Browsing by Subject "Non-local damage"

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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
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.