factors for equivalent conversion cannot accurately reflect the true service environment of the bridge. The 33.8-h salt spray accelerated corrosion test using the standard conditions can be equivalent to one year of suspenders corrosion in a real service environment.

The equivalent accelerated corrosion method for steel wires proposed in this study can effectively predict the corrosion degree of the suspenders, which has been verified to be correct and can provide theoretical guidance for the development of corrosion test plans for steel wires and engineering technical basis for anti-corrosion control and calendar life research of suspension bridge suspenders.