Static and dynamic mechanical behaviors of cracked Mindlin plates in ordinary state-based peridynamic framework

Abstract

An ordinary state-based peridynamic (PD) model based on the Mindlin plate theory is pre sented to deal with fracture mechanics problems. Static and dynamic stress resultant intensity factors regarded as the primary fracture parameters for plate structures are evaluated by the displacement extrapolation method. Owing to the PD surface effect, however, the accuracy of the displacement field near crack surfaces is significantly affected. Therefore, the arbitrary horizon domain method is adopted to correct the surface effect. It derives the variable PD parameters to properly describe mechanical behaviors for each material point. Several numerical examples are investigated to examine the per formance of the presented method. It indicates that the PD Mindlin plate model incorporated with the arbitrary horizon domain method validly minimizes the influence from the PD surface effect and provides an effective approach to evaluate static and dynamic moment intensity factors. Keywords Peridynamics • Plate structures • Arbitrary horizon domain • PD surface effect • Moment intensity factors 1 IntroductionPeridynamics (PD) [1,2], which does not require spatial derivatives in its governing equations, has been developed to simulate different kinds of complicated fracture problems. For thin-walled struc tures, a shell model is an effective approach with less computation time than a 3D solid model. In the shell model, 2D plane stress and plate bending formulae are adopted to treat in-plane and out of-plane deformations, respectively. However, in contrast to 2D plane stress problems, the studies in plate bending problems are relatively few in the PD literature. O'Grady and Foster derived a non ordinary state-based peridynamic (NOSPD) model for Kirchhoff-Love plates [3] and shells [4] from the concept of rotational springs between interaction bonds. Diyaroglu et al.[5] developed a bond-based peridynamic (BBPD) model for beams and plates with transverse shear deformation. Chowdhury et al. [6] intro<lnc.e<l a surfar.e-ha. <;e<l NOSPD mo<lel with c.nrve<l hon<ls for linear elastic. shells. Nguyen

Dynamic analysis of cracked plates based on a first-order shear deformation theory formulation by using an extended meshfree method

“…Figure 14 shows the variation of the normalized 1 K with respect to time. The XMK result is compared to the Peridynamic solution in reference [41], showing good agreement. During the examined time period in the figure, the normalized 1 K trivially decreases at the beginning then turns to rise sharply and peaks, after that falls sharply.…”

“…The variation of the normalized 1 K with respect to time is shown in Figure 8. The XMK result is compared to the Peridynamic solution in reference [41], showing good agreement. In both methods, the curve has the same shape.…”

“…The normalized DSIF is shown in Figure 11 for the CCCC case and Figure 12 for the SSSS case. The XMK result is compared to the Peridynamic solution in reference [41], showing good agreement. In both figures, the curves of both methods have the same shape.…”

“…Nevertheless, the number of studies on fracture analysis of cracked plates using extended meshfree methods is still limited, especially dynamic fracture analysis. Dynamic fracture analysis for bending plates is a challenging problem, a small number of publications on this topic can be mentioned as follows: dynamic fracture analysis of Kane-Mindlin plates by using the dual boundary element method (DBEM) [38], using DBEM [39] and dual reciprocity BEM (DRBEM) [40] for dynamic analysis of cracked Reissner-Mindlin plates (also known as the FSDT plate), the Peridynamic (PD) approach for solving dynamic cracked Mindlin plates is shown in [41]. In the scope of this study, dynamic analysis of cracked FSDT plates is conducted by using the extended MK (XMK) for the first time.…”

Shear rupture mechanism and dissipation phenomena in bias-extension test of pantographic sheets: Numerical modeling and experiments

“…The genesis in conceiving the pantographic sheet can be traced back in the grounding idea of non-local materials, and in particular of second or higher gradient theories [28][29][30][31][32][33][34][35][36][37], in which the constitutive law is a function also of the second or higher gradient of the displacement field. In the same context of non-local formulation, it is worth mentioning the peridynamic approach proposed, among the others, in previous studies [38][39][40][41][42].…”