Yongchang Cai

Dual‐horizon peridynamics

Summary In this paper, we develop a dual-horizon peridynamics (DH-PD) formulation that naturally includes varying horizon sizes and completely solves the ‘ghost force’ issue. Therefore, the concept of dual horizon is introduced to consider the unbalanced interactions between the particles with different horizon sizes. The present formulation fulfills both the balances of linear momentum and angular momentum exactly. Neither the ‘partial stress tensor’ nor the ‘slice’ technique is needed to ameliorate the ghost force issue. We will show that the traditional peridynamics can be derived as a special case of the present DH-PD. All three peridynamic formulations, namely, bond-based, ordinary state-based, and non-ordinary state-based peridynamics, can be implemented within the DH-PD framework. Our DH-PD formulation allows for h-adaptivity and can be implemented in any existing peridynamics code with minimal changes. A simple adaptive refinement procedure is proposed, reducing the computational cost. Both two-dimensional and three-dimensional examples including the Kalthoff–Winkler experiment and plate with branching cracks are tested to demonstrate the capability of the method. Copyright

HIGH ROCK SLOPE STABILITY ANALYSIS USING THE ENRICHED MESHLESS SHEPARD AND LEAST SQUARES METHOD

The meshless methods are particularly suitable for modeling problems with discontinuities such as joints in rock mass. The meshless Shepard and least squares (MSLS) method is a newly developed meshless method, which overcomes some limitations with other meshless methods. In the present paper, the MSLS method is extended for modeling jointed rock mass and the joint is modeled as discontinuity governing the near-field stress. A substantial high rock slope by the dam shoulder of Jinping Hydropower Station is analyzed by the developed method. Safety factors are evaluated based on the stress results along potential slip surfaces and compared with the conventional slice methods. The results demonstrate the feasibility of using the MSLS method in rock slope stability analysis and also reveal some interesting differences from the conventional slice methods. Some findings and outstanding issues demonstrated in this study are discussed in the end, which can be the topics for future development.

A Meshless Local Petrov-Galerkin Shepard and Least-Squares Method Based on Duo Nodal Supports

The meshless Shepard and least-squares (MSLS) interpolation is a newly developed partition of unity- (PU-) based method which removes the difficulties with many other meshless methods such as the lack of the Kronecker delta property. The MSLS interpolation is efficient to compute and retain compatibility for any basis function used. In this paper, we extend the MSLS interpolation to the local Petrov-Galerkin weak form and adopt the duo nodal support domain. In the new formulation, there is no need for employing singular weight functions as is required in the original MSLS and also no need for background mesh for integration. Numerical examples demonstrate the effectiveness and robustness of the present method.

ARBITRARY DISCONTINUITIES IN THE NUMERICAL MANIFOLD METHOD

An overview of modeling arbitrary discontinuities within the numerical manifold method (NMM) framework is presented. The NMM employs a dual cover system, namely mathematical covers (MCs) and physical covers (PCs), to describe a physical problem. MCs are constructed totally independent of geometries of the problem domain, over which a partition of unity is defined. PCs are the intersections of MCs and the problem domain, over which local approximations with unknowns to be determined are defined. With such a dual cover system, arbitrary discontinuities involving jumps, kinks, singularities, and other nonsmooth features can be modeled in a convenient manner by constructing special PCs and designing tailored local approximations. Several typical discontinuities in solid mechanics are discussed. Among them are the simulations of material boundaries, voids, brittle cracks, cohesive cracks, material interfaces, interface cracks, dislocations, shear bands, high gradient zones, etc.

Method for Estimating Normal Contact Parameters in Collision Modeling Using Discontinuous Deformation Analysis

AbstractThis paper presents a contact parameter estimation method for collision modeling using discontinuous deformation analysis (DDA). Most DDA codes and discrete element method (DEM) codes use the viscoelastic contact model for contact-stress calculation. The contact parameters of the viscoelastic contact model, such as normal stiffness and damping constant, affect the computation results observably. Although the DDA method has been proposed for more than 20 years, the contact parameters in DDA modeling are still difficult to determine. In collision dynamics, the coefficient of restitution (COR) is considered the critical parameter for describing the changes of motion state after collision between two objects. In the proposed method, the normal COR is used for evaluating calculation results of rockfall modeling with three-dimensional DDA. The normal COR of the two-object model is obtained by tests or empirical methods. The relation curve of contact parameters and the normal COR is generated on the basi...

Modelling 3D rock slope with a single elliptic joint surface by a meshless method

Summary Meshless methods have shown advantages in dealing with problems of moving interfaces such as crack propagation in rock. In Tongji University, meshless methods, the meshless Shepard and least squares (MSLS) method and the element-free Galerkin (EFG) method have been applied to slope stability analysis, especially for rock slope stability governed by a number of dominating discontinuities. Previous studies have focused on 2D problems where a joint surface is modelled as a crack line [1]. In this paper, the EFG method is extended for analyzing 3D rock slope with a single planner elliptic joint. Due to the increasing complexity in geometric description of joint surface in 3D, level set functions are utilized to describe the curved joint front and to capture the joint propagation [2]. Preliminary testing results are presented showing the performance of the proposed method. Remaining issues to be addressed in further studies are discussed, namely, the use of level sets for intersecting joints and the construction of meshless approximation for cohesive zone ahead of joint front.