Browsing by Subject "Cohesive zone"

Now showing 1 - 4 of 4

Open Access
Coherent energetic interfaces accounting for in-plane degradation
(Springer Netherlands, 2016) Esmaeili, A.; Javili, A.; Steinmann, P.
Interfaces can play a dominant role in the overall response of a body. The importance of interfaces is particularly appreciated at small length scales due to large area to volume ratios. From the mechanical point of view, this scale dependent characteristic can be captured by endowing a coherent interface with its own elastic resistance as proposed by the interface elasticity theory. This theory proves to be an extremely powerful tool to explain size effects and to predict the behavior of nano-materials. To date, interface elasticity theory only accounts for the elastic response of coherent interfaces and obviously lacks an explanation for inelastic interface behavior such as damage or plasticity. The objective of this contribution is to extend interface elasticity theory to account for damage of coherent interfaces. To this end, a thermodynamically consistent interface elasticity theory with damage is proposed. A local damage model for the interface is presented and is extended towards a non-local damage model. The non-linear governing equations and the weak forms thereof are derived. The numerical implementation is carried out using the finite element method and consistent tangents are listed. The computational algorithms are given in detail. Finally, a series of numerical examples is studied to provide further insight into the problem and to carefully elucidate key features of the proposed theory. © 2016, Springer Science+Business Media Dordrecht.
Open Access
Micro-to-macro transition accounting for general imperfect interfaces
(Elsevier B.V., 2017) Javili, A.; Steinmann, P.; Mosler, J.
The objective of this contribution is to establish a micro-to-macro transition framework to study the behavior of heterogeneous materials whereby the influence of interfaces at the microscale is taken into account. The term “interface” refers to a zero-thickness model that represents the finite thickness “interphase” between the constituents of the micro-structure. For geometrically equivalent samples, due to increasing area-to-volume ratio with decreasing size, interfaces demonstrate a more pronounced effect on the material response at small scales. A remarkable outcome is that including interfaces introduces a length-scale and our interface-enhanced computational homogenization captures a size effect in the material response even if linear prolongation conditions are considered. Furthermore, the interface model in this contribution is general imperfect in the sense that it allows for both jumps of the deformation as well as for the traction across the interface. Both cohesive zone model and interface elasticity theory can be derived as two limit cases of this general model. We establish a consistent computational homogenization scheme accounting for general imperfect interfaces. Suitable boundary conditions to guarantee meaningful averages are derived. Clearly, this general framework reduces to classical computational homogenization if the effect of interfaces is ignored. Finally, the proposed theory is elucidated via a series of numerical examples. © 2016 Elsevier B.V.
Open Access
Non-coherent energetic interfaces accounting for degradation
(Springer Verlag, 2017) Esmaeili, A.; Steinmann, P.; Javili, A.
Within the continuum mechanics framework, there are two main approaches to model interfaces: classical cohesive zone modeling (CZM) and interface elasticity theory. The classical CZM deals with geometrically non-coherent interfaces for which the constitutive relation is expressed in terms of traction–separation laws. However, CZM lacks any response related to the stretch of the mid-plane of the interface. This issue becomes problematic particularly at small scales with increasing interface area to bulk volume ratios, where interface elasticity is no longer negligible. The interface elasticity theory, in contrast to CZM, deals with coherent interfaces that are endowed with their own energetic structures, and thus is capable of capturing elastic resistance to tangential stretch. Nonetheless, the interface elasticity theory suffers from the lack of inelastic material response, regardless of the strain level. The objective of this contribution therefore is to introduce a generalized mechanical interface model that couples both the elastic response along the interface and the cohesive response across the interface whereby interface degradation is taken into account. The material degradation of the interface mid-plane is captured by a non-local damage model of integral-type. The out-of-plane decohesion is described by a classical cohesive zone model. These models are then coupled through their corresponding damage variables. The non-linear governing equations and the weak forms thereof are derived. The numerical implementation is carried out using the finite element method and consistent tangents are derived. Finally, a series of numerical examples is studied to provide further insight into the problem and to carefully elucidate key features of the proposed theory. © 2016, Springer-Verlag Berlin Heidelberg.
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.