10 October 2012 The Non Linear Behaviour of the Microplane Model in COMSOL. A. Frigerio. COMSOL Conference 2012 Milan (Italy)

Transcription

1 0 October 202 The Non Linear Behaviour of the Microplane Model in COMSOL A. Frigerio COMSOL Conference 202 Milan (Italy) Excerpt from the Proceedings of the 202 COMSOL Conference in Milan

2 Agenda Aims of the wor The Microplane Model A few hints on the main theory aspects The non-linear behaviour Implementation process of the non-linear behaviour within COMSOL Conclusions

3 Aims of the wor Why the need to have another constitutive model for concrete? Classical constitutive models are able to properly simulate only a few specific characteristic of concrete The Microplane Model is a promising alternative approach able to simulate the overall behaviour of concrete

4 The Microplane Model: theory Logical scheme of the linear elastic behaviour of the Microplane Model compared with that of classical approaches

5 The Microplane model: the non-linear behaviour (/2) The non-linear behaviour is based on the definition of stress-strain boundaries at the microplane level: Within the domain these boundaries mar out the material response is incremental elastic Movements along these boundaries are permitted only if strain and stress increments have the same sign, otherwise elastic unloading occurs

6 The Microplane model: the non-linear behaviour (2/2) Damage can be modelled reducing progressively the elastic moduli of the incremental laws within the elastic domain The boundaries are characterized by 7 constant material parameters and 4 free parameters c, c 2 c 7 &, 2 4 The constant parameters should be ept fixed for all types of concrete The free parameters should be identified fitting test data

7 The stress-strain boundaries Tensile normal boundary N D olumetric boundaries E Deviatoric boundaries D E D D Frictional yield boundary T 2 M 2 L M EM M E L L L

8 Implementation within COMSOL Model Builder window Model Definitions node SigmaN

9 Tensile normal boundary b N E c exp c 3 N c c c 4 2 / E The initial descending part describes the tensile cracing parallel to the microplane The tail defines the frictional pullout of fragments bridging the crac surfaces snb = Young**c*exp(-max(eNint-c*c2*,0.)/(*c3+max(-c4*(sc/E),0.))) sn = min(snb,sc+sdc)

10 olumetric boundaries b E3 exp 4 b c / c 2 4 E c 3 3 A tensile volumetric boundary is needed to prevent unreasonable lateral strains in post pea softening under uniaxial, unconfined, tension Under hydrostatic pressure a progressive stronger hardening is considered to primarily represent the collapse and closure of pores sbn = -Young**3*exp(-eint/(*4)) sbp = Young**c3/(+(c4/)*max(eint-*c3,0.))^2 sc = (s>=0)*min(sbp,s)+(s<0)*max(sbn,s)

11 Deviatoric boundaries The compressive deviatoric curve controls the axial crushing strain of concrete in compression when lateral confinement is too wea to prevent crushing The tensile deviatoric curve: simulates transverse crac opening of axial distributed cracs in compression controls the volumetric expansion and lateral strains in unconfined compression tests b D c c / c 2 D E 8 c b D c c / c c 2 D E 5 6 c sdbn = -Young**c8/(+(max(-eDint-c8*c9*,0.)/(*c7))^2) sdbp = Young**c5/(+(max(eDint-c5*c6*,0.)/(*c7*c7))^2) sdc = (sd>=0)*min(sdbp,sd)+(sd<0)**max(sdbn,sd)

12 Frictional yield boundary lim N E b T T E E T T 2 2 c T 0 c At very high confining pressures, concrete becomes a plastic but frictionless material 0 2 N N 0 N 0 N E 0 T N c2 c d T d N N 0 c For small volumetric strain, a finite cohesive stress, which decreases to zero with increasing volumetric strain, is provided 0 snt = ET**c/(+c2*max(eint,0.)) stb = ET**2*c0*max(-sN+sNT,0.)/(ET**2+c0*max(-sN+sNT,0.)) st =(sm^2+sl^2)^0.5 smc = if(st>stb,sm*stb/st,sm) slc = if(st>stb,sl*stb/st,sl)

13 alidation of the model Compression test Results in terms of stress

14 alidation of the model Non-linear boundaries chec during a compression/traction test

15 Conclusions An accurate identification of the free material parameters and the constant ones is needed Applying the Microplane Model to simulate the concrete behaviour of large structures, such as dams, presenting an evident crac pattern

16 The end