Browsing by Author "Steinmann, Paul"

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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
Nonlocal interfaces accounting for progressive damage within continuum kinematics inspired peridynamics
(Elsevier Ltd., 2024-01-02) Laurien, Marie; Javili, Ali; Steinmann, Paul
In this work, we present a modeling approach to nonlocal material interfaces in the framework of continuum-kinematics-inspired peridynamics. The nonlocal model accounts for progressive damage within a finite-thickness interface, as opposed to the more common practice of abrupt bond breakage across a zero-thickness interface. Our approach is based on an overlap of the constituents within the interface. Interfacial bonds between initially overlapping partner points are governed by a constitutive law reminiscent of a traction-separation-law. The governing equations for continuum-kinematics-inspired peridynamics in the presence of an interface are derived using a rate-variational principle. The damage formulation is established using the classical concept of internal variables. Following the notion of a standard dissipative material, thermodynamic consistency of the constitutive laws and the evolution of the internal variables is ensured. The latter results in a straightforward evaluation of a damage function. We give details about the computational implementation comprising a peridynamic discretization and a Newton–Raphson scheme. A sound approach to approximate the interface normal during deformation is presented, which allows to penalize material penetration across the interface. The proposed model is explored in a series of numerical examples, i.e., classical peeling and shearing tests, for a variety of damage functions. A key feature of our interface model are the nonlocal characteristics that are assumed to play a role especially at small scales. We, first, observe that an increasing thickness of the nonlocal interface leads to stronger interfacial bonding and less damage. Second, an increase in horizon size results in stiffer material behavior. When studying the wrinkling and delamination behavior of a compressed bilayer, it is found that an increase in interface stiffness leads to a smaller wrinkling wavelength. Moreover, delamination due to progressive damage of interfacial bonds in the post-wrinkling regime is observed, which, to the best of our knowledge, has not been studied in a nonlocal model before.
Open Access
Open system peridynamics
(Springer Science and Business Media Deutschland GmbH, 2022-05-10) Schaller, Emely; Javili, Ali; Steinmann, Paul
We propose, for the first time, a thermodynamically consistent formulation for open system (continuum-kinematics-inspired) peridynamics. In contrast to closed system mechanics, in open system mechanics mass can no longer be considered a conservative property. In this contribution, we enhance the balance of mass by a (nonlocal) mass source. To elaborate a thermodynamically consistent formulation, the balances of momentum, energy and entropy need to be reconsidered as they are influenced by the additional mass source. Due to the nonlocal continuum formulation, we distinguish between local and nonlocal balance equations. We obtain the dissipation inequality via a Legendre transformation and derive the structure and constraints of the constitutive expressions based on the Coleman–Noll procedure. For the sake of demonstration, we present an example for a nonlocal mass source that can model the complex process of bone remodelling in peridynamics. In addition, we provide a numerical example to highlight the influence of nonlocality on the material density evolution. © 2022, The Author(s).