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A gradient-enhanced large-deformation continuum damage model for fibre-reinforced materials

Tobias, Waffenschmidt; Cesar, Polindara; Menzel, Andreas LU and Sergio, Blanco (2014) In Computer Methods in Applied Mechanics and Engineering 268. p.801-842
Abstract
A non-local gradient-based damage formulation within a geometrically non-linear setting is presented. The hyperelastic constitutive response at local material point level is governed by a strain energy which is additively composed of an isotropic matrix and of an anisotropic fibre-reinforced material, respectively. The inelastic constitutive response is governed by a scalar [1–d]-type damage formulation, where only the anisotropic elastic part is assumed to be affected by the damage. Following the concept in Dimitrijević and Hackl [28], the local free energy function is enhanced by a gradient-term. This term essentially contains the gradient of the non-local damage variable which, itself, is introduced as an additional independent... (More)
A non-local gradient-based damage formulation within a geometrically non-linear setting is presented. The hyperelastic constitutive response at local material point level is governed by a strain energy which is additively composed of an isotropic matrix and of an anisotropic fibre-reinforced material, respectively. The inelastic constitutive response is governed by a scalar [1–d]-type damage formulation, where only the anisotropic elastic part is assumed to be affected by the damage. Following the concept in Dimitrijević and Hackl [28], the local free energy function is enhanced by a gradient-term. This term essentially contains the gradient of the non-local damage variable which, itself, is introduced as an additional independent variable. In order to guarantee the equivalence between the local and non-local damage variable, a penalisation term is incorporated within the free energy function. Based on the principle of minimum total potential energy, a coupled system of Euler–Lagrange equations, i.e., the balance of linear momentum and the balance of the non-local damage field, is obtained and solved in weak form. The resulting coupled, highly non-linear system of equations is symmetric and can conveniently be solved by a standard incremental-iterative Newton–Raphson-type solution scheme. Several three-dimensional displacement- and force-driven boundary value problems—partially motivated by biomechanical application—highlight the mesh-objective characteristics and constitutive properties of the model and illustratively underline the capabilities of the formulation proposed. (Less)
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organization
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type
Contribution to journal
publication status
published
subject
in
Computer Methods in Applied Mechanics and Engineering
volume
268
pages
801 - 842
publisher
Elsevier
external identifiers
  • wos:000331348000039
  • scopus:84888841493
ISSN
0045-7825
DOI
10.1016/j.cma.2013.10.013
language
English
LU publication?
yes
id
21985b48-8478-44e8-9954-1c2aa7f95042 (old id 4248150)
date added to LUP
2014-01-14 11:32:50
date last changed
2017-11-05 03:53:53
@article{21985b48-8478-44e8-9954-1c2aa7f95042,
  abstract     = {A non-local gradient-based damage formulation within a geometrically non-linear setting is presented. The hyperelastic constitutive response at local material point level is governed by a strain energy which is additively composed of an isotropic matrix and of an anisotropic fibre-reinforced material, respectively. The inelastic constitutive response is governed by a scalar [1–d]-type damage formulation, where only the anisotropic elastic part is assumed to be affected by the damage. Following the concept in Dimitrijević and Hackl [28], the local free energy function is enhanced by a gradient-term. This term essentially contains the gradient of the non-local damage variable which, itself, is introduced as an additional independent variable. In order to guarantee the equivalence between the local and non-local damage variable, a penalisation term is incorporated within the free energy function. Based on the principle of minimum total potential energy, a coupled system of Euler–Lagrange equations, i.e., the balance of linear momentum and the balance of the non-local damage field, is obtained and solved in weak form. The resulting coupled, highly non-linear system of equations is symmetric and can conveniently be solved by a standard incremental-iterative Newton–Raphson-type solution scheme. Several three-dimensional displacement- and force-driven boundary value problems—partially motivated by biomechanical application—highlight the mesh-objective characteristics and constitutive properties of the model and illustratively underline the capabilities of the formulation proposed.},
  author       = {Tobias, Waffenschmidt and Cesar, Polindara and Menzel, Andreas and Sergio, Blanco},
  issn         = {0045-7825},
  language     = {eng},
  pages        = {801--842},
  publisher    = {Elsevier},
  series       = {Computer Methods in Applied Mechanics and Engineering},
  title        = {A gradient-enhanced large-deformation continuum damage model for fibre-reinforced materials},
  url          = {http://dx.doi.org/10.1016/j.cma.2013.10.013},
  volume       = {268},
  year         = {2014},
}