Coherent Energetic Interfaces Accounting for In-Plane Degradation

Abstract

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 A. Esmaeili · P. Steinmann (B) Chair of Applied Mechanics, University of Erlangen-Nuremberg, Egerlandstrasse 5, 91058 Erlangen, Germany e-mail: paul.steinmann@ltm.uni-erlangen.de A. Esmaeili e-mail: ali.esmaeili@ltm.uni-erlangen.de A. Javili Department of Mechanical Engineering, Bilkent University, 06800 Ankara, Turkey e-mail: ajavili@bilkent.edu.tr 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.

Surface plasticity: theory and computation

“…Note that surface deformation gradientF is not invertible. For further details on how the definitions of the inverse must be computed see [19]. Finally the bulk and surface Jacobians are denoted by J := det F > 0, andĴ :=d etF > 0, respectively, withd et{•} denoting the area determinant [64].…”

“…In this section we establish a numerical framework that encompasses elastoplasticity of surfaces. For further details of the finite element implementation on surfaces see [18][19][20][21][22] . The weak form, together with its temporal and spatial discretizations will be presented next.…”

“…The bulk and surface elements consist of n nB and n nS nodes respectively. The numerical integration in the bulk and on the surface is performed using Gaussian quadrature formula, see [19] for further details.…”

“…Nonetheless, the surface elasticity theory suffers from the fact that the surface behavior remains elastic regardless of the strain level at the surface. To address this problem, the authors have recently extended the surface elasticity theory to also account for damage along the surface [18][19][20][21][22] . The objective of this contribution is to further extend surface elasticity to account for another form of surface inelasticity, i.e.…”

A damage to crack transition model accounting for stress triaxiality formulated in a hybrid nonlocal implicit discontinuous Galerkin‐cohesive band model framework

“…Besides, a coupling can be introduced between the irreversible evolution of a cohesive law and the damage process of an energetic interface. [54][55][56] The cohesive behaviour can also be extracted from microscale localisation in a multiscale analysis. 57,58 The objective of this paper is to develop a computationally efficient and energetically consistent damage to crack transition framework for fracture analyses of elastic material, capturing triaxiality effects, and paving the way to more complex behaviours.…”