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Framework for non-coherent interface models at finite displacement jumps and finite strains

Ottosen, Niels Saabye LU ; Ristinmaa, Matti LU and Mosler, Jörn (2016) In Journal of the Mechanics and Physics of Solids 90. p.124-141
Abstract

This paper deals with a novel constitutive framework suitable for non-coherent interfaces, such as cracks, undergoing large deformations in a geometrically exact setting. For this type of interface, the displacement field shows a jump across the interface. Within the engineering community, so-called cohesive zone models are frequently applied in order to describe non-coherent interfaces. However, for existing models to comply with the restrictions imposed by (a) thermodynamical consistency (e.g., the second law of thermodynamics), (b) balance equations (in particular, balance of angular momentum) and (c) material frame indifference, these models are essentially fiber models, i.e. models where the traction vector is collinear with the... (More)

This paper deals with a novel constitutive framework suitable for non-coherent interfaces, such as cracks, undergoing large deformations in a geometrically exact setting. For this type of interface, the displacement field shows a jump across the interface. Within the engineering community, so-called cohesive zone models are frequently applied in order to describe non-coherent interfaces. However, for existing models to comply with the restrictions imposed by (a) thermodynamical consistency (e.g., the second law of thermodynamics), (b) balance equations (in particular, balance of angular momentum) and (c) material frame indifference, these models are essentially fiber models, i.e. models where the traction vector is collinear with the displacement jump. This constraints the ability to model shear and, in addition, anisotropic effects are excluded. A novel, extended constitutive framework which is consistent with the above mentioned fundamental physical principles is elaborated in this paper. In addition to the classical tractions associated with a cohesive zone model, the main idea is to consider additional tractions related to membrane-like forces and out-of-plane shear forces acting within the interface. For zero displacement jump, i.e. coherent interfaces, this framework degenerates to existing formulations presented in the literature. For hyperelasticity, the Helmholtz energy of the proposed novel framework depends on the displacement jump as well as on the tangent vectors of the interface with respect to the current configuration - or equivalently - the Helmholtz energy depends on the displacement jump and the surface deformation gradient. It turns out that by defining the Helmholtz energy in terms of the invariants of these variables, all above-mentioned fundamental physical principles are automatically fulfilled. Extensions of the novel framework necessary for material degradation (damage) and plasticity are also covered.

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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
Angular momentum, Cohesive zone, Dissipation inequality, Interface model, Large displacements, Non-coherent interfaces, Objectivity, Principle of frame indifference
in
Journal of the Mechanics and Physics of Solids
volume
90
pages
18 pages
publisher
Elsevier
external identifiers
  • Scopus:84960417390
ISSN
0022-5096
DOI
10.1016/j.jmps.2016.02.034
language
English
LU publication?
yes
id
579a86ec-a655-4952-b356-8e2b14760ec1
date added to LUP
2016-05-10 12:06:43
date last changed
2016-07-07 07:43:24
@misc{579a86ec-a655-4952-b356-8e2b14760ec1,
  abstract     = {<p>This paper deals with a novel constitutive framework suitable for non-coherent interfaces, such as cracks, undergoing large deformations in a geometrically exact setting. For this type of interface, the displacement field shows a jump across the interface. Within the engineering community, so-called cohesive zone models are frequently applied in order to describe non-coherent interfaces. However, for existing models to comply with the restrictions imposed by (a) thermodynamical consistency (e.g., the second law of thermodynamics), (b) balance equations (in particular, balance of angular momentum) and (c) material frame indifference, these models are essentially fiber models, i.e. models where the traction vector is collinear with the displacement jump. This constraints the ability to model shear and, in addition, anisotropic effects are excluded. A novel, extended constitutive framework which is consistent with the above mentioned fundamental physical principles is elaborated in this paper. In addition to the classical tractions associated with a cohesive zone model, the main idea is to consider additional tractions related to membrane-like forces and out-of-plane shear forces acting within the interface. For zero displacement jump, i.e. coherent interfaces, this framework degenerates to existing formulations presented in the literature. For hyperelasticity, the Helmholtz energy of the proposed novel framework depends on the displacement jump as well as on the tangent vectors of the interface with respect to the current configuration - or equivalently - the Helmholtz energy depends on the displacement jump and the surface deformation gradient. It turns out that by defining the Helmholtz energy in terms of the invariants of these variables, all above-mentioned fundamental physical principles are automatically fulfilled. Extensions of the novel framework necessary for material degradation (damage) and plasticity are also covered.</p>},
  author       = {Ottosen, Niels Saabye and Ristinmaa, Matti and Mosler, Jörn},
  issn         = {0022-5096},
  keyword      = {Angular momentum,Cohesive zone,Dissipation inequality,Interface model,Large displacements,Non-coherent interfaces,Objectivity,Principle of frame indifference},
  language     = {eng},
  month        = {05},
  pages        = {124--141},
  publisher    = {ARRAY(0xe664fb8)},
  series       = {Journal of the Mechanics and Physics of Solids},
  title        = {Framework for non-coherent interface models at finite displacement jumps and finite strains},
  url          = {http://dx.doi.org/10.1016/j.jmps.2016.02.034},
  volume       = {90},
  year         = {2016},
}