Taylor, Michael; Steigmann, David J. A two-dimensional peridynamic model for thin plates. (English) Zbl 1330.74111 Math. Mech. Solids 20, No. 8, 998-1010 (2015). Summary: A general plate model based on the peridynamic theory of solid mechanics is presented. The model is derived as a two-dimensional approximation of the three-dimensional bond-based theory of peridynamics via an asymptotic analysis. The resulting plate theory is demonstrated using a specially designed peridynamics code to simulate the fracture of a brittle plate with a central crack under tensile loading. Cited in 21 Documents MSC: 74K20 Plates 74H10 Analytic approximation of solutions (perturbation methods, asymptotic methods, series, etc.) of dynamical problems in solid mechanics Keywords:peridynamics; plates; membranes; fracture PDFBibTeX XMLCite \textit{M. Taylor} and \textit{D. J. Steigmann}, Math. Mech. Solids 20, No. 8, 998--1010 (2015; Zbl 1330.74111) Full Text: DOI References: [1] Silling SA, J Mech Phys Solids 28 pp 175– (2000) · Zbl 0970.74030 [2] Camacho GT, Int J Solids Struct 33 (20) pp 2899– (1996) · Zbl 0929.74101 [3] DOI: 10.1002/(SICI)1097-0207(19990330)44:9<1267::AID-NME486>3.0.CO;2-7 · Zbl 0932.74067 [4] Elices M, Eng Frac Mech 69 pp 137– (2002) [5] Zhang Z, Int J Plast 21 pp 1195– (2005) · Zbl 1154.74391 [6] DOI: 10.1002/(SICI)1097-0207(19990910)46:1<131::AID-NME726>3.0.CO;2-J · Zbl 0955.74066 [7] Daux C, Int J Numer Meth Eng 48 pp 1741– (2000) · Zbl 0989.74066 [8] Moes N, Eng Frac Mech 69 pp 813– (2002) [9] Mariani S, Int J Numer Meth Eng 58 pp 103– (2003) · Zbl 1032.74673 [10] Silling SA, Int J Nonlin Mech 40 pp 395– (2005) · Zbl 1349.74231 [11] DOI: 10.1016/j.compstruc.2004.11.026 [12] Kilic B, Int J Frac 156 pp 165– (2009) · Zbl 1273.74455 [13] Silling SA, Int J Frac 162 (1) pp 219– (2010) · Zbl 1425.74045 [14] Ha Y, Int J Frac 162 (1) pp 229– (2010) · Zbl 1425.74416 [15] Ha Y, Eng Frac Mech 78 pp 1156– (2011) [16] Agwai A, Int J Frac 171 (1) pp 65– (2011) · Zbl 1283.74052 [17] Hu W, Comput Meth Appl Mech Eng 217 pp 247– (2012) · Zbl 1253.74008 [18] Oterkus E, J Mech Mat Struct 7 (1) pp 45– (2012) [19] DOI: 10.1007/s10659-007-9125-1 · Zbl 1120.74003 [20] Taylor M. Numerical simulation of thermo-elasticity, inelasticity and rupture in membrane theory. PhD Thesis, University of California, CA, 2008. [21] Foster JT, Int J Numer Meth Eng 81 pp 1242– (2010) [22] Weckner O, Int J Multisc Comput Eng 9 (6) pp 623– (2011) [23] Bobaru F, Int J Heat Mass Transf 53 (19) pp 4047– (2010) · Zbl 1194.80010 [24] Bobaru F, J Comput Phys 231 (7) pp 2764– (2012) · Zbl 1253.80002 [25] Bobaru F, Cent Eur J Eng 2 pp 551– (2012) [26] Parks ML, Comput Phys Comm 179 pp 777– (2008) · Zbl 1197.82014 [27] Gerstle W, 18th International Conference on Structural Mechanics in Reactor Technology (2005) [28] Oterkus E. Peridynamic theory for modeling three-dimensional damage growth in metallic and composite structures. PhD Thesis, University of Arizona, AZ, 2010. [29] Steigmann DJ, Math Mech Solids 13 pp 103– (2013) [30] Schlick T, Molecular Modeling and Simulation: An Interdisciplinary Guide (2010) · Zbl 1320.92007 [31] Juvinall RC, Fundamentals of Machine Component Design, 3. ed. (2000) [32] Song JH, Comput Mech 42 pp 239– (2008) · Zbl 1160.74048 [33] Katzav E, Int J Frac 143 pp 245– (2007) · Zbl 1197.74111 [34] Shi HJ, Int J Fatigue 22 pp 457– (2000) [35] Seelig T, J Mech Phys Solids 47 pp 935– (1999) · Zbl 0959.74058 [36] Bobaru F, Int J Frac 176 pp 215– (2012) This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.