Bond-associated non-ordinary state-based peridynamic model for multiple spalling simulation of concrete

The non-ordinary state-based peridynamic(NOSB PD)model has the capability of incorporating existing constitutive relationships in the classical continuum mechanics.In the present work,we first develop an NOSB PD model corresponding to the Johnson–Holmquist II(JH-2)constitutive damage model,which can describe the severe damage of concrete under intense impact compression.Besides,the numerical oscillation problem of the NOSB PD caused by zero-energy mode is analyzed and hence a bond-associated non-ordinary state-based peridynamic(BA-NOSB PD)model is adopted to remove the oscillation.Then,the elastic deformation of a three-dimensional bar is analyzed to verify the capability of BA-NOSB PD in eliminating the numerical oscillation.Furthermore,concrete spalling caused by the interaction of incident compression wave and reflected tension wave is simulated.The dynamic tensile fracture process of concrete multiple spalling is accurately reproduced for several examples according to the spalling number and spalling thickness analysis,illustrating the approach can well simulate and analyze the concrete spalling discontinuities.

Simulation of Inviscid Compressible Flows Using PDE Transform

The solution of systems of hyperbolic conservation laws remains an interesting and challenging task due to the diversity of physical origins and complexity of the physical situations.The present work introduces the use of the partial differential equation(PDE)transform,paired with the Fourier pseudospectral method(FPM),as a new approach for hyperbolic conservation law problems.The PDE transform,based on the scheme of adaptive high order evolution PDEs,has recently been applied to decompose signals,images,surfaces and data to various target functional mode functions such as trend,edge,texture,feature,trait,noise,etc.Like wavelet transform,the PDE transform has controllable time-frequency localization and perfect reconstruction.A fast PDE transform implemented by the fast Fourier Transform(FFT)is introduced to avoid stability constraint of integrating high order PDEs.The parameters of the PDE transform are adaptively computed to optimize the weighted total variation during the time integration of conservation law equations.A variety of standard benchmark problems of hyperbolic conservation laws is employed to systematically validate the performance of the present PDE transform based FPM.The impact of two PDE transform parameters,i.e.,the highest order and the propagation time,is carefully studied to deliver the best effect of suppressing Gibbs’oscillations.The PDE orders of 2-6 are used for hyperbolic conservation laws of low oscillatory solutions,while the PDE orders of 8-12 are often required for problems involving highly oscillatory solutions,such as shock-entropy wave interactions.The present results are compared with those in the literature.It is found that the present approach not only works well for problems that favor low order shock capturing schemes,but also exhibits superb behavior for problems that require the use of high order shock capturing methods.