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Abstract: In Problems with large deformation including fracture and fragmentation, the grid based methods have some limitations which make them unsuitable for simulating these types of problems. An example is extreme mesh distortion in a lagrangian approach like Finite element method. Another situation is the inability of Eulerian based formulations in tracking the history of a desired physical property at the interface of multi materials including impact problems. A promising solution is taking the advantage of meshless and particle based methods which do not use any kind of grid in the physical domain of problem. In this paper, corrective smoothed particle algorithm (CSPM) as a meshless particle method is used to study the mechanical behavior of a ceramic–metal functionally graded material (FGM) under high velocity impact conditions. A mixed strength model with sigmoid formulation has been used to describe both yielding and fracture phenomena in the FGM. The strength model includes the JC dynamic yield relation and Johnson–Holmquist–Beissel (JHB) fracture model with a continuum damage description approach. An efficient renormalization in continuity density approach is used to improve the smoothed particle hydrodynamics (SPH) approximation of boundary physical variables. This study shows that CSPM in combination with the proper strength model describing the FGM dynamic behavior, can predict the mixed plastic and brittle response of a ceramic–metal functionally graded material under high impact velocities. [Copyright &y& Elsevier]

Abstract: In this paper, the corrective smoothed particle method (CSPM) numerical algorithm as a modification of traditional SPH particle method has been employed to predict fracture and fragmentation in ceramics using a thermo-mechanical basis under hypervelocity impact conditions. In order to study the brittle behavior in ceramic, the JHB computational constitutive model which considers phase transition in a solid continuum has been applied. An appropriate heat conduction equation has been coupled with the Johnson–Cook yield criteria in order to get more accurate temperature field especially in impact zone which consequently gives a more exact solution in such problems coming with highly produced magnitude of pressure and temperature in the material. It has been shown that implementation of the CSPM scheme with a thermo-mechanical basis can predict the brittle fracture and fragmentation in ceramics under hyper velocity impact conditions. [Copyright &y& Elsevier]

A meshless shell method for large deformation and a linear relation between the Cauchy stress tensor and the Almansi strain tensor based on the corrective smoothed particle method (CSPM) is presented in this paper. Due to the use of the shell theory, only one layer of particles in the reference plane is required to discretize the shell model. The CSPM combining the kernel estimate with the Taylor series expansion is adopted, which resolves the general problems of low precision and particle deficiency in standard smoothed particle hydrodynamics (SPH). The discrete governing equations of the shell in the strong form are derived using the conservation condition and the CSPM interpolation function. Aiming at the sore point of the free boundary in the meshless method, the developed model enables the modified governing equations to automatically satisfy the free boundary condition without additional treatment. Moreover, the total Lagrangian kernel function and stress points are employed to eliminate tensile instability and instability induced by the rank deficiency. Finally, several numerical examples are used to verify the validity and accuracy of the meshless shell model. [ABSTRACT FROM AUTHOR]

This paper presents a meshless model for quasi-static and dynamic analysis of a three-dimensional Timoshenko beam with geometric nonlinearity. A general mathematical formulation is constructed based on the corrective smoothed particle method (CSPM), which can correct the low precision and completeness deficiency of the standard smoothed particle hydrodynamics(SPH) method. The discrete governing equations as well as the boundary conditions in strong form for the three-dimensional beam are then derived by using the conservation conditions and the CSPM interpolation function. The developed model enables one to expediently discretize the geometric nonlinear beam with only a row of particles at the central axis and to automatically satisfy the free boundary condition without any additional treatment. Moreover, Lagrangian kernel function and stress points are adopted to eliminate tensile instability and instability induced by the rank deficiency within the particle methods. Finally, comparisons with several results obtained from the existing literature are provided to demonstrate the validity and potential of the present procedure. • A three-dimensional meshless beam model with geometric nonlinearity is presented. • The beam formulation is constructed using the corrective smoothed particle method. • A free boundary treatment method is proposed for the meshless beam formulation. [ABSTRACT FROM AUTHOR]