Abstract
A numerical technique of high-order piecewise parabolic method in combination of HLLD (”D” denotes Discontinuities) Riemann solver is developed for the numerical simulation of elastic-plastic flow. The introduction of the plastic effect is realized by decomposing the total deformation gradient tensor as the product of elastic and plastic deformation gradient tensors and adding plastic source term to the conservation law model equation with the variable of the elastic deformation gradient tensor. For the solution of the resulting inhomogeneous equation system, a temporal splitting strategy is adopted and a semi-implicit scheme is performed to solve the ODES in the plastic step, which is conducted to account for the contributions from plastic source terms. As seen from the results of test cases involving large deformation and high strain rate, the computational model used can reflect the characteristics of constitutive relation of material under strong impact action and our numerical method can realize the exact simulation of the elastic-plastic behavior of solid material, especially the accurate capture of the elastic-plastic waves. Further, it could also deal with high-speed impact problems with multi-material components, catching material interfaces correctly and keeping the interfaces sharp, when combined with interface tracking technique such as the level-set algorithm.
Highlights
The elastic-plastic flow problem of solid material under high-load conditions are often encountered in martial and industrial applications
This paper has constructed the Piecewise Parabolic Method (PPM) method suitable for the elastic-plastic deformation problem of solid material under the impact action. This method is based on the elastic-plastic model equation under Eulerian framework, which is formed by the addition of plastic source term into the elastic model equation with deformation gradient tensor as the original variables
With the purpose of extending the numerical technique of PPM + HLLD to the elastic-plastic problem, the difficulty lies in the fact that the plastic source term may range from zero to positive infinity, leading to very small time scale with potentially quite high strain rate
Summary
The elastic-plastic flow problem of solid material under high-load conditions are often encountered in martial and industrial applications. This description way is only applicable to perfect plasticity and has some difficulty in the achievement of the reflection of elastic-plastic shock wave on free interfaces Another way to depict plastic behavior based on hyperelastic model is to decompose the total deformation tensor (deformation gradient tensor or its inverse) into the two parts of elastic and plastic deformation by using multiplicative decomposition method and to realize the characterization of plastic effect by means of the additional source term. Considering that elastic-plastic shock wave and discontinuousness exist in the elastic-plastic flow problem widely and the numerical method of Godunov type has been proven to have apparent superiority for capturing both shock wave and discontinuousness in fluid mechanics, it is natural to extend the use of high-order scheme of Godunov type based on the solution of local Riemann problem to solid mechanics in Eulerian framework, in case that the control equations are constructed to be of properly conservative form. The numerical scheme of Godunov type with higher order accuracy, such as Piecewise Parabolic Method (PPM) which has third-order accuracy and stronger ability of processing discontinuousness, has not been utilized in the problem of elastic-plastic deformation
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