A peridynamic material model for the analysis of dynamic crack propagation in orthotropic media

Abstract

A new material model for the dynamic fracture analysis of anisotropic materials has been proposed within the framework of the bond-based peridynamic theory. This model enables predicting complex fracture phenomena such as spontaneous crack nucleation and crack branching, curving and arrest, a capability inherited from the bond-based peridynamic theory. An important feature of the model is that the bond properties, i.e. the stiffness constant and critical stretch, are continuous functions of bond orientation in the principal material axes. This facilitates fracture analysis of anisotropic materials with random orientations, such as polycrystalline microstructures. Elastic and fracture behaviour of the model has been verified through simulating uniaxial tension of a composite plate and fracture of a cortical bone compact tension specimen, and making quantitative comparisons to analytical and experimental data. To further demonstrate the capabilities of the proposed model, dynamic fracture of a polycrystalline microstructure (alumina ceramic) has been simulated. The influence of the grain boundary and grain interior fracture energies on the interacting and competing fracture modes of polycrystalline materials, i.e. intergranular and transgranular fracture, has been studied.

Numerical convergence of nonlinear nonlocal continuum models to local elastodynamics

“…Computational fracture modeling using peridynamics features formation and evolution of interfaces associated with fracture, see other works. [2][3][4][5][6][7][8][9][10][11][12][13][14][15] In the absence of fracture, earlier work demonstrates the convergence of linear peridynamic models to the local model of linear elasticity as goes to zero, see the works of Weckner and Emmrich 16 and Silling and Lehoucq. 17 The convergence of an equilibrium peridynamic model to the Navier equation in the sense of solution operators is established in the work of Mengesha and Du.…”

Peridynamic Modeling of Granular Fracture in Polycrystalline Materials

“…Askari et al [19] performed PD simulations of granular fracture in a silicon polycrystal (cubic system); they investigated the effect of the grain boundary strength on the fracture mechanisms. Recently, Ghajari et al [20] applied PD for modeling the dynamic fracture response of alumina (hexagonal system).…”

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

“…The first introduced as well as the most widely used PD formulation in the past decade is the so-called bond-based PD model. Some representative researches using the bond-based PD model include the dynamic fracture of homogeneous and heterogeneous bar [6][7][8], damage and fracture of membranes and fibers [9,10], brittle fracture of polycrystals [11,12] and quenched glass [13], failure analysis of composites [14,15], and failure and structural stability of concrete structures [16][17][18]. At the micro-and nano-scales, the bond-based PD method has also been utilized to analyze various problems such as phase transformation [19] and the mechanical behavior of nano-scale materials and structures [20,21].…”