Continuum-kinematics-inspired peridynamics: Thermo-mechanical problems

Abstract

The recently proposed continuum-kinematics-inspired peridynamics (CPD) is extended to account for thermo-mechanical coupling at large deformations. The key features of CPD are that it is geometrically exact and is built upon multi-neighbour interactions. The bond-based interactions of the original PD formalism are equivalent to one-neighbour interactions of CPD. Two-and three-neighbour interactions, however, are fundamentally different from state-based PD in that the basic elements of continuum kinematics are preserved exactly. We elaborate on thermodynamic restrictions on the interaction energies and derive thermodynamically consistent constitutive laws through a Coleman-Noll-like procedure. Notably, we show that various choices for temperature, or coldness, satisfy the dissipation inequality and provide meaningful temperature, or coldness, evolution equations together with Fourier-like conduction relations.

Open system peridynamics

“…Based on the general forms of the balance equation, we will elaborate in the following the mechanical and thermodynamic governing equations that are valid for open system peridynamics. The respective governing equations for closed systems can be found in [9,22] and are recovered in the present formulation by setting the temporal rate of mass to zero. Table 1 provides a comparison of the governing equations in the peridynamic and classic continuum formulation.…”

“…the ones of Kilic et al [19], Bobaru and Duangpanya [20] and Oterkus et al [21], address thermomechanical problems. Additionally, Javili et al extended recently the CPD formulation to account for thermomechanical coupling [22] and elasto-plastic material behaviour [23].…”

A nonlocal interface approach to peridynamics exemplified by continuum‐kinematics‐inspired peridynamics

“…17 Due to these promising benefits, CPD has been further developed by now. [18][19][20][21][22][23][24] In most real-world problems, materials are heterogeneous. Numerous fields of applications of PD are concerned with modeling heterogeneous media, such as micro-structured materials, 6,7 functionally graded materials, [25][26][27][28] or bilayers, 29 to name a few.…”

“…CPD differs from state‐based PD, which faces issues when transferring local material models to peridynamic ones via a correspondence model — a concept that state‐based PD commonly relies on 17 . Due to these promising benefits, CPD has been further developed by now 18‐24 …”