Linearized Theory of Peridynamic States

By Stewart A. Silling. 2010

356 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Electrical and Electronic Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/063b9540b515d2053993cbb9cebd0f1ef448f7cf

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In Civil and Structural Engineering

In Electrical and Electronic Engineering

In Mechanics of Materials

Citations in the corpus

Fractional Piola identity and polyconvexity in fractional spaces (2018, background): “More recently, a nonlocal alternative theory in solid mechanics, named peridynamics, has been proposed in [37, 36].”
Non-ordinary state-based peridynamic analysis of stationary crack problems (2014, unknown): “A reformulation of the bond-based PD relations proposed by Silling and coworkers [15,16] led to two new PD formulations referred to as ordinary state-based (OSB) and non-ordinary state-based (NOSB) PD.”
Surface corrections for peridynamic models in elasticity and fracture (2017, methodology): “Other ways to find static solutions in PD are: using a direct method to solve the system given by the stiffness matrix [23,36], or using dynamic relaxation [37,38].”
A conservative nonlocal convection–diffusion model and asymptotically compatible finite difference discretization (2017, methodology): “The basic structure of the model is consistent to the state-based approach proposed in [38] for the peridynamic model of nonlocal mechanics.”
Analysis of the Volume-Constrained Peridynamic Navier Equation of Linear Elasticity (2013, methodology): “The resulting derivative defines the force state and leads to the peridynamic Navier operator; see [18] for details.”
Fully coupled peridynamic thermomechanics (2012, background): “Silling (2009) developed a linearized form of the state-based peridynamics for small elastic deformation by introducing the force vector state, T , as T = T U , (24) where U is the displacement vector state.”
A morphing approach to couple state-based peridynamics with classical continuum mechanics (2016, methodology): “In fact, this linearized force vector state for an isotropic material can also be calculated by the dot product between the displacement state and the modulus state [21], which has been derived in “5.”
Crack nucleation in a peridynamic solid (2010, background): “For an elastic material, it can be shown (Silling 2010) that C and P have the following symmetries: CT (x, q) = C(q, x), PT (x) = P(x).”