Non-ordinary state-based peridynamic analysis of stationary crack problems

Meshless modeling framework for fiber reinforced concrete structures

“…The capability of peridynamics in 3D problems has been successfully illustrated in numerous studies [19,31]. Therefore, it is possible to extend the proposed fiber modeling approach to 3D problems.…”

“…For a linearly elastic material, Breitenfeld et al [31] developed a numerical discretization scheme to solve the peridynamic equilibrium equations (Eq. (6)).…”

“…Additional analysis methods had been introduced to generalize the peridynamic formulation: (1) The ordinary state based peridynamics (OSBPD) generalizes the bond-based peridynamics to include any Poissons ratio by defining central force states of unequal magnitudes [24,30]; and (2) in the non-ordinary state based peridynamic (NOSBPD) method, non-parallel and unequal force states are used to model interactions between material points [24,26,31]. Therefore, the NOSBPD method can be applied to material models with any Poissons ratio.…”

An improved peridynamic approach for quasi-static elastic deformation and brittle fracture analysis

“…The response of a bond is independent of the other bonds in the bond-based peridynamic formulation, which makes it limited to the constitutive models with a fixed Poisson's ratio [5,28]. To eliminate the limitations including the limited Poisson's ratio, a reformulation of the bond-based PD relation, called the state-based peridynamic model, was proposed by Silling and coworkers [29][30][31], and it has been employed to describe the mechanical and fracture behavior of more general materials [32,33].…”

Nonlocal Peridynamic Modeling and Simulation on Crack Propagation in Concrete Structures

“…Since then, peridynamics has been successfully utilized to analyze various problems including progressive failure [11,12], phase transformation [13], and stationary and dynamic fracture [14][15][16] at both macro-and microscales, and it shows great potential analogous but advantageous to both classical meshfree and molecular dynamic methods.…”