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

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Framework for non-coherent interface models at finite displacement jumps and finite strains. / Ottosen, Niels Saabye; Ristinmaa, Matti; Mosler, Jörn.

I: Journal of the Mechanics and Physics of Solids, Vol. 90, 01.05.2016, s. 124-141.

Forskningsoutput: TidskriftsbidragArtikel i vetenskaplig tidskrift

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TY - JOUR

T1 - Framework for non-coherent interface models at finite displacement jumps and finite strains

AU - Ottosen, Niels Saabye

AU - Ristinmaa, Matti

AU - Mosler, Jörn

PY - 2016/5/1

Y1 - 2016/5/1

N2 - 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.

AB - 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.

KW - Angular momentum

KW - Cohesive zone

KW - Dissipation inequality

KW - Interface model

KW - Large displacements

KW - Non-coherent interfaces

KW - Objectivity

KW - Principle of frame indifference

UR - http://www.scopus.com/inward/record.url?scp=84960417390&partnerID=8YFLogxK

U2 - 10.1016/j.jmps.2016.02.034

DO - 10.1016/j.jmps.2016.02.034

M3 - Article

AN - SCOPUS:84960417390

VL - 90

SP - 124

EP - 141

JO - Journal of the Mechanics and Physics of Solids

JF - Journal of the Mechanics and Physics of Solids

SN - 1873-4782

ER -