Mechanically driven mass diffusion in solids plays an important role in many technological processes. One of the most known effects is the so called hydrogen embrittlement, which may occur in metals containing an initially uniform dilute concentration of hydrogen. The phenomenon is characterized by a two-way interaction between mechanical and diffusive quantities: changes in mass concentration induce strains in the solid (swelling effect) and strain gradients induce mass fluxes (piezo-diffusive effect). The aim of this paper is to present some recent advances in the numerical analysis of these problems in the linear, steady state case. In the standard finite element setting based on assumed concentration and displacement, the presence of the strain gradient in the piezo-diffusive coupling term demands C1 continuous displacement interpolation, which is difficult to construct in spatial dimension higher than one. To avoid C1 continuity various techniques can be used. A mixed approach where displacements and volumetric strain are interpolated as independent variables was early explored by Girrens & Smith (1987). However, the computational effort increases and some inconsistency issues may arise. An alternative approach is to establish a staggered solution strategy in conjunction with a smoothing procedure. This method was employed by Garikipati et al. (2001) using the standard L2 projection. Here, a more efficient and accurate solution scheme is presented by resorting to a superconvergent patch-based recovery procedure, recently proposed by Ubertini (2004). Another possibility to avoid C1 continuity is to operate within the numerical setting of discontinuous Galerkin methods. Here, a new formulation which requires standard C0 interpolation for both displacement and concentration is proposed. The three approaches are discussed and compared by a benchmark test. The numerical results show that both the recovery-based and the discontinuous approach can be successfully applied.
S. de Miranda, L. Molari, F. Ubertini (2005). Recent advances in the analysis of mechanically driven mass diffusion in elastic solids. FIRENZE : Firenze University Press.
Recent advances in the analysis of mechanically driven mass diffusion in elastic solids
DE MIRANDA, STEFANO;MOLARI, LUISA;UBERTINI, FRANCESCO
2005
Abstract
Mechanically driven mass diffusion in solids plays an important role in many technological processes. One of the most known effects is the so called hydrogen embrittlement, which may occur in metals containing an initially uniform dilute concentration of hydrogen. The phenomenon is characterized by a two-way interaction between mechanical and diffusive quantities: changes in mass concentration induce strains in the solid (swelling effect) and strain gradients induce mass fluxes (piezo-diffusive effect). The aim of this paper is to present some recent advances in the numerical analysis of these problems in the linear, steady state case. In the standard finite element setting based on assumed concentration and displacement, the presence of the strain gradient in the piezo-diffusive coupling term demands C1 continuous displacement interpolation, which is difficult to construct in spatial dimension higher than one. To avoid C1 continuity various techniques can be used. A mixed approach where displacements and volumetric strain are interpolated as independent variables was early explored by Girrens & Smith (1987). However, the computational effort increases and some inconsistency issues may arise. An alternative approach is to establish a staggered solution strategy in conjunction with a smoothing procedure. This method was employed by Garikipati et al. (2001) using the standard L2 projection. Here, a more efficient and accurate solution scheme is presented by resorting to a superconvergent patch-based recovery procedure, recently proposed by Ubertini (2004). Another possibility to avoid C1 continuity is to operate within the numerical setting of discontinuous Galerkin methods. Here, a new formulation which requires standard C0 interpolation for both displacement and concentration is proposed. The three approaches are discussed and compared by a benchmark test. The numerical results show that both the recovery-based and the discontinuous approach can be successfully applied.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
