Browsing by Subject "Continuum kinematics"

Now showing 1 - 6 of 6

Open Access
The computational framework for continuum-kinematics-inspired peridynamics
(Springer Science and Business Media B.V., 2020) Javili, Ali; Firooz, Soheil; McBride, A. T.; Steinmann, P.
Peridynamics (PD) is a non-local continuum formulation. The original version of PD was restricted to bond-based interactions. Bond-based PD is geometrically exact and its kinematics are similar to classical continuum mechanics (CCM). However, it cannot capture the Poisson effect correctly. This shortcoming was addressed via state-based PD, but the kinematics are not accurately preserved. Continuum-kinematics-inspired peridynamics (CPD) provides a geometrically exact framework whose underlying kinematics coincide with that of CCM and captures the Poisson effect correctly. In CPD, one distinguishes between one-, two- and three-neighbour interactions. One-neighbour interactions are equivalent to the bond-based interactions of the original PD formalism. However, two- and three-neighbour interactions are fundamentally different from state-based interactions as the basic elements of continuum kinematics are preserved precisely. The objective of this contribution is to elaborate on computational aspects of CPD and present detailed derivations that are essential for its implementation. Key features of the resulting computational CPD are elucidated via a series of numerical examples. These include three-dimensional problems at large deformations. The proposed strategy is robust and the quadratic rate of convergence associated with the Newton–Raphson scheme is observed.
Open Access
Continuum-kinematics-inspired peridynamics. Mechanical problems
(Elsevier, 2019) Javili, Ali; McBride, A. T.; Steinmann, P.
The main objective of this contribution is to develop a novel continuum-kinematicsinspired 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, twoand 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.
Open Access
Continuum-kinematics-inspired peridynamics: thermo-mechanical problems
(Springer, 2021-03-31) Javili, Ali; Ekiz, Ekim; McBride, A. T.; Steinmann, P.
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 Access
A geometrically exact formulation of peridynamics
(Elsevier BV, 2021-02) Javili, Ali; McBride, A. T.; Steinmann, P.
The main objective of this contribution is to develop a geometrically exact peridynamics (PD) formulation wherein the basic elements of continuum kinematics are preserved. The proposed formulation accounts for large deformations and is variationally consistent. We distinguish between one-, two- and three-neighbour interactions. One-neighbour interactions recover the original (bond-based) PD formalism. Two- and three-neighbour interactions are fundamentally different to state-based PD. We account for material frame indifference and provide a set of appropriate arguments for objective interaction potentials accordingly. This contribution is presented in a manner such that the established theory is immediately suitable for computational implementation. From a computational perspective, the proposed strategy is fully implicit and the quadratic rate of convergence associated with the Newton–Raphson scheme is observed. Finally, we demonstrate the capability of our proposed framework via a series of numerical examples at large deformations.
Open Access
A nonlocal interface approach to peridynamics exemplified by continuum-kinematics-inspired peridynamics
(John Wiley and Sons Ltd, 2022-08-15) Laurien, Marie; Javili, Ali; Steinmann, Paul
In this contribution, we present a novel approach on how to treat material interfaces in nonlocal models based on peridynamics (PD) and in particular continuum-kinematics-inspired peridynamics (CPD), a novel variationally consistent peridynamic formulation. Our method relies on a nonlocal interface where the material subdomains overlap. Within this region, a kinematic coupling of the two constituents is enforced. The contact is purely geometrical as interaction forces act only between points of the same material. We provide a detailed description of the computational implementation within the framework of CPD, that is in principle applicable to all formulations of PD. A variety of numerical examples for modeling bimaterial interfaces illustrate the utility of the technique for both two-dimensional and three-dimensional problems, including examples at large deformations. Our model approaches a local model when the nonlocality parameter, the horizon size, is decreased. The proposed methodology offers a viable alternative to previous approaches in PD, which are essentially imposing mixture rules for the interfacial material parameters. © 2022 The Authors. International Journal for Numerical Methods in Engineering published by John Wiley & Sons Ltd.
Open Access
Towards elasto-plastic continuum-kinematics-inspired peridynamics
(Elsevier BV, 2021-07-01) Javili, Ali; McBride, A. T.; Mergheim, J.; Steinmann, P.
The main objective of this contribution is to develop a dissipation-consistent elasto-plastic peridynamic (PD) formulation that is also geometrically exact. We distinguish between one-neighbour, two-neighbour and three-neighbour interactions. One-neighbour interactions are equivalent to the bond-based interactions of the original PD formalism. However, two- and three-neighbour interactions are fundamentally different to state-based interactions, as the basic elements of continuum kinematics are preserved exactly. We investigate the consequences of the angular momentum balance and provide a set of appropriate arguments for the interaction potentials accordingly. Furthermore, we elaborate on restrictions on the interaction energies and derive dissipation-consistent constitutive laws through a Coleman–Noll-like procedure. Although the framework is suitable for finite deformations, an additive decomposition of the kinematic quantities into elastic and plastic parts is rigorously proven to be a correct choice. Crucially, in our proposed scheme, the elasto-plastic framework resembles standard one-dimensional plasticity, for all interactions. Finally, we demonstrate the capability of our proposed framework via a series of numerical examples.