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A stabilized non-ordinary state-based peridynamic model. (English) Zbl 1440.74028
Summary: Non-ordinary state-based peridynamics suffers from zero-energy modes due to nodal integration, causing instabilities of the displacement, stress and strain fields. A stabilized non-ordinary state-based peridynamic model is derived according to the linearized bond-based peridynamic theory. The incorporation of supplemented force state excludes a zero-energy modes control coefficient and eliminates the need for complicated parameter adjustment. Finally, the parameter of strain energy ratio is defined to study the degree of influence of the zero-energy modes on the computation process. Four numerical examples are analyzed to demonstrate the effectiveness of the present model in controlling the zero-energy modes in non-ordinary state-based peridynamics.

MSC:
74A45 Theories of fracture and damage
74S05 Finite element methods applied to problems in solid mechanics
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[1] Silling, S. A.; Lehoucq, R. B., Peridynamic theory of solid mechanics, Adv. Appl. Mech., 44, 73-168 (2010)
[2] Silling, S. A.; Bobaru, F., Peridynamic modeling of membranes and fibers, Int. J. Non-Linear Mech., 40, 395-409 (2005) · Zbl 1349.74231
[3] Silling, S. A.; Askari, E., A meshfree method based on the peridynamic model of solid mechanics, Comput. Struct., 83, 1526-1535 (2005)
[4] Gerstle, W.; Sau, N.; Silling, S. A., Peridynamic modeling of concrete structures, Nucl. Eng. Des., 237, 1250-1258 (2007)
[5] Kilic, B.; Agwai, A.; Madenci, E., Peridynamic theory for progressive damage prediction in center-cracked composite laminates, Compos. Struct., 90, 141-151 (2009)
[6] Foster, J. T., Dynamic Crack Initiation Toughness: Experiments and Peridynamic Modeling, 2009-7217 (2009), Puedue University: Puedue University Albuquerque, New Mexico, Reprinted in SAND2009-7217
[7] Madenci, E.; Oterkus, E., Peridynamic Theory and its Applications (2014), Springer: Springer New York, NY · Zbl 1295.74001
[8] Silling, S. A.; Epton, M.; Wechner, O.; Xu, J.; Askari, E., Peridynamic states and constitutive modeling, J. Elasticity, 88, 151-184 (2007) · Zbl 1120.74003
[9] Warren, T. L.; Silling, S. A.; Askari, A.; Weckner, O.; Epton, M. A.; Xu, J., A non-ordinary state-based peridynamic method to model solid material deformation and fracture, Int. J. Solids Struct., 46, 1186-1195 (2009) · Zbl 1236.74012
[10] Foster, J. T.; Silling, S. A.; Chen, W. W., Viscoplasticity using peridynamics, Internat. J. Numer. Methods Engrg., 81, 1242-1258 (2010) · Zbl 1183.74035
[11] Ganzenmuller, G. C.; Hiermaier, S.; May, M., On the similarity of meshless discretizations of peridynamics and smooth-particle hydrodynamics, Comput. Struct., 150, 71-78 (2015)
[12] Beissel, S.; Belytschko, T., Nodal integration of the element-free Galerkin method, Comput. Methods Appl. Mech. Engrg., 139, 49-74 (1996) · Zbl 0918.73329
[13] Duan, Q. L.; Li, X. K.; Zhang, H. W.; Wang, B. B.; Gao, X., Quadratically consistent one-point (QC1) quadrature for meshfree Galerkin methods, Comput. Methods Appl. Mech. Engrg., 245-246, 256-272 (2012) · Zbl 1354.74266
[14] Littlewood, D. J., A nonlocal approach to modeling crack nucleation in AA 7075-T651, IMECE2011-64236, (ASME 2011 International Mechanical Engineering Congress and Exposition (2011), American Society of Mechanical Engineers), 567-576
[15] Breitenfeld, M. S.; Geubelle, P. H.; Weckner, O.; Silling, S. A., Non-ordinary state-based peridynamic analysis of stationary crack problems, Comput. Methods Appl. Mech. Engrg., 272, 233-250 (2014) · Zbl 1296.74099
[16] Breitenfeld, M. S., Quasi-Static Non-Ordinary State-Based Peridynamics for the Modeling of 3D Fracture (2014), University of Illinois at Urbana-Champaign, (Ph.D. dissertation)
[17] Wu, C. T.; Ren, B., A stabilized non-ordinary state-based peridynamics for the nonlocal ductile material failure analysis in metal machining process, Comput. Methods Appl. Meth. Eng., 291, 197-215 (2015) · Zbl 1423.74067
[18] R. Becker, R.L. Lucas, An assessment of peridynamics for pre and post failure deformation, No. ARL-TR-5811. Army research lab Aberdeen proving ground md weapons and materials research directorate, 2011.
[19] Yaghoobi, A.; Chorzepa, M. G., Higher-order approximation to suppress the zero-energy mode in non-ordinary state-based peridynamics, Comput. Struct., 188, 63-79 (2017)
[20] Silling, S. A., Stability of peridynamic correspondence material models and their particle discretization, Comput. Methods Appl. Mech. Engrg., 322, 42-57 (2017)
[21] Yaghoobi, A.; Chorzepa, M. G.; Kim, S. S.; Durham, S. A., Mesoscale fracture analysis of multiphase cementitious composites using peridynamics, Materials, 10, 162 (2017)
[22] Ouchi, H., Development of Peridynamics-Based Hydraulic Model for Fracture Growth in Heterogeneous Reservoirs (2016), The University of Texas: The University of Texas Austin, (Ph.D. dissertation)
[23] Huang, D.; Lu, G. D.; Qiao, P. Z., An improved peridynamic approach for quasi-static elastic deformation and brittle fracture analysis, Int. J. Mech. Sci., 94- 95, 111-122 (2015)
[24] Foster, J. T.; Silling, S. A.; Chen, W., An energy based failure criterion for use with peridynamic states, Int. J. Multiscale Comput., 9, 675-688 (2011)
[25] Zhou, X. P.; Wang, Y. T.; Xu, X. M., Numerical simulation of initiation, propagation and coalescence of cracks using the non-ordinary state-based peridynamics, Int. J. Fract., 201, 213-234 (2016)
[26] Kilic, B.; Madenci, E., An adaptive dynamic relaxation method for quasi-static simulations using the peridynamic theory, Theor. Appl. Fract. Mech., 53, 194-204 (2010)
[27] Underwood, P., Dynamic relaxation, Comput. Methods Trans. Anal., 1, 245-265 (1983)
[28] Sauve, R. G.; Metzger, D. R., Advances in dynamic relaxation techniques for nonlinear finite element analysis, J. Press. Vessel Technol., 117, 170-176 (1997)
[29] Silling, S. A., Reformulation of elasticity theory for discontinuities and long-range forces, J. Mech. Phys. Solids, 48, 175-209 (2000) · Zbl 0970.74030
[30] Macek, R. W.; Silling, S. A., Peridynamics via finite element analysis, Finite Elem. Anal. Des., 43, 1169-1178 (2007)
[31] Tan, H.; Liu, C.; Huang, Y.; Geubelle, P. H., The cohesive law for the particle/matrix interfaces in high explosives, J. Mech. Phys. Solids, 53, 1892-1917 (2005)
[32] Ayatollahi, M. R.; Aliha, M. R.M., Analysis of a new specimen for mixed mode fracture tests on brittle materials, Eng. Fract. Mech., 76, 1563-1573 (2009)
[33] Ravi-Chandar, K.; Knauss, W. G., An experimental investigation into dynamic fracture: II. Microstructural aspects, Int. J. Fract., 26, 65-80 (1984)
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