Abstract
The main objective of this contribution is to develop a novel continuum-kinematics-inspired approach for peridynamics (PD), and to revisit PD’s thermodynamic foundations. We distinguish between three types of interactions, namely, one-neighbour interactions, two-neighbour interactions and three-neighbour interactions. While one-neighbour interactions are equivalent to the bond-based interactions of the original PD formalism, two- and three-neighbour interactions are fundamentally different to state-based interactions in that the basic elements of continuum kinematics are preserved exactly. In addition, we propose that an externally prescribed traction on the boundary of the continuum body emerges naturally and need not vanish. This is in contrast to, but does not necessarily violate, standard PD. We investigate the consequences of the angular momentum balance and provide a set of appropriate arguments for the interactions accordingly. Furthermore, we elaborate on thermodynamic restrictions on the interaction energies and derive thermodynamically-consistent constitutive laws through a Coleman–Noll-like procedure.
Highlights
Peridynamics (PD) is an alternative approach to formulate continuum mechanics (Silling, 2000) the roots of which can be traced back to the pioneering works of Piola which prepared the foundations for nonlocal continuum mechanics and peridynamics
Elastic two-neighbour interactions can be interpreted as the resistance against the change of the area of the triangle formed by a point and a pair of neighbours, analogous to Poisson-like effects of classical continuum mechanics in two dimensions
Recall the one-neighbour interaction energy density per volume squared in the material configuration w1 in its most generic form is a function of the relative position ξ|, i.e. the finite line element, between two points with the force density per volume squared denoted as p1|, that is w1| = w1 (ξ| )
Summary
Peridynamics (PD) is an alternative approach to formulate continuum mechanics (Silling, 2000) the roots of which can be traced back to the pioneering works of Piola (dell’Isola et al, 2015; 2016; 2017) which prepared the foundations for nonlocal continuum mechanics and peridynamics. The original PD theory of Silling (2000) was restricted to bond-based interactions This limited its applicability for material modelling, including the inability to account for Poisson’s ratio other than 1/4 for isotropic materials. This shortcoming was addressed in various contributions and rectified by Silling et al (2007) via the introduction of the notion of state and categorising the interactions as bond-based, ordinary state-based and non-ordinary state-based as schematically illustrated in Fig. 1 (left). Point-wise equations at each X in CPD include integrals over the horizon and are non-local.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
