Tian Tian¹, Huayi Wei^2,*

The International Conference on Computational & Experimental Engineering and Sciences, Vol.33, No.4, pp. 1-2, 2025, DOI:10.32604/icces.2025.011175

Abstract Brittle fracture is a critical failure mode in structural materials, and accurately simulating its evolution is essential for engineering design, material performance evaluation, and failure prediction. Traditional numerical methods, however, face significant challenges when dealing with higher-order fracture models and complex fracture behaviors. To overcome these challenges, this study proposes an innovative simulation framework based on higher-order finite element methods and adaptive mesh refinement, effectively balancing computational efficiency and simulation accuracy.
The research first develops a higher-order finite element method for the continuum damage fracture phase-field model. By incorporating higher-order finite element techniques, the proposed method… More >

Yuheng Cao, Chunyu Zhang^*

The International Conference on Computational & Experimental Engineering and Sciences, Vol.33, No.2, pp. 1-1, 2025, DOI:10.32604/icces.2025.010692

Abstract A unified high-order damaged elasticity theory is proposed for quasi-brittle fracture problems by incorporating higher-order gradients for both strain and damage fields. The single scale parameter is defined by the size of the representative volume element (RVE). It formulates the degraded strain energy density to capture size effects and localized damage initiation/propagation with a damage criterion grounded in experimental observations. The structural deformation is solved by using the principle of minimum potential energy with the Augmented Lagrangian Method (ALM) enforcing damage evolution constraints. This simplifies the equilibrium equations, enabling efficient numerical solutions via the Galerkin More >

Anshul Pandey, Sachin Kumar^*

CMES-Computer Modeling in Engineering & Sciences, Vol.144, No.3, pp. 3251-3286, 2025, DOI:10.32604/cmes.2025.067858 - 30 September 2025

Abstract The phase field model can coherently address the relatively complex fracture phenomenon, such as crack nucleation, branching, deflection, etc. The model has been extensively implemented in the finite element package Abaqus to solve brittle fracture problems in recent studies. However, accurate numerical analysis typically requires fine meshes to model the evolving crack path effectively. A broad region must be discretized without prior knowledge of the crack path, further augmenting the computational expenses. In this proposed work, we present an automated framework utilizing a posteriori error-indicator (MISESERI) to demarcate and sufficiently refine the mesh along the… More >

Shaoqi Zheng¹, Zihao Yang^1,*

The International Conference on Computational & Experimental Engineering and Sciences, Vol.29, No.1, pp. 1-1, 2024, DOI:10.32604/icces.2024.012200

Abstract This study proposes a novel method for predicting the microcrack propagation in composites based on coupling the local and non-local micromechanics. The special feature of this method is that it can take full advantages of both the continuum micromechanics as a local model and peridynamic micromechanics as a non-local model to achieve composite fracture simulation with a higher level of accuracy and efficiency. Based on the energy equivalence, we first establish the equivalent continuum micromechanics model with equivalent stiffness operators through peridynamic micromechanics model. These two models are then coupled into a closed equation system, More >

Zhiqiang Yang^1,*, Yipeng Rao², Yi Sun¹, Junzhi Cui², Meizhen Xiang^3,*

The International Conference on Computational & Experimental Engineering and Sciences, Vol.27, No.1, pp. 1-1, 2023, DOI:10.32604/icces.2023.09513

Abstract An effective fracture model is established for the brittle materials with periodic distribution of micro-cracks using the second-order multiscale asymptotic methods. The main features of the model are: (i) the secondorder strain gradient included in the fracture criterions and (ii) the strain energy and the Griffith criterions for micro-crack extensions established by the multiscale asymptotic expansions. Finally, the accuracy of the presented model is verified by the experiment data and some typical fracture problems. These results illustrate that the second-order fracture model is effective for analyzing the brittle materials with periodic distribution of micro-cracks. More >

Fei Han^1,*, Zhibin Li¹, Jianyu Zhang¹, Zhiying Liu¹, Chen Yao¹, Wenping Han¹

The International Conference on Computational & Experimental Engineering and Sciences, Vol.26, No.3, pp. 1-1, 2023, DOI:10.32604/icces.2023.09023

Abstract The classical finite element method has been successfully applied to many engineering problems but not to cases with space discontinuity. A peridynamics-based finite element method (PeriFEM) is presented according to the principle of minimum potential energy, which enables discontinuity. First, the integral domain of peridynamics is reconstructed, and a new type of element called peridynamic element (PE) is defined. Although PEs are generated by the continuous elements (CEs) of classical FEM, they do not affect each other. Then, spatial discretization is performed based on PEs and CEs, and the linear equations about nodal displacement are… More >

Zeyuan Zhou, Ming Yu, Xinfeng Wang^*, Zaixing Huang

CMES-Computer Modeling in Engineering & Sciences, Vol.137, No.3, pp. 2593-2620, 2023, DOI:10.32604/cmes.2023.027384 - 03 August 2023

Abstract How to simulate fracture mode and crack propagation path in a plate with multiple cracks is an attractive but dicult issue in fracture mechanics. Peridynamics is a recently developed nonlocal continuum formulation that can spontaneously predict the crack nucleation, branch and propagation in materials and structures through a meshfree discrete technique. In this paper, the peridynamic motion equation with boundary traction is improved by simplifying the boundary transfer functions. We calculate the critical cracking load and the fracture angles of the plate with multiple cracks under uniaxial tension. The results are consistent with those predicted More > Graphic Abstract

Fei Han^*, Zhibin Li, Jianyu Zhang, Zhiying Liu, Chen Yao, Wenping Han

CMES-Computer Modeling in Engineering & Sciences, Vol.136, No.3, pp. 2715-2740, 2023, DOI:10.32604/cmes.2023.026922 - 09 March 2023

Abstract In this study, we propose the first unified implementation strategy for peridynamics in commercial finite element method (FEM) software packages based on their application programming interface using the peridynamics-based finite element method (PeriFEM). Using ANSYS and ABAQUS as examples, we present the numerical results and implementation details of PeriFEM in commercial FEM software. PeriFEM is a reformulation of the traditional FEM for solving peridynamic equations numerically. It is considered that the non-local features of peridynamics yet possesses the same computational framework as the traditional FEM. Therefore, this implementation benefits from the consistent computational frameworks of… More >

Zhijian Wu, Li Guo^*, Jun Hong

CMES-Computer Modeling in Engineering & Sciences, Vol.134, No.1, pp. 611-636, 2023, DOI:10.32604/cmes.2022.020694 - 24 August 2022

Abstract The local arc-length method is employed to control the incremental loading procedure for phase-field brittle fracture modeling. An improved staggered algorithm with energy and damage iterative tolerance convergence criteria is developed based on the residuals of displacement and phase-field. The improved staggered solution scheme is implemented in the commercial software ABAQUS with user-defined element subroutines. The layered system of finite elements is utilized to solve the coupled elastic displacement and phase-field fracture problem. A one-element benchmark test compared with the analytical solution was conducted to validate the feasibility and accuracy of the developed method. Our More >

Sai Li¹, Xin Lai^2,*, Lisheng Liu³

CMES-Computer Modeling in Engineering & Sciences, Vol.131, No.2, pp. 715-746, 2022, DOI:10.32604/cmes.2022.018544 - 14 March 2022

Abstract In this work, we modeled the brittle fracture of shell structure in the framework of Peridynamics Mindlin-Reissener shell theory, in which the shell is described by material points in the mean-plane with its drilling rotation neglected in kinematic assumption. To improve the numerical accuracy, the stress-point method is utilized to eliminate the numerical instability induced by the zero-energy mode and rank-deficiency. The crack surface is represented explicitly by stress points, and a novel general crack criterion is proposed based on that. Instead of the critical stretch used in common peridynamic solid, it is convenient to More >