• Coupled systems mechanics
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• v.4 no.1
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• pp.1-18
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• 2015

The state-based peridynamics is considered a nonlocal method in which the equations of motion utilize integral form as opposed to the partial differential equations in the classical continuum mechanics. As a result, the enforcement of boundary conditions in solid mechanics analyses cannot follow the standard way as in a classical continuum theory. In this paper, a new approach for the boundary condition enforcement in the state-based peridynamic formulation is presented. The new method is first formulated based on a convex kernel approximation to restore the Kronecker-delta property on the boundary in 1-D case. The convex kernel approximation is further localized near the boundary to meet the condition that recovers the correct boundary particle forces. The new formulation is extended to the two-dimensional problem and is shown to reserve the conservation of linear momentum and angular momentum. Three numerical benchmarks are provided to demonstrate the effectiveness and accuracy of the proposed approach.

• Interaction and multiscale mechanics
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• v.7 no.1
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• pp.525-542
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• 2014

The state-based peridynamics is considered a nonlocal method in which the equations of motion utilize integral form as opposed to the partial differential equations in the classical continuum mechanics. As a result, the enforcement of boundary conditions in solid mechanics analyses cannot follow the standard way as in a classical continuum theory. In this paper, a new approach for the boundary condition enforcement in the state-based peridynamic formulation is presented. The new method is first formulated based on a convex kernel approximation to restore the Kronecker-delta property on the boundary in 1-D case. The convex kernel approximation is further localized near the boundary to meet the condition that recovers the correct boundary particle forces. The new formulation is extended to the two-dimensional problem and is shown to reserve the conservation of linear momentum and angular momentum. Three numerical benchmarks are provided to demonstrate the effectiveness and accuracy of the proposed approach.

• International Journal of Naval Architecture and Ocean Engineering
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• v.9 no.2
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• pp.209-218
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• 2017

Sea ice is the main factor affecting the safety of the Arctic engineering. However, traditional numerical methods derived from classical continuum mechanics have difficulties in resolving discontinuous problems like ice damage. In this paper, a non-local, meshfree numerical method called "peridynamics", which is based on integral form, was applied to simulate the interaction between level ice and a cylindrical, vertical, rigid structure at different velocities. Ice in the simulation was freshwater ice and simplified as elastic-brittle material with a linear elastic constitutive model and critical equivalent strain criterion for material failure in state-based peridynamics. The ice forces obtained from peridynamic simulation are in the same order as experimental data. Numerical visualization shows advantages of applying peridynamics on ice damage. To study the repetitive nature of ice force, damage zone lengths of crushing failure were computed and conclude that damage zone lengths are 0.15-0.2 times as ice thickness.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.32 no.1
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• pp.37-44
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• 2019

A bond-based peridynamic model has been reported dynamic fracture characteristic of brittle materials through a simple constitutive model. In the model, each bond is assumed to be a simple spring operating independently. As a result, this simple bond interaction modeling restricts the material behavior having a fixed Poisson's ratio of 1/4 and not being capable of expressing shear deformation. We consider a state-based peridynamics as a generalized peridynamic model. Constitutive models in the state-based peridynamics are corresponding to those in continuum theory. In state-based peridynamics, thus, the response of a material particle depends collectively on deformation of all bonds connected to other particles. So, a state-based peridynamic theory can represent the volume and shear changes of the material. In this paper, the perfect plasticity is considered to express plastic deformation of material by the state-based peridynamic constitutive model with perfect plastic flow rule. The elastic-plastic behavior of the material is verified through the stress-strain curves of the flat plate example. Furthermore, we simulate the high-speed impact on 3D granite model with a nonlocal contact modeling. It is observed that the damage patterns obtained by peridynamics are similar to experimental observations.