Smoothed point interpolation methods for the regularization of material instabilities in scalar damage models

Abstract

Summary The nonlocal character embedded in the formulation of smoothed point interpolation methods is exploited, in order to regularize the behavior of the simulations of scalar damage problems affected by strain localization. The use of these methods is made possible by the extension of the weakened weak form that they are based on to the case of elastic‐degrading media, with specific focus on the scalar damage case. The provided numerical simulations emphasize the regularization effects of this class of meshfree methods and the improved mesh objectivity with respect to the standard finite element method. Different strategies for support node selection are considered, pointing out the role played by the size of the support domains regarding the regularization effects.

Meshless smoothed point interpolation methods for damage modelling

“…Among the methods that have been shown to possess certain regularisation effects in localisation problems there are moving least square (MLS) and reproducing kernel (RK) approximations, as well as methods based on strain smoothing techniques [Liu et al, 1999, Li et al, 2000, Chen et al, 2004, 2007, Wang and Li, 2012, Pozo et al, 2014. As strain smoothing methods, also the smoothed point interpolation methods (SPIMs) discussed in this manuscript have been shown to exhibit regularisation properties, as illustrated by Gori et al [Gori et al, 2019b], both alone as well as when combined with other regularisation strategies, like the micropolar continuum theory [Gori et al, 2019a,c]. Particle methods, like the SPH, have also been shown to be capable to deal with strain-softening problems [Vignjevic et al, 2014].…”

“…The first application of SPIM strategies to the modelling of damage problems was proposed by Gori et al [2019b], where the authors also pointed out the regularisation properties induced by the SPIM approach; later, in Saliba et al [2021], a strategy was proposed to analyse damage models with a coupled SPIM-FEM model. Some of the results discussed in Gori et al [2019b] are recalled in this section.…”

“…As discussed by Gori et al [2019b], the main issue for the application of SPIM strategies to elastic-degradation is the transition from Eq. 40 to Eq.…”

“…where the admissible variation of the smoothed strain tensor (δ ε) coincides with its rate ( ˙ ε), and where the tangent constitutive operator Êt is the one defined in Eq. 56 (see Gori et al [2019b] for further details). The linearised weakened-weak form can then be recast into: find the increments δ ū ∈ δV(D) such that…”

A computational framework for the constitutive modeling of nonlinear micropolar media

“…These properties are due to the use of tensor objects for the numerical representation of the constitutive equations, as proposed by Jeremić and its co-authors in earlier works [36][37][38]. The versatility of such approach to constitutive modeling has been shown in a number of works, where the proposed computational framework has been also applied to the Boundary Element Method (BEM) [39], the Generalized/Extended Finite Element Method (G/XFEM) [40], the hp-Cloud meshfree method [41], and the Smoothed Point Interpolation Methods [42].…”