A novel constrained LArge Time INcrement method for modelling quasi-brittle failure

Vandoren, Bram; Proft, K. De; Simone, A.; Sluys, L.J.

doi:10.1016/j.cma.2013.06.005

Cited by 23 publications

(15 citation statements)

References 36 publications

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“…We shall denote the solution at the ith LATIN iteration and the nth time step by u (i) n . Using a notation similar to that in [16], after solving the local problem, we will obtain a solution denoted by u (i+1∕2) n . Then, after solving the global problem, the solution will become u (i+1) n .…”

Section: The Large Time Increment Iterative Processmentioning

confidence: 99%

“…The global problem solved in each LATIN iteration consists of all the original problem's equations except the nonlinear constitutive equation (16), which is replaced by a linear equation that determines the progress direction. The latter has the form…”

Section: The Global Problemmentioning

confidence: 99%

“…It was also applied to sheet cutting problems [11,12], to thermomechanical problems [13], to fatigue crack propagation, in conjunction with XFEM [14], and to tensegrity media [15].Most of the papers on LATIN consider such nonlinearity that after finite element (FE) discretization leads to a single-valued load vector as a function of the displacement vector. In [16], the LATIN method was extended to deal with more general nonlinear behavior, namely, one where the load-displacement curve may 'bend backwards'. The method was applied to models of quasi-brittle failure.In [17], LATIN was applied to elastic beams with large deformation.…”

mentioning

confidence: 99%

“…Most of the papers on LATIN consider such nonlinearity that after finite element (FE) discretization leads to a single-valued load vector as a function of the displacement vector. In [16], the LATIN method was extended to deal with more general nonlinear behavior, namely, one where the load-displacement curve may 'bend backwards'. The method was applied to models of quasi-brittle failure.…”

mentioning

confidence: 99%

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LATIN: A new view and an extension to wave propagation in nonlinear media

Givoli

Bharali

Sluys

2017

Numerical Meth Engineering

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The LATIN (acronym of LArge Time INcrement) method was originally devised as a non-incremental procedure for the solution of quasi-static problems in continuum mechanics with material nonlinearity. In contrast to standard incremental methods like Newton and modified Newton, LATIN is an iterative procedure applied to the entire loading path. In each LATIN iteration, two problems are solved: a local problem, which is nonlinear but algebraic and miniature, and a global problem, which involves the entire loading process but is linear. The convergence of these iterations, which has been shown to occur for a large class of nonlinear problems, provides an approximate solution to the original problem. In this paper, the LATIN method is presented from a different viewpoint, taking advantage of the causality principle. In this new view, LATIN is an incremental method, and the LATIN iterations are performed within each load step, similarly to the way that Newton iterations are performed. The advantages of the new approach are discussed. In addition, LATIN is extended for the solution of time-dependent wave problems. As a relatively simple model for illustrating the new formulation, lateral wave propagation in a flat membrane made of a nonlinear material is considered. Numerical examples demonstrate the performance of the scheme, in conjunction with finite element discretization in space and the Newmark trapezoidal algorithm in time. 126D. GIVOLI, R. BHARALI AND L. SLUYS 2. A 'local' problem, which consists of the nonlinear algebraic relations, and an auxiliary equation, which determines a progress direction. This problem is nonlinear but algebraic and miniature.The convergence of these iterations, which has been shown to occur for a large class of nonlinear problems [2,4], provides an approximate solution to the original problem.The terms 'global' and 'local' are used here as in the LATIN literature. Namely, a global problem is a problem involving differential equations, whereas a local problem is a problem involving only algebraic relations. We stress this point, because in other contexts (such as absorbing boundary conditions or certain material models in plasticity that prevent mesh-dependent behavior), the word 'nonlocal' refers to an integral operator, whereas a 'local relation' means that the relation involves only functions and derivatives at a single point.The LATIN method was applied to quasi-static problems in damage mechanics [5], anisotropic plasticity [6], cyclic viscoplasticity [7,8], poroelasticity [9], and rigid plasticity (with a special modified implementation) [10]. It was also applied to sheet cutting problems [11,12], to thermomechanical problems [13], to fatigue crack propagation, in conjunction with XFEM [14], and to tensegrity media [15].Most of the papers on LATIN consider such nonlinearity that after finite element (FE) discretization leads to a single-valued load vector as a function of the displacement vector. In [16], the LATIN method was extended to deal with more general nonlinear behavior, na...

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Section: The Large Time Increment Iterative Processmentioning

confidence: 99%

Section: The Global Problemmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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LATIN: A new view and an extension to wave propagation in nonlinear media

Givoli

Bharali

Sluys

2017

Numerical Meth Engineering

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“…This implementation of the cohesive crack model is based on two stages: (a) a global one in which the FCT is moved ahead of one increment; (b) a local one in which the non-linear conditions occurring in the FPZ are taken into account. O This two-stage approach is known in the literature as a Large Time Increment approach [12,13]. The main consequences of this two-stage approach are: (a) a previous converged load increment is not required.…”

Section: Traction-separation Law Applied To the Fracture Process Zonementioning

confidence: 99%

Sub-critical cohesive crack propagation with hydro-mechanical coupling and friction

Valente¹,

Alberto²,

Barpi³

2015

Frattura Ed Integrità Strutturale

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Looking at the long-time behaviour of a dam, it is necessary to assume that the water can penetrate a possible crack washing away some components of the concrete. This type of corrosion reduces the tensile strength and fracture energy of the concrete compared to the same parameters measured during a short-time laboratory test. This phenomenon causes the so called sub-critical crack propagation. That is the reason why the International Commission of Large Dams recommends to neglect the tensile strength of the joint between the dam and the foundation, which is the weakest point of a gravity dam. In these conditions a shear displacement discontinuity starts growing in a point, called Fictitious Crack Tip (shortened FCT), which is still subjected to a compression stress. In order to manage this problem, in this paper the cohesive crack model is re-formulated with the focus on the shear stress component. In this context, the classical Newton-Raphson method fails to converge to an equilibrium state. Therefore the approach used is based on two stages: (a) a global one in which the FCT is moved ahead of one increment; (b) a local one in which the non-linear conditions occurring in the Fracture Process Zone are taken into account. This two-stage approach, which is known in the literature as a Large Time Increment method, is able to model three different mechanical regimes occurring during the crack propagation between a dam and the foundation rock.

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