The bond-based peridynamic system with Dirichlet-type volume constraint. Issue 1 (30th January 2014)

• Record Type: Journal Article
• Authors: Mengesha, Tadele; Du, Qiang
• Is Part Of: Proceedings. Volume 144:Issue 1(2014)
• Page Start: 161
• Page End: 186
• Publication Date: 2014-01-30
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1017/S0308210512001436
• Languages: English
• ISSNs: 0308-2105

Abstract

Abstract : In this paper, the bond-based peridynamic system is analysed as a non-local boundary-value problem with volume constraint. The study extends earlier works in the literature on non-local diffusion and non-local peridynamic models, to include non-positive definite kernels. We prove the well-posedness of both linear and nonlinear variational problems with volume constraints. The analysis is based on some non-local Poincaré-type inequalities and the compactness of the associated non-local operators. It also offers careful characterizations of the associated solution spaces, such as compact embedding, separability and completeness. In the limit of vanishing non-locality, the convergence of the peridynamic system to the classical Navier equations of elasticity with Poisson ratio ¼ is demonstrated.