An Algorithm to compute damage from load in composites

doi:10.1007/s11709-011-0107-9

Front Arch Civil Eng Chin

2011, Vol. 5

Issue (2) : 180-193 https://doi.org/10.1007/s11709-011-0107-9

RESEARCH ARTICLE

An Algorithm to compute damage from load in composites

Cyrille F. DUNANT¹, Stéphane P. A. BORDAS², Pierre KERFRIDEN², Karen L. SCRIVENER², Timon RABCZUK³(

)

1. University of Toronto, Department of civil engineering, Galbraith building, Toronto M5S 1A4, Canada; 2. Laboratory of Construction Materials, EPFL, Lausanne, Switzerland; 3. Institute of Structural Mechanics, Chair of Computational Mechanics, Bauhaus University Weimar, Weimar 99423, Germany

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Abstract

We present a new method to model fracture of concrete based on energy minimisation. The concrete is considered on the mesoscale as composite consisting of cement paste, aggregates and micro pores. In this first step, the alkali-silica reaction is taken into account through damage mechanics though the process is more complex involving thermo-hygro-chemo-mechanical reaction. We use a non-local damage model that ensures the well-posedness of the boundary value problem (BVP). In contrast to existing methods, the interactions between degrees of freedom evolve with the damage evolutions. Numerical results are compared to analytical and experimental results and show good agreement.

Keywords Concrete damage prediction modelling energy minimisation ASR

Corresponding Author(s): RABCZUK Timon,Email:timon.rabczuk@uni-weimar.de

Issue Date: 05 June 2011

Cite this article:

Cyrille F. DUNANT,Stéphane P. A. BORDAS,Pierre KERFRIDEN, et al. An Algorithm to compute damage from load in composites[J]. Front Arch Civil Eng Chin, 2011, 5(2): 180-193.

URL:

https://academic.hep.com.cn/fsce/EN/10.1007/s11709-011-0107-9
https://academic.hep.com.cn/fsce/EN/Y2011/V5/I2/180

Fig.1 Principle of cohesive crack models

Fig.2 Principle of non-local constitutive models with the typical bell shaped domain of influence

Fig.3 Graphical description of the algorithm.

Fig.4 Computation setup. Displacements are imposed on the top and bottom sides of the sample. Although the setup is symmetric, both parts were computed to show that the algorithms correctly capture the symetry and are not affected by the underlying mesh.

Fig.5 Comparison of the stress-strain curve of an elastic-plastic sample under uniaxial tension when computed using a classical non-local method, and when using the proposed algorithm. There is no significant difference between the methods.

Fig.6 Damage patterns obtained with a classical non-local method (left) and with the proposed algorithm (right). Damage= 1 is black, and damage= 0 is white.

Fig.7 Number of iterations to convergence at each step. The peak in the new algorithm comes from the formation of the large damaged zone in the center of the specimen: if large amounts of damage are required to reach convergence, the algorithm takes longer to converge.

Fig.8 Geometrical setup of the numerical experiment. The displacements are imposed on the top and bottom boundaries, as (0, 1) and (0, -1).

Fig.9 Damage localization with successive refinements of the mesh. Damage is greyscale-coded from black, 1, to light gray, undamaged material is white. This figure shows how the damaged surface stays relatively constant as the mesh becomes finer. The effect of choosing different fracture criteria is apparent. The more ductile von Mises (b) produces more spread-out damage patterns (reference solution using a classical non-local method on the top (a)), whereas Mohr-Coulomb (c) leads to the apparition of crack-like patterns. A material which can only fail along shear planes is also shown as an example (d)

Fig.10 (a) Convergence of the absolute energy stored in the system with increasing number of unknowns. The absolute energy is different also because of different discretisations of the sample geometry. (b) Log-log plot of the iterations to convergence and the number of unknowns. The order is .

Fig.11 A micrograph showing an aggregate degraded by asr (a). For comparison, a detail of a fracture pattern generated by the asr model: in black with a white border, the crack paths, in white with a black border, the gel pockets. (b).

Fig.12 Predicted and measured loss of stiffness (measured as the apparent Young’s modulus) of the sample (a), the bounding box of experimental values outline is shown as the solid gray background. Simulation of the free expansion of an ASR-affected sample related to the observed damage- the “apparent reaction” (b), the bounding-box of the experimental values is in solid gray, simulated points are the black dots.

1	Bazant Z P, Belytschko T. Wave propagation in a strain-softening bar: Exact solution. Journal of Engineering Mechanics , 1985, 111(3): 381-389 doi: 10.1061/(ASCE)0733-9399(1985)111:3(381)
2	Bazant Z, Jirasek M. Non-local integral formulations of plasticity and damage: survey of process. Journal of Engineering Mechanics , 2002, 128(1): 1119-1149 doi: 10.1061/(ASCE)0733-9399(2002)128:11(1119)
3	Babu?ka I, Melenk I. Partition of unity method. International Journal for Numerical Methods in Engineering , 1997, 40(4): 727-758 doi: 10.1002/(SICI)1097-0207(19970228)40:4<727::AID-NME86>3.0.CO;2-N
4	Belytschko T, Black T. Elastic crack growth in finite elements with minimal remeshing. International Journal for Numerical Methods in Engineering , 1999, 45(5): 601-620 doi: 10.1002/(SICI)1097-0207(19990620)45:5<601::AID-NME598>3.0.CO;2-S
5	Strouboulis T, Babu?ka I, Copps K. The design and analysis of the generalized finite element method.Computer Methods in Applied Mechanics and Engineering , 2000, 181(1-3): 43-69 doi: 10.1016/S0045-7825(99)00072-9
6	Rabczuk T, Bordas S, Zi G. A three-dimensional meshfree method for continuous crack initiation, nucleation and propagation in statics and dynamics. Computational Mechanics , 2007, 40(3): 473-495 doi: 10.1007/s00466-006-0122-1
7	Bordas S, Rabczuk T, Zi G. Three-dimensional crack initiation, propagation, branching and junction in non-linear materials by an extended meshfree method without asymptotic enrichment. International Journal of Solids and Structures , 2008, 75(5): 943-960
8	Bordas S, Duot M, Le P. A simple a posteriori error estimator for the extended finite element method. Communications in Numerical Methods in Engineering , 2007 (In press) doi: 10.1002/cnm.1001 pmid:19829757
9	Stratonovitch R L. Derivation of irreversibility of thermodynamic processes from microscopic reversibility. Theoretical and Mathematical Physics , 1978, 36(1): 607-616 doi: 10.1007/BF01035874
10	Simo J C, Hughes T J R. Computational Inelasticity,vol. 7. Springer , 1998.
11	Ba?ant Z P, Jirásek M. Nonlocal integral formulations of plasticity and damage: Survey of progress. Journal of Engineering Mechanics , 2002, 128(11): 1119 doi: 10.1061/(ASCE)0733-9399(2002)128:11(1119)
12	Francfort G A, Marigo J J. Revisiting brittle fracture as an energy minimisation problem. Journal of the Mechanics and Physics of Solids , 1998, 46(8): 1319-1342 doi: 10.1016/S0022-5096(98)00034-9
13	Dunant C, Vinh P N, Belgasmia M, Bordas S, Guidoum A. Architecture tradeoffs of integrating a mesh generator to partition of unity enriched object-oriented finite element software. Revue Européenne de Mécanique Numérique , 2007, 16(2): 237-258 doi: 10.3166/remn.16.237-258
14	Bordas S, Nguyen V P, Dunant C, Nguyen-Dang H, Guidoum A. An extended finite element library. International Journal for Numerical Methods in Engineering , 2007, 71(6): 703-732 doi: 10.1002/nme.1966
15	Ponce J M, Batic O R. Different manifestations of the alkali-silica reaction in concrete according to the reaction kinetics of the reactive aggregate. Cement and Concrete Research , 2006, 36(6): 1148-1156 doi: 10.1016/j.cemconres.2005.12.022
16	Ben Haha M, Gallucci E, Guidoum A, Scrivener K L. Relation of expansion due to alkali silica reaction to the degree of reaction measured by sem image analysis. Cement and Concrete Research , 2007, 37(8): 1206-1214 doi: 10.1016/j.cemconres.2007.04.016
17	Dunant C F, Scrivener K L. Micro-mechanical modelling of alkali silica-reaction-induced degradation using the amie framework. Cement and Concrete Research , 2010, 4(4): 517-525 doi: 10.1016/j.cemconres.2009.07.024
18	Kawamura M, Iwahori K. Asr gel composition and expansive pressure in mortars under restraint. Cement and Concrete Composites , 2004, 26(1): 47-56 doi: 10.1016/S0958-9465(02)00135-X

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