Constitutive modeling of discontinuities by means of discrete and continuum approximations and damage models

Fernández, Luis E.; Ayala, Gustavo

doi:10.1016/j.ijsolstr.2003.10.010

Cited by 6 publications

(8 citation statements)

References 15 publications

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“…To overcome this limitation, Oliver et al [30] proposed a variable bandwidth model. Another way to fulfill such conditions is using an anisotropic damage model [31].…”

Section: A Mathematical Modelling Of Materials Failure By Edmmentioning

confidence: 99%

Variational formulation of the material failure process in solids by embedded discontinuities model

Juarez

Ayala

2008

Numerical Methods Partial

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This work presents a variational formulation of the material failure process, idealized as strain or displacement discontinuities, by weak, strong, or discrete embedded discontinuities into a continuum. It is shown that the solution of the proposed variational formulation may be approximated by different types of finite elements with embedded discontinuities. The developed displacement approximation of a finite element split by the discontinuity leads to a symmetric stiffness matrix, which considers not only the continuity of tractions but also the rigid body relative motions of the portions in which the element is split. The variational formulation of a continuum with more than one discontinuity in its interior is developed. It is shown that this formulation may lead to finite elements with embedded discontinuities that can be classified as displacement, force, mixed, and hybrid models. To show the effectiveness of the proposed formulation, the classical example of a bar under tension is solved using one and 2D finite element approximations.

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“…To overcome this limitation, Oliver et al [30] proposed a variable bandwidth model. Another way to fulfill such conditions is using an anisotropic damage model [31].…”

Section: A Mathematical Modelling Of Materials Failure By Edmmentioning

confidence: 99%

Variational formulation of the material failure process in solids by embedded discontinuities model

Juarez

Ayala

2008

Numerical Methods Partial

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“…The terms on the right of (8) enforce the fulfillment of equilibrium in the subdomains + h \S and h \S; this equilibrium was also fulfilled by (7). From the boxed term in (8) and the equilibrium at the discontinuity (obtained from (7): σ + ·n * = σ − ·n * ), the second equation used in the numerical implementation of this approximation is obtained:…”

Section: Discrete Approximationmentioning

confidence: 99%

“…This equation is used in the numerical implementation of this approximation and is equal to that obtained for the discrete approximation (7). Integrating by parts the first term of (11), 1 …”

Section: Continuum Approximation With Weak Discontinuitiesmentioning

confidence: 99%

“…when k → 0 the approximation is refered as strong discontinuity approximation; when k 0 the approximation is called weak discontinuity approximation (Oliver [7]). The second equation used in the numerical implementation corresponds to the strong form of the equilibrium equation at S − and S + :…”

Section: ∇ · (•) Is the Divergence Of (•)mentioning

confidence: 99%

“…For example, the discrete approximation uses a traction-displacement jump relationship for the discontinuity response and the discontinuity is considered to take place in a line for the two-dimensional case; on the other hand, the continuum approximation uses a stress-strain relationship for the discontinuity response and the discontinuity is considered to take place in an area (called strain localization zone) for the two-dimensional case. It should be pointed out that these two approximations can be energetically equivalent if the appropriate constitutive models are used (Fernandez and Ayala [7]). …”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A unifying formulation of the discrete and continuum approximations for embedded discontinuities

Fernández

Ayala

2006

Numer. Methods Partial Differential Eq.

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A methodology for the numerical implementation of embedded discontinuities into the finite element method is developed. This is applicable for the discrete and continuum approximations of discontinuities. The variational formulation of the problem of a solid with discontinuities is established for both approximations, yielding the equations used in this methodology. Three sets of equations are obtained by applying this methodology; all are suitable to be numerically implemented. To show the application potential of this method, the numerical simulation of the formation and propagation of a discontinuity in a concrete specimen is carried out and the results are compared with those from the physical experiment, demonstrating the adequacy of the methodology and its corresponding implementations to model discontinuities.

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New constitutive model based on disturbed state concept for shear deformation of rock joints

Xie

Lin

Chen

2022

Archiv.Civ.Mech.Eng

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Constitutive modeling of discontinuities by means of discrete and continuum approximations and damage models

Cited by 6 publications

References 15 publications

Variational formulation of the material failure process in solids by embedded discontinuities model

Variational formulation of the material failure process in solids by embedded discontinuities model

A unifying formulation of the discrete and continuum approximations for embedded discontinuities

New constitutive model based on disturbed state concept for shear deformation of rock joints

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