No abstract

No abstract

A perfectly matched layer (PML) absorbing boundary is formulated for and numerically applied to peridynamics in two dimensions. Peridynamics is a nonlocal method, derived to be insensitive to discontinuities, more easily simulating fracture. A PML is an absorbing boundary layer, which decays impinging waves exponentially without introducing reflections at the boundary between the computational region and the absorbing layer. Here, we use state-based peridynamics as PMLs are essentially anisotropic absorbing materials, therefore requiring arbitrary material parameters. State-based peridynamics is also more convenient for auxiliary field formulations, facilitating the implementation of the PML. Results show the efficacy of the approach.

No abstract

This paper describes the use of genetic algorithms (GAs) for the optimal design of phononic bandgaps in periodic elastic two-phase media. In particular, we link a GA with a computational finite element method for solving the acoustic wave equation, and find optimal designs for both metal-matrix composite systems consisting of Ti/SiC, and H 2 O-filled porous ceramic media, by maximizing the relative acoustic bandgap for these media. The term acoustic here implies that, for simplicity, only dilatational wave propagation is considered, although this is not an essential limitation of the method. The inclusion material is found to have a lower longitudinal modulus (and lower wave speed) than the surrounding matrix material, a result consistent with observations that stronger scattering is observed if the inclusion material has a lower wave velocity than the matrix material.

A method is presented for the modeling of brittle elastic fracture which combines peridynamics and a finite difference method to mitigate the wave dispersion properties of peridynamics. Essentially, a finite difference method is used in the bulk for wave propagation modeling, while peridynamics is automatically inserted in high strain areas to model crack initiation and growth. The dispersion properties of finite difference methods and discretized peridynamics are reviewed and the interface reflection properties between the two regions are investigated. Results show that the augmented method can improve the modeling of wave propagation and boundary conditions. In addition, the numerical stress intensity factor computed at a crack tip shows reduced oscillations in the augmented method, likely due to the improved dispersion properties of the bulk. Dynamic fracture simulations show a difference in crack paths between the methods.

Typical implementations of peridynamics use a constant or tapered micromodulus (or influence) function, the choice of which has been shown to have a large impact on the dispersion relation. In this work, a method for computing micromodulus function values at discretized points within a node's horizon is presented for linearized peridynamics. The technique involves constructing a system of equations representing the desired dispersion relation and solving for the micromodulus function coefficients at discretized node locations. Both 1D and 2D formulations are presented. A straightforward implementation of the method results in negative coefficients, which improve wave propagation accuracy, but results in unstable solutions of fracture problems using a bond-breakage scheme. Two methods for addressing this issue are discussed: A hybrid method that uses a constant micromodulus function after damage has occurred at a node, and a constrained solution that results in only positive coefficients. The dispersion properties of the method are examined in detail, including the numerical anisotropy in 2D. Finally, results for wave propagation in 1D and 2D, static fracture, and dynamic fracture are given.

Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing the burden, ARL-RP-130 SPONSOR/MONITOR'S ACRONYM(S) 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) SPONSOR/MONITOR'S REPORT NUMBER(S) DISTRIBUTION/AVAILABILITY STATEMENTApproved for public release; distribution is unlimited. SUPPLEMENTARY NOTES ABSTRACTThis report describes the use of genetic algorithms (GAs) for the optimal design of phononic bandgaps in periodic elastic twophase media. In particular, we link a GA with a computational finite element method for solving the acoustic wave equation, and find optimal designs for both metal-matrix composite systems consisting of Ti/SiC, and H 2 O-filled porous ceramic media, by maximizing the relative acoustic bandgap for these media. The term acoustic here implies that, for simplicity, only dilatational wave propagation is considered, although this is not an essential limitation of the method. The inclusion material is found to have a lower longitudinal modulus (and lower wave speed) than the surrounding matrix material, a result consistent with observations that stronger scattering is observed if the inclusion material has a lower wave velocity than the matrix material. SUBJECT TERMS AbstractThis paper describes the use of genetic algorithms (GAs) for the optimal design of phononic bandgaps in periodic elastic two-phase media. In particular, we link a GA with a computational finite element method for solving the acoustic wave equation, and find optimal designs for both metal-matrix composite systems consisting of Ti/SiC, and H 2 O-filled porous ceramic media, by maximizing the relative acoustic bandgap for these media. The term acoustic here implies that, for simplicity, only dilatational wave propagation is considered, although this is not an essential limitation of the method. The inclusion material is found to have a lower longitudinal modulus (and lower wave speed) than the surrounding matrix material, a result consistent with observations that stronger scattering is observed if the inclusion material has a lower wave velocity than the matrix material.