Integration of finite displacement interface element in reference and current configurations

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Abstract

In the present paper the non-linear behaviour of a solid body with embedded cohesive interfaces is examined in a finite displacements context. The principal target is the formulation of a two dimensional interface finite element which is referred to a local reference frame, defined by normal and tangential unit vectors to the interface middle surface. All the geometric operators, such as the interface elongation and the reference frame, are computed as function of the actual nodal displacements. The constitutive cohesive law is defined in terms of Helmholtz free energy for unit undeformed interface surface and, in order to obtain the same nodal force vector and stiffness matrix by the two integration schemes, the cohesive law in the deformed configuration is defined in terms of Cauchy traction, as a function of separation displacement and of interface elongation. Explicit expression of the nodal force vector is integrated either over the reference configuration or over the current configuration, which is shown to produce the same analytical finite element operators. No differences between the integration carried out in the reference and in the current configuration are shown, provided that elongation of the interface is taken in to account.
Lingua originaleEnglish
pagine (da-a)1455-1468
Numero di pagine14
RivistaMeccanica
Volume53
Stato di pubblicazionePublished - 2017

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Elongation
configurations
elongation
Stiffness matrix
Free energy
Mathematical operators
operators
stiffness matrix
traction
free energy
formulations
matrices

All Science Journal Classification (ASJC) codes

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

Cita questo

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title = "Integration of finite displacement interface element in reference and current configurations",
abstract = "In the present paper the non-linear behaviour of a solid body with embedded cohesive interfaces is examined in a finite displacements context. The principal target is the formulation of a two dimensional interface finite element which is referred to a local reference frame, defined by normal and tangential unit vectors to the interface middle surface. All the geometric operators, such as the interface elongation and the reference frame, are computed as function of the actual nodal displacements. The constitutive cohesive law is defined in terms of Helmholtz free energy for unit undeformed interface surface and, in order to obtain the same nodal force vector and stiffness matrix by the two integration schemes, the cohesive law in the deformed configuration is defined in terms of Cauchy traction, as a function of separation displacement and of interface elongation. Explicit expression of the nodal force vector is integrated either over the reference configuration or over the current configuration, which is shown to produce the same analytical finite element operators. No differences between the integration carried out in the reference and in the current configuration are shown, provided that elongation of the interface is taken in to account.",
author = "Guido Borino and Francesco Parrinello",
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pages = "1455--1468",
journal = "Meccanica",
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TY - JOUR

T1 - Integration of finite displacement interface element in reference and current configurations

AU - Borino, Guido

AU - Parrinello, Francesco

PY - 2017

Y1 - 2017

N2 - In the present paper the non-linear behaviour of a solid body with embedded cohesive interfaces is examined in a finite displacements context. The principal target is the formulation of a two dimensional interface finite element which is referred to a local reference frame, defined by normal and tangential unit vectors to the interface middle surface. All the geometric operators, such as the interface elongation and the reference frame, are computed as function of the actual nodal displacements. The constitutive cohesive law is defined in terms of Helmholtz free energy for unit undeformed interface surface and, in order to obtain the same nodal force vector and stiffness matrix by the two integration schemes, the cohesive law in the deformed configuration is defined in terms of Cauchy traction, as a function of separation displacement and of interface elongation. Explicit expression of the nodal force vector is integrated either over the reference configuration or over the current configuration, which is shown to produce the same analytical finite element operators. No differences between the integration carried out in the reference and in the current configuration are shown, provided that elongation of the interface is taken in to account.

AB - In the present paper the non-linear behaviour of a solid body with embedded cohesive interfaces is examined in a finite displacements context. The principal target is the formulation of a two dimensional interface finite element which is referred to a local reference frame, defined by normal and tangential unit vectors to the interface middle surface. All the geometric operators, such as the interface elongation and the reference frame, are computed as function of the actual nodal displacements. The constitutive cohesive law is defined in terms of Helmholtz free energy for unit undeformed interface surface and, in order to obtain the same nodal force vector and stiffness matrix by the two integration schemes, the cohesive law in the deformed configuration is defined in terms of Cauchy traction, as a function of separation displacement and of interface elongation. Explicit expression of the nodal force vector is integrated either over the reference configuration or over the current configuration, which is shown to produce the same analytical finite element operators. No differences between the integration carried out in the reference and in the current configuration are shown, provided that elongation of the interface is taken in to account.

UR - http://hdl.handle.net/10447/263085

M3 - Article

VL - 53

SP - 1455

EP - 1468

JO - Meccanica

JF - Meccanica

SN - 0025-6455

ER -