Discontinuous Galerkin method based on peridynamic theory for linear elasticity

• Published in: International journal for numerical methods in engineering Vol. 88; no. 7; pp. 673 - 692
• Main Authors: Aksoy, H. G., Şenocak, E.
• Format: Journal Article
• Language: English
• Published: Chichester, UK John Wiley & Sons, Ltd 18-11-2011; Wiley
• Subjects: Derivation; Discontinuity; discontinuous Galerkin; Elastostatics; Exact sciences and technology; Exact solutions; finite element method; Fracture mechanics (crack, fatigue, damage...); Fundamental areas of phenomenology (including applications); Galerkin methods; Mathematical analysis; Mathematical models; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Partial differential equations, initial value problems and time-dependant initial-boundary value problems; peridynamics; Physics; Sciences and techniques of general use; Solid mechanics; Static elasticity (thermoelasticity...); Structural and continuum mechanics; Solid mechanics; Discontinuity; Surface crack; Elasticity; Surface wave; Elastic wave; Modeling; Shock wave; Exact solution; Finite element method; Weak solution; Linear theory; Problem solving; discontinuous Galerkin; Integral equation; Galerkin method; Elasticity theory; Structural analysis; peridynamics
• ISSN: 0029-5981; 1097-0207; 1097-0207
• DOI: 10.1002/nme.3196

Modeling of discontinuities (shock waves, crack surfaces, etc.) in solid mechanics is one of the major research areas in modeling the mechanical behavior of materials. Among the numerical methods, the discontinuous Galerkin method (DGM) poses some advantages in solving these problems. In this study, a novel formulation for DGM is derived for elastostatics based on the peridynamic theory. Derivation of the proposed formulation is presented. Numerical analyses are performed for different problems, and the numerical results are compared to that of the known exact solutions of the problems. The proposed weak formulation is stable and coercive. Peridynamic discontinuous Galerkin formulation is found to be robust and successful in modeling elastostatic problems. Copyright © 2011 John Wiley & Sons, Ltd.