Browsing by Subject "Interface elasticity"

Now showing 1 - 8 of 8

Open Access
Aspects of interface elasticity theory
(Sage Publications Ltd., 2018) Javili, Ali; Ottosen, N. S.; Ristinmaa, M.; Mosler, J.
Interfaces significantly influence the overall material response especially when the area-to-volume ratio is large, for instance in nanocrystalline solids. A well-established and frequently applied framework suitable for modeling interfaces dates back to the pioneering work by Gurtin and Murdoch on surface elasticity theory and its generalization to interface elasticity theory. In this contribution, interface elasticity theory is revisited and different aspects of this theory are carefully examined. Two alternative formulations based on stress vectors and stress tensors are given to unify various existing approaches in this context. Focus is on the hyper-elastic mechanical behavior of such interfaces. Interface elasticity theory at finite deformation is critically reanalyzed and several subtle conclusions are highlighted. Finally, a consistent linearized interface elasticity theory is established. We propose an energetically consistent interface linear elasticity theory together with its appropriate stress measures.
Open Access
Bounds on size-dependent behaviour of composites
(Taylor & Francis, 2018) Saeb, S.; Steinmann, P.; Javili, Ali
Computational homogenisation is a powerful strategy to predict the effective behaviour of heterogeneous materials. While computational homogenisation cannot exactly compute the effective parameters, it can provide bounds on the overall material response. Thus, central to computational homogenisation is the existence of bounds. Classical firstorder computational homogenisation cannot capture size effects. Recently, it has been shown that size effects can be retrieved via accounting for elastic coherent interfaces in the microstructure. The primary objective of this contribution is to present a systematic study to attain computational bounds on the sizedependent response of composites. We show rigorously that interface-enhanced computational homogenisation introduces two relative length scales into the problem and investigate the interplay between them. To enforce the equivalence of the virtual power between the scales, a generalised version of the Hill–Mandel condition is employed, and accordingly, suitable boundary conditions are derived. Macroscopic quantities are related to their microscopic counterparts via extended average theorems. Periodic boundary conditions provide an effective behaviour bounded by traction and displacement boundary conditions. Apart from the bounds due to boundary conditions for a given size, the size-dependent response of a composite is bounded, too. The lower bound coincides with that of a composite with no interface. Surprisingly, there also exists an upper bound on the size-dependent response beyond which the expected ‘smaller is stronger’ trend is no longer observed. Finally, we show an excellent agreement between our numerical results and the corresponding analytical solution for linear isotropic materials which highlights the accuracy and broad applicability of the presented scheme.
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
Coupled thermally general imperfect and mechanically coherent energetic interfaces subject to in-plane degradation
(Mathematical Sciences Publishers, 2017) Esmaeili, A.; Steinmann, P.; Javili, A.
To date, the effects of interface in-plane damage on the thermomechanical response of a thermally general imperfect (GI) and mechanically coherent energetic interface are not taken into account. A thermally GI interface allows for a discontinuity in temperature as well as in the normal heat flux across the interface. A mechanically coherent energetic interface permits a discontinuity in the normal traction but not in the displacement field across the interface. The temperature of a thermally GI interface is a degree of freedom and is computed using a material parameter known as the sensitivity. The current work is the continuation of the model developed by Esmaeili et al. (2016a) where a degrading highly conductive (HC) and mechanically coherent energetic interface is considered. An HC interface only allows for the jump in normal heat flux and not the jump in temperature across the interface. In this contribution, a thermodynamically consistent theory for thermally GI and mechanically coherent energetic interfaces subject to in-plane degradation is developed. A computational framework to model this class of interfaces using the finite element method is established. In particular, the influence of the interface in-plane degradation on the sensitivity is captured. To this end, the equations governing a fully nonlinear transient problem are given. They are solved using the finite element method. The results are illustrated through a series of three-dimensional numerical examples for various interfacial parameters. In particular, a comparison is made between the results of the intact and the degraded thermally GI interface formulation. © 2017 Mathematical Sciences Publishers.
Open Access
Generalized interfaces via weighted averages for application to graded interphases at large deformations
(Elsevier Ltd, 2021-04) Saeb, S.; Firooz, S.; Steinmann, P.; Javili, Ali
Finite-thickness interphases between different constituents in heterogeneous materials are often replaced by a zero-thickness interface model. Commonly accepted interface models intuitively assume that the interface layer is situated exactly in the middle of its associated interphase. Furthermore, it has been reported in the literature that this assumption is necessary to guarantee the balance of angular momentum on the interface. While the interface coincides with the mid-layer of a uniform interphase, we argue that this assumption fails to sufficiently capture the behavior of graded or inhomogeneous interphases. This contribution extends the formulation of the general interface model to account for arbitrary interface positions. The issue of angular momentum balance on general interfaces is critically revisited. It is proven that the interface position does not necessarily have to coincide with the mid-layer in order to satisfy the angular momentum balance. The analysis here leads to a unique definition of the controversially discussed interface configuration. The presented general interface model is essentially based upon the weighted average operator instead of the commonly accepted classical average operator. The framework is geometrically exact and suitable for finite deformations. The significance of the interface position is demonstrated via a series of examples where the interface position is identified based on a full resolution interphase.
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
A note on traction continuity across an interface in a geometrically non-linear framework
(SAGE Publications, 2018) Javili, Ali
The objective of this contribution is to elaborate on the notion of “traction continuity” across an interface at finite deformations. The term interface corresponds to a zero-thickness model representing the interphase between different constituents in a material. Commonly accepted interface models are the cohesive interface model and the elastic interface model. Both the cohesive and elastic interface models are the limit cases of a generalized interface model. This contribution aims to rigorously analyze the concept of the traction jump for the general interface model. The governing equations of the general interface model in the material as well as spatial configurations are derived and the traction jump across the interface for each configuration is highlighted. It is clearly shown that the elastic interface model undergoes a traction jump in both the material and spatial configurations according to a generalized Young-Laplace equation. For the cohesive interface model, however, while the traction field remains continuous in the material configuration, it can suffer a jump in the spatial configuration. This finding is particularly important since the cohesive interface model is based on the assumption of traction continuity across the interface and that the term “traction” often refers to the spatial configuration and not the material one. Thus, additional care should be taken when formulating an interface model in a geometrically non-linear framework. The theoretical findings for various interface models are carefully illustrated via a series of two-dimensional and three-dimensional numerical examples using the finite element method.