Abstract
When moving discontinuities in solids need to be simulated, standard finite element (FE) procedures usually attain low accuracy because of spurious oscillations appearing behind the discontinuity fronts. To assure an accurate tracking of traveling stress waves in heterogeneous media, we propose here a flux-corrected transport (FCT) technique for structured as well as unstructured space discretizations. The FCT technique consists of post-processing the FE velocity field via diffusive/antidiffusive fluxes, which rely upon an algorithmic length-scale parameter. To study the behavior of heterogeneous bodies featuring compliant interphases of any shape, a general scheme for computing diffusive/antidiffusive fluxes close to phase boundaries is proposed too. The performance of the new FE-FCT method is assessed through one-dimensional and two-dimensional simulations of dilatational stress waves propagating along homogeneous and composite rods.
Highlights
The propagation of waves in elastic solids is governed by a second-order, hyperbolic differential equation
finite element (FE) solution: diffusive and antidiffusive fluxes, the latter being appropriately limited in size, are handled to improve the discrete velocity field around the discontinuities, and to filter out spurious oscillations
In this paper we have proposed a finite element flux-corrected transport (FE-FCT) method for the simulation of stress wave propagation in homogeneous as well as heterogeneous bodies
Summary
The propagation of waves in elastic solids is governed by a second-order, hyperbolic differential equation. FE solution: diffusive and antidiffusive fluxes, the latter being appropriately limited in size, are handled to improve the discrete velocity field around the discontinuities, and to filter out spurious oscillations This method has been extensively used to simulate the propagation of shock waves in fluids [5, 6]; recently, it has been adopted to simulate traveling stress waves in solids [7]. The rationale behind the computation of diffusive/antidiffusive fluxes close to body or phase boundaries is revisited, so as to permit the treatment of compliant interphases confined along loci of zero measure (i.e. surfaces in three-dimensional frames and lines in two-dimensional frames) These two enhancements are of paramount importance when dynamic failure of quasi-brittle polycrystals (like, e.g., polysilicon) needs to be modeled, since damaging phenomena at the micro-scale are incepted as soon as the tensile strength is locally attained. As far as notation is concerned, a matrix one will be adopted throughout the whole paper with uppercase and lowercase bold symbols respectively denoting matrices and vectors, a superscript T standing for transpose, and a superposed dot representing time rates
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