A nonlocal interface approach to peridynamics exemplified by continuum‐kinematics‐inspired peridynamics - Laurien, Marie; Javili, Ali; Steinmann, Paul (International Journal for Numerical Methods in Engineering, 2022)
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.<br
Keywords: peridynamics; nonlocality; material interface; continuum mechanics

Nonlocal interfaces accounting for progressive damage within continuum-kinematics-inspired peridynamics - Laurien, Marie; Javili, Ali; Steinmann, Paul (International Journal of Solids and Structures, 2024)
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.
CRIS-Team Scopus Importer:2024-02-02
Keywords: Cohesive zone; Damage; Material interface; Nonlocality; Peridynamics; Rate-variational principle

Nonlocal interfaces accounting for progressive damage within continuum-kinematics-inspired peridynamics - Laurien, Marie; Javili, Ali; Steinmann, Paul (International Journal of Solids and Structures, 2024)
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.<br
Keywords: Peridynamics; Material interface; Damage; Nonlocality; Cohesive zone; Rate-variational principle

Nonlocal wrinkling instabilities in bilayered systems using peridynamics - Laurien, Marie; Javili, Ali; Steinmann, Paul (Computational Mechanics, 2021)
Wrinkling instabilities occur when a stiff thin film bonded to an elastic substrate undergoes compression. Regardless of the nature of compression, this phenomenon has been extensively studied through local models based on classical continuum mechanics. However, the experimental behavior is not yet fully understood and the influence of nonlocal effects remains largely unexplored. The objective of this paper is to fill this gap from a computational perspective by investigating nonlocal wrinkling instabilities in a bilayered system. Peridynamics (PD), a nonlocal continuum formulation, serves as a tool to model nonlocal material behavior. This manuscript presents a methodology to precisely predict the critical conditions by employing an eigenvalue analysis. Our results approach the local solution when the nonlocality parameter, the horizon size, approaches zero. An experimentally observed influence of the boundaries on the wave pattern is reproduced with PD simulations which suggests nonlocal material behavior as a physical origin. The results suggest that the level of nonlocality of a material model has quantitative influence on the main wrinkling characteristics, while most trends qualitatively coincide with predictions from the local analytical solution. However, a relation between the film thickness and the critical compression is revealed that is not existent in the local theory. Moreover, an approach to determine the peridynamic material parameters across a material interface is established by introducing an interface weighting factor. This paper, for the first time, shows that adding a nonlocal perspective to the analysis of bilayer wrinkling by using PD can significantly advance our understanding of the phenomenon.
CRIS-Team WoS Importer:2021-08-13

Peridynamic modeling of nonlocal degrading interfaces in composites - Laurien, Marie; Javili, Ali; Steinmann, Paul (Forces in Mechanics, 2022)
When modeling composite materials at small scales, the consideration of nonlocal effects is fundamental. In addition, the overall response of matrix-inclusion composites is strongly affected by the behavior of the interface between inclusion and matrix. This can be attributed to a possible detachment of the constituents as well as the high interface-to-volume ratio especially for nano-sized inclusions. Peridynamics is a nonlocal theory that is suitable to introduce a length-scale into a continuum description and take into account nonlocal interactions. Complex interface models within a peridynamic framework are, however, rarely studied. The objective of this work is to present a modeling approach to nonlocal interfaces accounting for opening and degradation within the framework of continuum-kinematics-inspired peridynamics (CPD). The proposed method is employed to study nonlocal effects in matrix-inclusion composites with focus on the effect of nonlocal interfaces. In our approach, the nonlocal interface is mdeled as a finite thickness interface, i.e. a region where the subdomains overlap. Within this region, the constituents are pair-wise connected through interface bonding forces that follow a characteristic force-opening law. In computational experiments, our model captures the influence of the strength and size of the interface as well as the inclusion volume fraction on the overall response. In particular, nonlocality manifests itself through a “smaller–stiffer” material behavior and an increased influence of the interface, which highlights the importance of an appropriate nonlocal interface model.<br

Peridynamic modeling of nonlocal degrading interfaces in composites - Laurien, Marie; Javili, Ali; Steinmann, Paul (Forces in Mechanics, 2023)
When modeling composite materials at small scales, the consideration of nonlocal effects is fundamental. In addition, the overall response of matrix-inclusion composites is strongly affected by the behavior of the interface between inclusion and matrix. This can be attributed to a possible detachment of the constituents as well as the high interface-to-volume ratio especially for nano- sized inclusions. Peridynamics is a nonlocal theory that is suitable to introduce a length-scale into a continuum description and take into account nonlocal interactions. Complex interface models within a peridynamic framework are, however, rarely studied. The objective of this work is to present a modeling approach to nonlocal interfaces accounting for opening and degradation within the framework of continuum-kinematics-inspired peridynamics (CPD). The proposed method is employed to study nonlocal effects in matrix-inclusion composites with focus on the effect of nonlocal interfaces. In our approach, the nonlocal interface is modeled as a finite thickness interface, i.e. a region where the subdomains overlap. Within this region, the constituents are pair-wise connected through interface bonding forces that follow a characteristic force-opening law. In computational experiments, our model captures the influence of the strength and size of the interface as well as the inclusion volume fraction on the overall response. In particular, nonlocality manifests itself through a “smaller–stiffer” material behavior and an increased influence of the interface, which highlights the importance of an appropriate nonlocal interface model.