Contact detection between interacting blocks is of great importance to discontinuity-based numerical methods, such as DDA, DEM, and NMM. A rigorous contact theory is a prerequisite to describing the interactions of mu...Contact detection between interacting blocks is of great importance to discontinuity-based numerical methods, such as DDA, DEM, and NMM. A rigorous contact theory is a prerequisite to describing the interactions of multiple blocks. Currently, the penalty method, in which mathematical springs with high stiffness values are employed, is always used to calculate the contact forces. High stiffness values may cause numerical oscillations and limit the time step. Furthermore, their values are difficult to identify. The intention of this study is to present a two-scale contact model for the calculation of forces between colliding blocks. In this new model, a calculation step taken from the moment of contact will be divided into two time stages: the free motion time stage and the contact time stage. Actually, these two time stages correspond to two real physical processes. Based on this, we present a new numerical model that is intended to be more precise and useful in calculating the contact forces without mathematical springs. The propagation of the elastic wave during collision is of a characteristic length, which determines the volume of material involved in the contact force calculation. In conventional contact models, this range is always regarded as the length of one element, which may lead to an inaccurate calculation of contact forces. In fact, the real scale of this range is smaller than the length of a single element, and subdivided elements, which are refined according to the characteristic length and are presented in the new contact model.展开更多
The XFEM(extended finite element method) has a lot of advantages over other numerical methods to resolve discontinuities across quasi-static interfaces due to the jump in fluidic parameters or surface tension.However,...The XFEM(extended finite element method) has a lot of advantages over other numerical methods to resolve discontinuities across quasi-static interfaces due to the jump in fluidic parameters or surface tension.However,singularities corresponding to enriched degrees of freedom(DOFs) embedded in XFEM arise in the discrete pressure Poisson equations.In this paper,constraints on these DOFs are derived from the interfacial equilibrium condition and introduced in terms of stabilized Lagrange multipliers designed for non-boundary-fitted meshes to address this issue.Numerical results show that the weak and strong discontinuities in pressure with straight and circular interfaces are accurately reproduced by the constraints.Comparisons with the SUPG/PSPG(streamline upwind/pressure stabilizing Petrov-Galerkin) method without Lagrange multipliers validate the applicability and flexibility of the proposed constrained algorithm to model problems with quasi-static interfaces.展开更多
基金supported by the National Basic Research Program of China("973"Project)(Grant No.2015CB250903)the CAS Strategic Priority Research Program(B)(Grant No.XDB10030303)+1 种基金the National Key Technology Research and Development Program of the Ministry of Science and Technology of China(Grant No.2012BAK10B01)the Youth Science Fund of the National Natural Science Foundation of China(Grant No.11302230)
文摘Contact detection between interacting blocks is of great importance to discontinuity-based numerical methods, such as DDA, DEM, and NMM. A rigorous contact theory is a prerequisite to describing the interactions of multiple blocks. Currently, the penalty method, in which mathematical springs with high stiffness values are employed, is always used to calculate the contact forces. High stiffness values may cause numerical oscillations and limit the time step. Furthermore, their values are difficult to identify. The intention of this study is to present a two-scale contact model for the calculation of forces between colliding blocks. In this new model, a calculation step taken from the moment of contact will be divided into two time stages: the free motion time stage and the contact time stage. Actually, these two time stages correspond to two real physical processes. Based on this, we present a new numerical model that is intended to be more precise and useful in calculating the contact forces without mathematical springs. The propagation of the elastic wave during collision is of a characteristic length, which determines the volume of material involved in the contact force calculation. In conventional contact models, this range is always regarded as the length of one element, which may lead to an inaccurate calculation of contact forces. In fact, the real scale of this range is smaller than the length of a single element, and subdivided elements, which are refined according to the characteristic length and are presented in the new contact model.
文摘The XFEM(extended finite element method) has a lot of advantages over other numerical methods to resolve discontinuities across quasi-static interfaces due to the jump in fluidic parameters or surface tension.However,singularities corresponding to enriched degrees of freedom(DOFs) embedded in XFEM arise in the discrete pressure Poisson equations.In this paper,constraints on these DOFs are derived from the interfacial equilibrium condition and introduced in terms of stabilized Lagrange multipliers designed for non-boundary-fitted meshes to address this issue.Numerical results show that the weak and strong discontinuities in pressure with straight and circular interfaces are accurately reproduced by the constraints.Comparisons with the SUPG/PSPG(streamline upwind/pressure stabilizing Petrov-Galerkin) method without Lagrange multipliers validate the applicability and flexibility of the proposed constrained algorithm to model problems with quasi-static interfaces.
