Peridynamics is a theory of continuum mechanics employing a nonlocal model that can simulate fractures and discontinuities (Askari et al. J Phys 125:012–078, 2008; Silling J Mech Phys Solids 48(1):175–209, 2000). It reformulates continuum mechanics in forms of integral equations rather than partial differential equations to calculate the force on a material point. A connection between bond forces and the stress in the classical (local) theory is established for the calculation of peridynamic stress, which is calculated by summing up bond forces passing through or ending at the cross section of a node. The peridynamic stress and the constitutive law in elasticity are used for the derivation of one- and three-dimensional numerical micromoduli. For three-dimensional discretized peridynamics, the numerical micromodulus is larger than the analytical micromodulus, and converges to the analytical value as the horizon to grid spacing ratio increases. A comparison of material responses in a three-dimensional discretized peridynamic model using numerical and analytical micromoduli, respectively, is performed for different horizons. As the horizon increases, the boundary effect is more conspicuous, and the errors increase in the back-calculated Young’s modulus and strains. For the simulation of materials of Poisson’s ratios other than 1/4, a pairwise compensation scheme for discretized peridynamics is proposed. Compared with classical (local) elasticity solutions, the computational results by applying the proposed scheme show good agreement in the strain, the resultant Young’s modulus and Poisson’s ratio.
Peridynamics Continuum mechanics Nonlocal theory
This is a preview of subscription content, log in to check access.
Bobaru F (2007) Influence of Van der Waals forces on increasing the strength and toughness in dynamic fracture of nanofibre networks: a peridynamic approach. Model Simul Mater Sci Eng 15: 397CrossRefGoogle Scholar
Bobaru F, Yang M, Alves LF, Silling SA, Askari E, Xu J (2009) Convergence, adaptive refinement, and scaling in 1D peridynamics. Int J Numer Methods Eng 77(6): 852–877zbMATHCrossRefGoogle Scholar
Emmrich E, Weckner O (2006) The peridynamic equation of motion in non-local elasticity theory. In: III European conference on computational mechanics. Solids, structures and coupled problems in engineering, vol 19. Springer, LisbonGoogle Scholar
Emmrich E, Weckner O (2007) On the well-posedness of the linear peridynamic model and its convergence towards the Navier equation of linear elasticity. Commun Math Sci 5(4): 851–864MathSciNetzbMATHGoogle Scholar
Ercolessi F (1997) A molecular dynamics primer. Spring College in Computational Physics, ICTP, Trieste, pp 24–25Google Scholar
Foster JT, Silling SA, Chen WW (2009) Viscoplasticity using peridynamics. Int J Numer Methods Eng 81(10): 1242–1258Google Scholar
Foulk JW, Allen DH, Helms KLE (2000) Formulation of a three-dimensional cohesive zone model for application to a finite element algorithm. Comput Methods Appl Mech Eng 183(1–2): 51–66zbMATHCrossRefGoogle Scholar
Gerstle W, Sau N, Silling SA (2005) Peridynamic modeling of plain and reinforced concrete structures. In: SMiRT18: 18th Int. conf. struct. mech. react. technol., BeijingGoogle Scholar
Gerstle W, Sau N, Silling SA (2007) Peridynamic modeling of concrete structures. Nucl Eng Des 237(12–13): 1250–1258CrossRefGoogle Scholar
Gils MAJV, van der Sluis O, Zhang GQ, Janssen JHJ, Voncken RMJ (2007) Analysis of Cu/low-k bond pad delamination by using a novel failure index. Microelectron Reliab 47(2–3): 179–186Google Scholar
Ha YD, Bobaru F (2010) Studies of dynamic crack propagation and crack branching with peridynamics. Int J Fract 162(1–2): 229–244zbMATHCrossRefGoogle Scholar
Tay TE (2003) Characterization and analysis of delamination fracture in composites: an overview of developments from 1990 to 2001. Appl Mech Rev 56: 1CrossRefGoogle Scholar
Warren TL, Silling SA, Askari A, Weckner O, Epton MA, Xu J (2009) A non-ordinary state-based peridynamic method to model solid material deformation and fracture. Int J Solids Struct 46(5): 1186–1195zbMATHCrossRefGoogle Scholar