Viscoelasticity Model for Peridynamics John A. Mitchell Sandia National Laboratories 1515 Eubank SE Albuquerque, NM 87185 Abstract A non-local, ordinary-state-based, peridynamics viscoelasticity model is developed. In this model, viscous effects are added to deviatoric deformations and the bulk re-sponse remains elastic.
Viscoplasticity using peridynamics · Handbook of peridynamic modeling · An energy based failure criterion for use with peridynamic states · A meshfree unification:
19–43. [Google Scholar] What is Peridynamics? Peridynamics is a nonlocal extension of classical solid mechanics that permits discontinuous solutions “In peridynamics, cracks are part of the solution, not part of the problem ” Peridynamic equation of motion (integral, nonlocal) u(x,t) f(u' u,x x)dV b(x,t) not part of the problem. The peridynamic theory, which is a nonlocal continuum theory, provides a suitable framework for modeling dynamic problems involving fracture. Prior research has focused mostly on the continuum, bulk response, neglecting any localized material failure, of granular materials.
Based on the strain energy equivalence between classic local model and non-local model, the bond force vector is derived. A new damage rule of maximal deviatoric bond strain for elastic brittle fracture is proposed in order to account for both the tensile damage and shear damage. 2D and 3D numerical examples are Peridynamics is a nonlocal extension of classical W.W. Chen, Viscoplasticity Using Peridynamics, Sandia National Laboratories Technical Report SAND2008-7835, 2008 Similar to the classical nonlocal models, the peridynamic dispersion of elastic waves occurs for high frequencies. It is shown to be stronger in the state-based than in the bond-based version, with multiple wavelengths giving a vanishing phase velocity, one of them longer than the horizon.
Viscoplasticity using peridynamics. JT Foster, SA Silling, WW Chen. International journal for numerical methods in engineering 81 (10), 1242-1258, 2010. 222: 2010:
It is shown to be stronger in the state-based than in the bond-based version, with multiple wavelengths giving a vanishing phase velocity, one of them longer than the horizon. Viscoplasticity using peridynamics. JT Foster, SA Silling, WW Chen. International journal for numerical methods in engineering 81 (10), 1242-1258, 2010.
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[Google Scholar] What is Peridynamics? Peridynamics is a nonlocal extension of classical solid mechanics that permits discontinuous solutions “In peridynamics, cracks are part of the solution, not part of the problem ” Peridynamic equation of motion (integral, nonlocal) u(x,t) f(u' u,x x)dV b(x,t) not part of the problem.
International journal for numerical methods in engineering 81 (10), 1242-1258, 2010. 220: 2010:
Based upon the integrodifferential equations, peridynamics enables predicting the complex fracture phenomena such as spontaneous crack nucleation and crack branching, curving, and arrest. In this paper, the bond-based peridynamic approach is used to study the impact damage in a beam with an offset notch, which is widely used to investigate the mixed I-II crack propagation in brittle materials. We propose a new peridynamic formulation with shear deformation for linear elastic solid. The key idea lies in subtracting the rigid body rotation part from the total deformation. Based on the strain energy equivalence between classic local model and non-local model, the bond force vector is derived.
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A new damage rule of maximal deviatoric bond strain for elastic brittle fracture is proposed in order to account for both the tensile damage and shear damage. 2D and 3D numerical examples are Peridynamics is a nonlocal extension of classical W.W. Chen, Viscoplasticity Using Peridynamics, Sandia National Laboratories Technical Report SAND2008-7835, 2008 Similar to the classical nonlocal models, the peridynamic dispersion of elastic waves occurs for high frequencies. It is shown to be stronger in the state-based than in the bond-based version, with multiple wavelengths giving a vanishing phase velocity, one of them longer than the horizon.
Application of peridynamics for rock mechanics and porous media 19. Viscoplasticity using peridynamics. International Journal for Numerical Methods in Engineering, 81(10):1242–1258, 2010. doi:10.1002/nme.2725.
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are inherently represented by defining a bond relationship between particles using a constitutive model. Furthermore, the bond relationship between dissimilar material phases is inherently integrated in the peridynamic method. Two methods are primarily used: bond-based peridynamics (BBPD) [26,27] and micro-polar peridynamics (MPPD) [28,29].
Bamgboye, T.A. Haynes, M. R. Wenman) at incorporating classical nonlinear constitutive models using the nonlocal ap-proximation to the deformation gradient tensor F . For example, state-based formulations of viscoplasticity models [13] and ductile damage models for met-als [14, 15] have recently been proposed and e ectively used in simulations based on particle discretizations. This novel method of coupling peridynamics with a highly efficient mesh in the hydraulic fracture model will be fully detailed in this dissertation. In addition, 2D and 3D results will be provided using this method, demonstrating the capability of the coupled model to simulate complex fracture behavior, as well as discuss its impact on simulation capabilities and performance.
Viscoplasticity using peridynamics · Handbook of peridynamic modeling · An energy based failure criterion for use with peridynamic states · A meshfree unification:
The computational implementation of fracture and fragmentation under high rates of loading is simple and effective with a PD based scheme. Authors: Foster, John T. Publication Date: Tue Dec 01 00:00:00 EST 2009 Research Org.: Sandia National Lab. (SNL-CA), Livermore, CA (United States) Viscoplasticity is usually modeled in three-dimensions using overstress models of the Perzyna or Duvaut-Lions types. In these models, the stress is allowed to increase beyond the rate-independent yield surface upon application of a load and then allowed to relax back to the yield surface over time. 2012-10-15 · Foster et al., studied viscoplasticity and the failure criterion for peridynamic states. Compared with FEM, peridynamics is computationally expensive.
It is also advantageous to solve moving boundary problems as in the lithiation process considered in this study which is difficult to handle by using traditional techniques Alternatively, viscoplasticity can be modeled by incorporating the rate-dependency in a yield function. This concept has been used to formulate the Consistency model (Wang, 1997; Wang et al., 1997), which appeared to be an efficient and useful tool in the simulation of Lüders bands and Portevin–Le Chatelier effects in metals. References Aziz, A. [2014] “ Simulation of Fracture of Concrete Using Micropolar Peridynamics,” Simulation 10, 16. Google Scholar; Aksoy, H. and Şenocak, E. [2011] “ Discontinuous Galerkin method based on peridynamic theory for linear elasticity,” International Journal for Numerical Methods in Engineering 88(7), 673–692. Peridynamics (PD) computations for state-based PD in 1D, 2D for elastic and viscoelastic materials. Also possible to import Digital Image Correlation results and compute PD forces for each pixel as a node. - lm2-poly/PeriPyDIC An approach to modeling extreme loading of structures using peridynamics.