On the strong discontinuity approach in finite deformation settings (original) (raw)
Related papers
Mechanics Research Communications, 2017
On the basis of the strong discontinuity analysis, a discrete model expressed in terms of traction vectordisplacement jump has been constructed from a continuous model expressed in terms of stress-strain law. In the first part of the paper, this approach has been extended to a class of anisotropic continuum damage constitutive models [1]. In this second part of the paper, the proposed class of discrete anisotropic damage constitutive models is particularized. More precisely, a micromechanical-based anisotropic damage constitutive model is derived. This model accounts in a natural manner for particular crack families orientation. The aims of this paper are (i) to illustrate the capabilities of the proposed discrete enhanced model in reproducing the induced anisotropy appearing in quasi-brittle materials when cracking and (ii) to assess the numerical robustness of the time integration scheme. For this purpose, two numerical examples at the material point level are exposed after a brief presentation of the time integration scheme. The correspondence between the continuous and the discrete model as well as the induced anisotropy features are emphasized.
Theory and numerics for finite deformation fracture modelling using strong discontinuities
International Journal for Numerical Methods in Engineering, 2006
A general finite element approach for the modelling of fracture is presented for the geometrically nonlinear case. The kinematical representation is based on a strong discontinuity formulation in line with the concept of partition of unity for finite elements. Thus, the deformation map is defined in terms of one continuous and one discontinuous portion, considered as mutually independent, giving rise to a weak formulation of the equilibrium consisting of two coupled equations. In addition, two different fracture criteria are considered. Firstly, a principle stress criterion in terms of the material Mandel stress in conjunction with a material cohesive zone law, relating the cohesive Mandel traction to a material displacement 'jump' associated with the direct discontinuity. Secondly, a criterion of Griffith type is formulated in terms of the material-crack-driving force (MCDF) with the crack propagation direction determined by the direction of the force, corresponding to the direction of maximum energy release. Apart from the material modelling, the numerical treatment and aspects of computational implementation of the proposed approach is also thoroughly discussed and the paper is concluded with a few numerical examples illustrating the capabilities of the proposed approach and the connection between the two fracture criteria.
From continuum mechanics to fracture mechanics: the strong discontinuity approach
Engineering Fracture Mechanics, 2002
The paper deals with the strong discontinuity approach and shows the links with the decohesive fracture mechanics provided by that approach. On the basis of 1D continuum damage models it is shown that, by introducing some few ingredients like the strong discontinuity kinematics, discrete constitutive models (traction vs. displacement jumps) are automatically induced. For the general 2D±3D cases it is shown that the weak discontinuity concept is an additional ingredient, necessary in order to ful®ll the strong discontinuity conditions, which allows to establish additional links with the fracture process zone concept. Also classical fracture mechanics properties as the fracture energy are related to the continuum model properties in a straightforward manner. Ó
Continuum approach to material failure in strong discontinuity settings
Computer Methods in Applied Mechanics and Engineering, 2004
The paper focuses the numerical modelling of material failure in a strong discontinuity setting using a continuum format. Displacement discontinuities, like fractures, cracks, slip lines, etc., are modelled in a strong discontinuity approach, enriched by a transition from weak to strong discontinuities to get an appropriate representation of the fracture process zone. The introduction of the strong discontinuity kinematics automatically projects any standard dissipative constitutive model, equipped with strain softening, into a discrete traction-separation law that is fulfilled at the discontinuity interface. Numerical issues like a global discontinuity tracking algorithm via a heat conduction-like problem are also presented. Some representative numerical simulations illustrate the performance of the presented approach.
Mechanics Research Communications, 2017
On the basis of the strong discontinuity analysis, a discrete model expressed in terms of traction vectordisplacement jump has been constructed from a continuous model expressed in terms of stress-strain law. In the first part of the paper, this approach has been extended to a class of anisotropic continuum damage constitutive models [1]. In this second part of the paper, the proposed class of discrete anisotropic damage constitutive models is particularized. More precisely, a micromechanical-based anisotropic damage constitutive model is derived. This model accounts in a natural manner for particular crack families orientation. The aims of this paper are (i) to illustrate the capabilities of the proposed discrete enhanced model in reproducing the induced anisotropy appearing in quasi-brittle materials when cracking and (ii) to assess the numerical robustness of the time integration scheme. For this purpose, two numerical examples at the material point level are exposed after a brief presentation of the time integration scheme. The correspondence between the continuous and the discrete model as well as the induced anisotropy features are emphasized.
Advances in Civil Engineering, 2020
is paper investigates the variational finite element formulation and its numerical implementation of the damage evolution in solids, using a new discrete embedded discontinuity approach. For this purpose, the kinematically optimal symmetric (KOS) formulation, which guarantees kinematics, is consistently derived. In this formulation, rigid body motion of the parts in which the element is divided is obtained. To guarantee equilibrium at the discontinuity surfaces, the length of the discontinuity is introduced in the numerical implementation at elemental level. To illustrate and validate this approach, two examples, involving mode-I failure, are presented. Numerical results are compared with those reported from experimental tests. e presented discontinuity formulation shows a robust finite element method to simulate the damage evolution processes in quasi-brittle materials, without modifying the mesh topology when cohesive cracks propagate.
Once strain localization occurs in softening solids, inelastic loading behavior is restricted within a narrow band while the bulk unloads elastically. Accordingly, localized failure in solids can be approached by embedding/smearing a traction-based inelastic discontinuity (band) within an (equivalent) elastic matrix along a specific orientation. In this context, the conformity of the strong/regularized and embedded/smeared discontinuity approaches are investigated, regarding the strategies dealing with the kinematics and statics. On one hand, the traction continuity condition imposed in weak form results in the strong and regularized discontinuity approaches, with respect to the approximation of displacement/strain discontinuities. In addition to the elastic bulk, consistent plastic-damage cohesive models for the discontinuities are established. The conformity between the strong discontinuity approach and its regularized counterpart is shown through the fracture energy analysis. On the other hand, the traction continuity condition can also be enforced point-wisely in strong form so that the standard principle of virtual work applies. In this case, the static constraint resulting from traction continuity can be used to eliminate the kinematic variable associated with the discontinuity (band) at the material level. This strategy leads to embedded/smeared discontinuity models for the overall weakened solid which can also be cast into the elastoplastic degradation framework with a different kinematic decomposition. Being equivalent to the kinematic constraint guaranteeing stress continuity upon strain localization, Mohr's maximization postulate is adopted for the determination of the discontinuity orientation. Closed-form results are presented in plane stress conditions, with the classical Rankine, Mohr-Coulomb, von Mises and Drucker-Prager criteria as illustrative examples. The orientation of the discontinuity (band) and the stress-based failure criteria consistent with the traction-based counterparts are given. Finally, a generic failure criterion of either elliptic, parabolic or hyperbolic type, appropriate for the modeling of mixed-mode failure, is analyzed in a unified manner. Furthermore, a novel method is proposed to calibrate the involved mesoscopic parameters from available macroscopic test data, which is then validated against Willam's numerical test.
Strong discontinuities and continuum plasticity models: the strong discontinuity approach
The paper presents the Strong Discontinuity Approach for the analysis and simulation of strong discontinuities in solids using continuum plasticity models. Kinematics of weak and strong discontinuities are discussed, and a regularized kinematic state of discontinuity is proposed as a mean to model the formation of a strong discontinuity as the collapsed state of a weak discontinuity (with a characteristic bandwidth) induced by a bifurcation of the stress± strain ®eld, which propagates in the solid domain. The analysis of the conditions to induce the bifurcation provides a critical value for the bandwidth at the onset of the weak discontinuity and the direction of propagation. Then a variable bandwidth model is proposed to characterize the transition between the weak and strong discontinuity regimes. Several aspects related to the continuum and, their associated, discrete constitutive equations, the expended power in the formation of the discontinuity and relevant computational details related to the ®nite element simulations are also discussed. Finally, some representative numerical simulations are shown to illustrate the proposed approach. #
A new continuum FE approach for fracture mechanics discontinuous problems
Computational Materials Science, 2009
A continuum finite elements (FE) formulation involving discontinuity of the displacement field to simulate fracture mechanics problems for brittle or quasi-brittle solids is proposed. A homogeneous discontinuity is assumed in a cracked finite element, and a new simple stress-based implementation of the displacement discontinuity is introduced by an appropriate stress field correction to simulate, as usually done in an elastic-plastic classical FE formulation, the mechanical effects of the crack, i.e. the proposed formulation does not introduce any discontinuous displacement field by mean of special or modified shape functions. Both linear elastic and elastic-plastic behaviour of the non-cracked material can be considered. 2D fracture problems are solved by the proposed procedure, to predict the load-displacement behaviour as well as the crack patterns in brittle structures. The new proposed simple FE formulation for discontinuous problems is computationally economic, and maintains the internal continuity of the numerical model with well-known numerical benefits.