diff --git a/README.md b/README.md index fdf533f..312facd 100644 --- a/README.md +++ b/README.md @@ -19,6 +19,7 @@ It is mainly decomposed in two parts: - `plasticity` - `viscoelasticity` - `viscoplasticity` + - `homogenization` - `materials`: this part gathers to specific materials. The last purpose of this project is to show how to build a compilation diff --git a/generic-behaviours/homogenization/CMakeLists.txt b/generic-behaviours/homogenization/CMakeLists.txt index 6f91a87..4177cfa 100644 --- a/generic-behaviours/homogenization/CMakeLists.txt +++ b/generic-behaviours/homogenization/CMakeLists.txt @@ -25,3 +25,5 @@ genericmtest(Homogenization BetaRule genericmtest(Homogenization Idiart_viscoelastic BEHAVIOUR Idiart_viscoelastic REFERENCE_FILE ${CMAKE_CURRENT_SOURCE_DIR}/references/Idiart_viscoelastic.ref) + +add_subdirectory(MassonAffineFormulation) diff --git a/generic-behaviours/homogenization/MassonAffineFormulation/Affine_tensors.mfront b/generic-behaviours/homogenization/MassonAffineFormulation/Affine_tensors.mfront new file mode 100644 index 0000000..08aef4e --- /dev/null +++ b/generic-behaviours/homogenization/MassonAffineFormulation/Affine_tensors.mfront @@ -0,0 +1,169 @@ +@DSL ImplicitII; +@Behaviour Affine_tensors; +@Author Martin Antoine; +@Date 06 / 03 / 26; +@Description{"Affine formulation for homogenization of a viscoplastic polycrystal, (Masson et al. 2001.), based on Green interaction tensors"}; +@UseQt false; +@Algorithm NewtonRaphson; +@Epsilon 1e-14; + +@TFELLibraries {"Material"}; + +@Includes{ +#include "TFEL/Material/IsotropicModuli.hxx" +#include "extra-headers/TFEL/Material/tensors.hxx" +#include "TFEL/Material/PolyCrystalsSlidingSystems.hxx"} + +//! number of phases +@IntegerConstant Np =10; + +//! normalization strainrate +@Parameter real gamma0 = 1.0; +//! bulk modulus of the reference medium used for the interaction tensors +@Parameter stress mu0 = 1; + +@ModellingHypothesis Tridimensional; +@OrthotropicBehaviour; +@CrystalStructure HCP; +@SlidingSystems{<1, 1, -2, 0>{1, -1, 0, 0}, + <-2, 1, 1, 3>{1, -1, 0, 1}, + <-2, 1, 1, 0>{0, 0, 0, 1}, + <1, 1, -2, 0>{1, -1, 0, 1}}; + +@MaterialProperty real nexp; +@MaterialProperty real tau1; +@MaterialProperty real tau2; +@MaterialProperty real kap; +//@MaterialProperty real r0; + +@StateVariable Stensor sigma[Np]; +sigma.setEntryName("PhaseReferenceStress"); + +@AuxiliaryStateVariable real ne; + +@LocalVariable Stensor4 I; +@LocalVariable Stensor4 J; +@LocalVariable Stensor4 K; +@LocalVariable Stensor4 L0; +@LocalVariable Stensor4 M0; +@LocalVariable real frac[Np]; +@LocalVariable real tau0[Np]; +@LocalVariable Stensor4 M[Np]; +@LocalVariable Stensor4 L[Np]; +@LocalVariable Stensor4 Ar[Np]; +@LocalVariable tmatrix<6*Np,6,real> A; +@LocalVariable std::array,Np>,Np> GAMMA; +@LocalVariable tmatrix<6*Np,6,real> dsigma_deto; +@LocalVariable real r0; +@LocalVariable real muhom; + +@InitLocalVariables{ +I=tfel::math::st2tost2<3u,real>::Id(); +J=tfel::math::st2tost2<3u,real>::J(); +K=tfel::math::st2tost2<3u,real>::K(); +GAMMA=Gamma::get_tensor(); +r0=1; +L0=2*mu0*K; +M0=1/(2*mu0)*K; +r0=max(real(1),r0); +} + + + +@Integrator { +ne=nexp; +using ExtendedPolyCrystalsSlidingSystems = + ExtendedPolyCrystalsSlidingSystems, real>; +const auto& gs = + ExtendedPolyCrystalsSlidingSystems::getPolyCrystalsSlidingSystems("polycrystal.csv"); + +//tangent modulus and polarization///////////////////////////////// +using namespace tfel::math; +Stensor e[Np]; +Stensor4 Chom; +Stensor dpsi_dsigma[Np]; + +for (int r=0;rint(Nss/12)){tau0rk=tau1;} + else{tau0rk=tau2;} + const auto Nkr = gs.mus[r][k]^gs.mus[r][k]; + const auto taukr = gs.mus[r][k] | (sigma[r]+dsigma[r]); + const auto puisn_1 = pow(abs(taukr)/tau0rk, nexp-1); + const auto fac= nexp*gamma0/tau0rk*puisn_1; + M[r]+=fac*Nkr; + const auto puisn = puisn_1*abs(taukr)/tau0rk; + const auto sgn= taukr< 0 ? -real(1) : real(1); + dpsi_dsigma[r]+=sgn*gamma0*puisn*gs.mus[r][k]; + } + e[r]=dpsi_dsigma[r]-M[r]*(sigma[r]+dsigma[r]); + M[r]=M[r]+kap*I; + L[r]=invert(M[r]); +} + +//Operators A and B///////////////////////////////// +tmatrix<6*Np,6*Np,real> MAT; +tmatrix<6*Np,6*Np,real> G; +tmatrix<6*Np,6,real> E; +for (int r=0;r(E,6*r,0)=I; + for (int s=0;s(MAT,6*r,6*s) =1/r0*GAMMA[r][s]*dL; + map_derivative(G,6*r,6*s) =1/r0*GAMMA[r][s]*L[s]; + } + map_derivative(MAT,6*r,6*r) +=I; +} + +TinyMatrixInvert<6*Np,real>::exe(MAT); +A = MAT*E; +tmatrix<6*Np,6*Np,real> B = MAT*G; + +Chom=Stensor4::zero(); +for (int r=0;r(A,6*r,0); + Chom+=frac[r]*L[r]*Ar[r]; +} + + +auto KGhom=tfel::material::computeKGModuli(Chom); +muhom=KGhom.mu; +r0=muhom/mu0; + +auto tau_eff=Stensor::zero(); +//residues///////////////////////////////////// +for (int r=0;r(B,6*r,6*s); + tau_eff+=frac[r]*L[r]*Brs*e[s]; + fsigma[r]-=L[r]*Brs*e[s]; + } + dfsigma_ddsigma(r,r)=I; +} + +//macroscopic stress////////////////////////////////////// +sig=Chom*(eto+deto)+tau_eff; + +} + + +@TangentOperator{ +for (int r=0;r(A,6*r,0)=L[r]*Ar[r]; +} +tmatrix<6*Np,6*Np,real> iJ = jacobian; +TinyMatrixInvert<6*Np,real>::exe(iJ); +dsigma_deto=iJ*A; +Dt=Stensor4::zero(); +for (int r=0;r(dsigma_deto,6*r,0); + Dt+=frac[r]*dsigmar_deto; +} + +} diff --git a/generic-behaviours/homogenization/MassonAffineFormulation/Affine_tensors.mtest b/generic-behaviours/homogenization/MassonAffineFormulation/Affine_tensors.mtest new file mode 100644 index 0000000..59e10e6 --- /dev/null +++ b/generic-behaviours/homogenization/MassonAffineFormulation/Affine_tensors.mtest @@ -0,0 +1,23 @@ +@ModellingHypothesis 'Tridimensional'; +@Behaviour<@interface@> @library@ @behaviour@; +@ExternalStateVariable 'Temperature' {0 : 1000,1:1000}; + +@MaterialProperty 'nexp' "1+0.9*(exp(2.4*t)-1)"; +@MaterialProperty 'tau1' 5.; +@MaterialProperty 'tau2' 1; + +@MaterialProperty 'kap' "0.05"; + +@ImposedStrain 'EXX' {0 : 1, 1 : 1}; +@ImposedStrain 'EYY' {0 : -1, 1 : -1}; +@ImposedStrain 'EZZ' {0 : 0, 1 : 0}; +@ImposedStrain 'EXY' {0 : 0, 1 : 0}; +@ImposedStrain 'EXZ' {0 : 0, 1 : 0}; +@ImposedStrain 'EYZ' {0 : 0, 1 : 0}; +@Times {0.,1 in 100}; + +@OutputFilePrecision 14; + +@Test @reference_file@ 'SXX' 8 1.e-3; +@Test @reference_file@ 'SYY' 9 1.e-3; +@Test @reference_file@ 'ne' 74 1e-5; diff --git a/generic-behaviours/homogenization/MassonAffineFormulation/CMakeLists.txt b/generic-behaviours/homogenization/MassonAffineFormulation/CMakeLists.txt new file mode 100644 index 0000000..6f2cc3d --- /dev/null +++ b/generic-behaviours/homogenization/MassonAffineFormulation/CMakeLists.txt @@ -0,0 +1,12 @@ +mfront_behaviours_library(MassonAffineFormulation + Affine_tensors + ) + +STRING(COMPARE EQUAL "${CMAKE_SOURCE_DIR}" "${CMAKE_BINARY_DIR}" _insource) +if(NOT _insource) + configure_file(polycrystal.csv polycrystal.csv) +endif() + +genericmtest(MassonAffineFormulation Affine_tensors + BEHAVIOUR Affine_tensors + REFERENCE_FILE ${CMAKE_CURRENT_SOURCE_DIR}/references/Affine_tensors.ref) diff --git a/generic-behaviours/homogenization/MassonAffineFormulation/include/extra-headers/TFEL/Material/tensors.hxx b/generic-behaviours/homogenization/MassonAffineFormulation/include/extra-headers/TFEL/Material/tensors.hxx new file mode 100644 index 0000000..85fe0c5 --- /dev/null +++ b/generic-behaviours/homogenization/MassonAffineFormulation/include/extra-headers/TFEL/Material/tensors.hxx @@ -0,0 +1,221 @@ +#ifndef LIB_TFEL_MATERIAL_TENSORS_HXX +#define LIB_TFEL_MATERIAL_TENSORS_HXX +template struct Delta{ +static const std::array,10>,10>& get_tensor(){ +static Delta Delta_; +return Delta_.tensor;} +std::array,10>,10> tensor; +private: +Delta(){ +this->tensor[0][0] = {{0.5945430477551809,-0.3046454930527178,-0.2898975547024628,0.03109966838201918,-0.02275044692467835,0.06215042634665133},{-0.30464549305271776,0.6096396863953976,-0.3049941933426795,0.038191966868115185,0.05027266606928688,-0.035054601642961196},{-0.2898975547024628,-0.3049941933426795,0.5948917480451426,-0.06929163525013435,-0.027522219144608555,-0.027095824703690145},{0.031099668382019167,0.03819196686811519,-0.06929163525013433,0.8935542531126408,-0.07320557570818965,-0.07042076667886654},{-0.022750446924678383,0.05027266606928687,-0.027522219144608503,-0.07320557570818968,0.8525171588835678,0.0922248481594444},{0.062150426346651334,-0.035054601642961224,-0.02709582470369014,-0.07042076667886651,0.09222484815944441,0.8832114685552341}}; +this->tensor[0][1] = {{0.1442996930754671,-0.035647228761016246,-0.10865246431445086,-0.001210774160664758,0.032894502094787004,-0.047423894887756834},{-0.035647228761016246,0.0581509798566589,-0.02250375109564268,-0.006417963895376264,-0.0715509108072539,0.023133886338176663},{-0.10865246431445087,-0.022503751095642677,0.13115621541009354,0.00762873805604102,0.03865640871246692,0.024290008549580182},{-0.0012107741606647608,-0.006417963895376256,0.007628738056041015,0.11005317825386993,0.06391463377296781,0.08990553926182801},{0.03289450209478701,-0.0715509108072539,0.03865640871246691,0.06391463377296781,0.17953347223621408,0.0011743810542721442},{-0.04742389488775683,0.02313388633817668,0.024290008549580164,0.08990553926182801,0.0011743810542721598,0.0438296430829956}}; +this->tensor[0][2] = {{0.029844016349361485,-0.05810559000900686,0.02826157365964536,-0.021949485500435385,-0.023326323984189695,-0.05678936600547912},{-0.05810559000900686,0.15098321512086105,-0.09287762511185417,-0.019528225277258986,0.044180991460923386,0.027886991312133104},{0.02826157365964536,-0.09287762511185416,0.0646160514522088,0.04147771077769436,-0.0208546674767337,0.028902374693346035},{-0.021949485500435382,-0.019528225277258983,0.041477710777694354,0.11227573813624832,0.06307228994817766,-0.049423815337716594},{-0.023326323984189698,0.044180991460923386,-0.02085466747673371,0.06307228994817768,0.012708175648329854,-0.056257909736794495},{-0.05678936600547911,0.027886991312133114,0.028902374693346014,-0.04942381533771659,-0.05625790973679448,0.2386967485292112}}; +this->tensor[0][3] = {{0.06793202262237963,0.0011388322973147796,-0.06907085491969442,0.004313723819170074,0.014857198875141132,-0.004914972740862806},{0.0011388322973147828,0.04292742562991761,-0.0440662579272324,0.0027036260427789212,-0.029087250448683485,0.002000894901362334},{-0.0690708549196944,-0.0440662579272324,0.11313711284692682,-0.007017349861948996,0.014230051573542363,0.002914077839500473},{0.004313723819170066,0.002703626042778923,-0.00701734986194899,0.05577818744604599,-0.00048481511232754813,0.03827140302295966},{0.014857198875141146,-0.02908725044868348,0.014230051573542344,-0.00048481511232755854,0.17833248467787047,-0.016947332637421937},{-0.004914972740862804,0.0020008949013623225,0.0029140778395004827,0.03827140302295966,-0.01694733263742193,0.1673116682203437}}; +this->tensor[0][4] = {{0.08747769745265871,-0.03143419873923528,-0.05604349871342342,-0.004847342111292547,0.017548312872971265,0.010246477222406458},{-0.031434198739235274,0.035570899145107776,-0.004136700405872514,-0.005341184812554292,-0.03161857510305235,-0.003542850202222323},{-0.05604349871342342,-0.00413670040587251,0.06018019911929594,0.010188526923846832,0.014070262230081095,-0.006703627020184138},{-0.004847342111292561,-0.005341184812554281,0.010188526923846837,0.08937434098232867,-0.0069259769008571765,0.02016346114470018},{0.01754831287297125,-0.031618575103052354,0.014070262230081109,-0.006925976900857178,0.22766114670272292,-0.034503019277278696},{0.010246477222406456,-0.0035428502022223233,-0.006703627020184135,0.02016346114470018,-0.03450301927727869,0.07827568413480798}}; +this->tensor[0][5] = {{0.02808330677786242,-0.027433673762136998,-0.0006496330157254389,-0.030419067231050104,-0.013529213296218727,0.03270398343493252},{-0.027433673762137005,0.12198589069250772,-0.09455221693037069,-0.03332022211394806,0.023022497924395362,-0.01196821296869054},{-0.0006496330157254328,-0.09455221693037069,0.09520184994609614,0.06373928934499815,-0.009493284628176642,-0.020735770466241987},{-0.030419067231050097,-0.03332022211394807,0.06373928934499815,0.09988399703500765,-0.029867406000886113,-0.014392298606359016},{-0.013529213296218713,0.023022497924395365,-0.00949328462817666,-0.0298674060008861,0.029680931095984173,-0.05809914957460548},{0.032703983434932506,-0.011968212968690538,-0.02073577046624198,-0.014392298606359025,-0.05809914957460548,0.1893262787860467}}; +this->tensor[0][6] = {{0.10137097562354838,-0.05159018906918552,-0.049780786554362855,0.009429653227701298,-0.04817347477138317,0.004581110081299397},{-0.05159018906918551,0.021745689776114158,0.029844499293071352,0.010153219010967504,0.08947887299324446,-0.0028966505910160848},{-0.04978078655436285,0.029844499293071352,0.019936287261291492,-0.019582872238668798,-0.04130539822186132,-0.0016844594902833154},{0.00942965322770131,0.010153219010967492,-0.019582872238668794,0.14296517616498036,-0.019937876994531308,-0.10551421771183421},{-0.048173474771383167,0.08947887299324447,-0.04130539822186133,-0.01993787699453132,0.150989944657637,0.02111406966398509},{0.004581110081299396,-0.0028966505910160948,-0.0016844594902833048,-0.10551421771183421,0.021114069663985092,-0.01005046621429049}}; +this->tensor[0][7] = {{0.0630006783645673,-0.12338820126586426,0.06038752290129697,0.021862578391544457,0.010864469435769103,0.01186138212563029},{-0.12338820126586426,0.1979396657485221,-0.07455146448265781,0.015694152298950034,-0.020694575428316035,-0.00425075537546615},{0.06038752290129696,-0.07455146448265781,0.014163941581360829,-0.03755673069049448,0.009830105992546937,-0.007610626750164141},{0.021862578391544468,0.01569415229895004,-0.0375567306904945,0.3107754410070934,-0.005833459949650531,0.010641617802334701},{0.010864469435769086,-0.020694575428316035,0.009830105992546953,-0.0058334599496505275,0.01878559721609017,0.045040707499128},{0.01186138212563029,-0.004250755375466137,-0.007610626750164154,0.0106416178023347,0.045040707499128,0.18669362383628943}}; +this->tensor[0][8] = {{0.18681721950908783,-0.08475083457932907,-0.10206638492975875,-0.016944285850827495,0.022231658704035206,0.0746663037674661},{-0.08475083457932907,0.03994986084724007,0.04480097373208898,-0.013502810351257421,-0.035131929229484854,-0.03662800409720833},{-0.10206638492975874,0.04480097373208898,0.057265411197669765,0.03044709620208491,0.012900270525449663,-0.038038299670257784},{-0.01694428585082749,-0.013502810351257433,0.030447096202084918,0.18639053149470647,-0.083304042210065,0.04095510986460311},{0.02223165870403522,-0.03513192922948486,0.012900270525449651,-0.083304042210065,0.16123449022937467,-0.024273805518820378},{0.07466630376746611,-0.03662800409720832,-0.03803829967025781,0.04095510986460311,-0.024273805518820375,0.006616679531981177}}; +this->tensor[0][9] = {{0.029964675803228782,0.04918991027451494,-0.07915458607774374,0.008665331033838453,0.00938331699376454,-0.08708144934428888},{0.04918991027451494,0.054440020121013455,-0.10362993039552841,0.011367442229580221,-0.01887178743105875,0.04131930232589571},{-0.07915458607774374,-0.10362993039552841,0.18278451647327218,-0.020032773263418666,0.009488470437294217,0.04576214701839319},{0.008665331033838458,0.011367442229580213,-0.020032773263418662,-0.0010508436329089122,0.09257222915534385,0.03981396723835139},{0.009383316993764547,-0.018871787431058742,0.009488470437294203,0.09257222915534383,0.1885565986521531,0.030527210368093975},{-0.08708144934428887,0.041319302325895695,0.0457621470183932,0.03981396723835139,0.03052721036809398,0.2160886715374058}}; +this->tensor[1][0] = {{0.09266819751833681,-0.022892387124339234,-0.06977581039399759,-0.000777550226748199,0.021124606382864397,-0.03045527516298434},{-0.02289238712433922,0.037344129931194306,-0.01445174280685509,-0.004121569029333075,-0.04594946665503941,0.014856411007274254},{-0.06977581039399758,-0.014451742806855086,0.08422755320085268,0.004899119256081273,0.024824860272175026,0.015598864155710095},{-0.0007775502267482092,-0.004121569029333061,0.00489911925608127,0.07067533854431796,0.04104550592278797,0.057736673535061796},{0.02112460638286441,-0.0459494666550394,0.024824860272175,0.04104550592278795,0.11529507036191695,0.0007541788425156381},{-0.03045527516298435,0.014856411007274271,0.015598864155710088,0.05773667353506181,0.0007541788425156275,0.02814707319057247}}; +this->tensor[1][1] = {{0.6244758402982266,-0.32132963291661515,-0.30314620738161113,0.0292219332782354,0.03989940550851447,-0.04904966839901347},{-0.3213296329166151,0.6389042534461596,-0.3175746205295442,0.027933102013665615,-0.07504278241498638,0.029732153237944314},{-0.30314620738161113,-0.31757462052954427,0.6207208279111557,-0.057155035291900996,0.03514337690647193,0.019317515161069176},{0.02922193327823541,0.02793310201366562,-0.057155035291901,0.913136516472739,0.058575804101554996,0.09203360055671941},{0.039899405508514466,-0.0750427824149864,0.03514337690647194,0.05857580410155499,0.9464490539153516,0.07363118329552047},{-0.049049668399013494,0.02973215323794434,0.019317515161069172,0.09203360055671941,0.07363118329552047,0.923336689871675}}; +this->tensor[1][2] = {{0.06844190916663,-0.04957406201834626,-0.018867847148283733,-0.02967897072714321,-0.013902207434665814,-0.08432127155732251},{-0.049574062018346264,0.09106930018777092,-0.04149523816942466,-0.028563469885619534,0.027289963701774313,0.04007440278255617},{-0.018867847148283733,-0.04149523816942465,0.06036308531770839,0.05824244061276273,-0.013387756267108506,0.044246868774766364},{-0.029678970727143254,-0.028563469885619506,0.058242440612762736,0.1393873491122543,0.09290262360446884,-0.04117969720006104},{-0.013902207434665824,0.027289963701774316,-0.013387756267108503,0.09290262360446884,0.04978938515435117,-0.06268084904875856},{-0.08432127155732254,0.04007440278255622,0.044246868774766336,-0.04117969720006104,-0.06268084904875856,0.2000729162974912}}; +this->tensor[1][3] = 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{{0.5555150405355964,-0.3467506466215318,-0.20876439391406443,0.0004644813999086205,0.0022318056371741185,-0.0493856205745074},{-0.3467506466215318,0.7330386665577346,-0.3862880199362025,0.010274544444604674,-0.007358401603446937,0.027866636150379577},{-0.20876439391406448,-0.38628801993620254,0.5950524138502672,-0.010739025844513292,0.005126595966272822,0.021518984424127828},{0.0004644813999085995,0.010274544444604692,-0.01073902584451329,0.9316007637728838,0.05280122563174289,0.0223239405891035},{0.0022318056371741155,-0.007358401603446952,0.005126595966272841,0.0528012256317429,0.764156837240429,0.0022241663637727},{-0.049385620574507405,0.02786663615037957,0.02151898442412785,0.022323940589103485,0.002224166363772689,1.0589104708531196}}; +this->tensor[8][9] = {{0.05065275438850607,-0.041069245920796894,-0.009583508467709185,0.022200338366248434,0.010608930472030181,0.05591695224636833},{-0.041069245920796894,0.1201961738917189,-0.07912692797092201,0.025471471666687912,-0.01034708286073083,-0.025434804536271855},{-0.009583508467709181,-0.07912692797092201,0.08871043643863119,-0.04767181003293633,-0.00026184761129934724,-0.030482147710096486},{0.022200338366248434,0.025471471666687912,-0.04767181003293633,0.11799447182760109,-0.04429468186249442,-0.005550228637273975},{0.010608930472030181,-0.010347082860730836,-0.0002618476112993448,-0.044294681862494405,0.1316372133778089,0.06905630690302839},{0.05591695224636834,-0.02543480453627186,-0.030482147710096493,-0.005550228637273983,0.06905630690302839,0.1615925890299036}}; +this->tensor[9][0] = {{0.019135215525913213,0.03141230497484098,-0.0505475205007542,0.005533614914600892,0.00599211532281607,-0.05560955547973803},{0.03141230497484098,0.0347649854479141,-0.0661772904227551,0.007259162704439938,-0.01205138084002384,0.02638619421676522},{-0.05054752050075421,-0.06617729042275508,0.11672481092350931,-0.012792777619040826,0.006059265517207775,0.02922336126297283},{0.005533614914600897,0.007259162704439923,-0.012792777619040815,-0.0006710608027873714,0.05911592597344745,0.025424898605628164},{0.005992115322816089,-0.012051380840023832,0.006059265517207748,0.05911592597344746,0.12041081898352454,0.019494445847983682},{-0.05560955547973803,0.02638619421676522,0.02922336126297283,0.025424898605628167,0.019494445847983682,0.137992592669117}}; +this->tensor[9][1] = {{0.10936050192745615,-0.008504959585751043,-0.1008555423417051,0.024091075617100017,-0.038435144658095714,0.02510134570649583},{-0.008504959585751039,0.03957119963321153,-0.031066240047460506,0.02704097898228829,0.07709624901707314,-0.011183932608667707},{-0.1008555423417051,-0.031066240047460506,0.13192178238916563,-0.05113205459938829,-0.03866110435897745,-0.013917413097828133},{0.024091075617100038,0.02704097898228828,-0.0511320545993883,0.07850571097802697,-0.033816638620780444,-0.09470489058959036},{-0.03843514465809571,0.07709624901707314,-0.03866110435897747,-0.03381663862078045,0.19948093159106345,0.0735543393261324},{0.025101345706495838,-0.011183932608667716,-0.013917413097828133,-0.09470489058959038,0.0735543393261324,0.10818305539635178}}; +this->tensor[9][2] = {{0.0749283350691948,-0.07876758988324307,0.003839254814048289,0.023460093277342612,0.016150931490294333,0.055169769926667216},{-0.07876758988324309,0.12371071928910536,-0.044943129405862245,0.02216210938696544,-0.03797183607966665,-0.02680950860415754},{0.003839254814048293,-0.04494312940586225,0.04110387459181395,-0.04562220266430805,0.021820904589372327,-0.028360261322509694},{0.02346009327734258,0.02216210938696546,-0.04562220266430803,0.16235074978558323,-0.062013208683877385,0.05430553373762525},{0.01615093149029434,-0.037971836079666664,0.021820904589372334,-0.06201320868387739,0.06481744058157068,0.028826327877218103},{0.05516976992666722,-0.026809508604157546,-0.02836026132250969,0.054305533737625235,0.028826327877218106,0.142212825918924}}; +this->tensor[9][3] = {{0.08252417959178208,-0.07656879813171377,-0.005955381460068306,-0.009903870158250788,-0.04019448035154448,-0.06347836443104105},{-0.07656879813171379,0.12564994534300217,-0.049081147211288395,-0.016644180386840495,0.0814651026723926,0.03332726914180584},{-0.005955381460068306,-0.04908114721128839,0.055036528671356694,0.026548050545091274,-0.04127062232084814,0.030151095289235222},{-0.0099038701582508,-0.016644180386840485,0.026548050545091274,0.16183150565087953,0.0720491151865461,-0.08939219149148092},{-0.040194480351544534,0.08146510267239261,-0.041270622320848105,0.07204911518654607,0.08462014405087624,-0.056363519846373424},{-0.06347836443104106,0.03332726914180581,0.030151095289235274,-0.08939219149148091,-0.05636351984637341,0.11575659813557865}}; +this->tensor[9][4] = {{0.07036319261171618,-0.010302366088641596,-0.060060826523074595,-0.0073810863184598455,0.0034395185738411065,-0.01957278712821449},{-0.010302366088641591,0.058861135681417355,-0.04855876959277576,-0.002920550356762748,-0.0061541581565107036,0.006923705889303275},{-0.06006082652307459,-0.04855876959277576,0.10861959611585036,0.010301636675222593,0.002714639582669599,0.01264908123891122},{-0.00738108631845985,-0.00292055035676274,0.010301636675222587,0.1113207040390908,0.028583947628215003,0.005359118416855702},{0.003439518573841111,-0.006154158156510701,0.0027146395826695914,0.028583947628215,0.11948793775723957,0.00565848007253872},{-0.019572787128214482,0.00692370588930328,0.012649081238911208,0.005359118416855701,0.005658480072538717,0.10988740133161697}}; +this->tensor[9][5] = {{0.04304528479863023,-0.04368537099141989,0.0006400861927896598,-0.011219481584695375,0.007497823542339717,-0.02057459194727249},{-0.04368537099141989,0.11667691798736443,-0.07299154699594453,-0.011984441592801766,-0.018446401976354186,0.00933417483212334},{0.000640086192789656,-0.07299154699594453,0.07235146080315487,0.023203923177497136,0.010948578434014472,0.01124041711514916},{-0.01121948158469537,-0.01198444159280177,0.023203923177497133,0.0934689352891388,0.038923037849133736,0.010964212982935529},{0.007497823542339721,-0.018446401976354183,0.010948578434014465,0.03892303784913376,0.0595441214346396,-0.006754151297469882},{-0.0205745919472725,0.009334174832123373,0.011240417115149136,0.010964212982935526,-0.006754151297469886,0.17907553402056756}}; +this->tensor[9][6] = {{0.12849614631921766,-0.0760267361826887,-0.05246941013652895,0.020296542437544033,0.0004484704021903587,-0.0056337745415533024},{-0.0760267361826887,0.041483411392431106,0.03454332479025758,0.012272458472578034,0.0017768052533846134,0.004134588345258765},{-0.05246941013652895,0.034543324790257575,0.017926085346271357,-0.032569000910122055,-0.0022252756555749716,0.001499186196294539},{0.020296542437544023,0.012272458472578037,-0.03256900091012205,0.11664460260406848,0.004150774919371337,0.006505145016946191},{0.0004484704021903627,0.001776805253384614,-0.0022252756555749763,0.004150774919371334,0.11335246409926755,0.04064804588239335},{-0.005633774541553308,0.004134588345258766,0.001499186196294543,0.006505145016946189,0.040648045882393354,0.009054897508025125}}; +this->tensor[9][7] = {{0.14477275781522647,-0.0805497994343822,-0.06422295838084424,-0.07187864138376002,0.014190876726951436,-0.0008513522654605203},{-0.08054979943438222,0.08073777899127195,-0.00018797955688974684,-0.07094593262950444,-0.028062157986750578,-0.0023137010549125745},{-0.06422295838084424,-0.00018797955688974041,0.06441093793773398,0.1428245740132644,0.013871281259799152,0.003165053320373094},{-0.07187864138376003,-0.07094593262950441,0.1428245740132644,0.233076142536312,-0.009327027263834015,0.03587654772881745},{0.014190876726951452,-0.02806215798675058,0.013871281259799143,-0.009327027263834008,0.1614860769630608,-0.1663603012216648},{-0.0008513522654605214,-0.002313701054912577,0.0031650533203730975,0.03587654772881745,-0.1663603012216648,0.10687525351028729}}; +this->tensor[9][8] = {{0.048197874908423276,-0.03907882999395107,-0.009119044914472208,0.021124401711589174,0.010094769968107918,0.05320694406782698},{-0.03907882999395108,0.11437088118190665,-0.07529205118795558,0.024236999940971594,-0.00984561276892281,-0.024202109878502256},{-0.009119044914472204,-0.07529205118795558,0.0844110961024278,-0.04536140165256075,-0.0002491571991851076,-0.029004834189324733},{0.021124401711589177,0.0242369999409716,-0.045361401652560765,0.1122758843361766,-0.04214794558143977,-0.005281237492450739},{0.010094769968107913,-0.009845612768922814,-0.00024915719918509833,-0.042147945581439784,0.1252574321035712,0.06570950152525161},{0.05320694406782699,-0.024202109878502284,-0.02900483418932472,-0.005281237492450755,0.06570950152525161,0.1537610241775734}}; +this->tensor[9][9] = {{0.6125098447657712,-0.2845945213497104,-0.3279153234160605,0.0058773514869984115,0.020815118983102426,0.032242366092288484},{-0.28459452134971036,0.597506358385731,-0.3129118370360203,0.009523395478661333,-0.047806609134624645,-0.015596680279014853},{-0.3279153234160605,-0.3129118370360203,0.6408271604520811,-0.015400746965659743,0.026991490151522232,-0.016645685813273647},{0.0058773514869983855,0.009523395478661368,-0.01540074696565975,0.9311968255836134,-0.05551798140678483,0.05094286308469998},{0.020815118983102416,-0.047806609134624645,0.026991490151522246,-0.05551798140678483,0.9515426324351965,-0.004413168166014},{0.032242366092288484,-0.015596680279014877,-0.016645685813273622,0.05094286308469999,-0.004413168166014002,0.93720081733192}}; +}}; + +template struct Gamma{ +static const std::array,10>,10>& get_tensor(){ +static Gamma Gamma_; +return Gamma_.tensor;} +std::array,10>,10> tensor; +private: +Gamma(){ +this->tensor[0][0] = {{0.26421658870254666,-0.014791750279982058,-0.014070424184452182,-0.024587973442701725,0.018196070196703225,-0.0012982834178405722},{-0.01479175027998206,0.2528314806734857,-0.014101738708901398,-0.026361048064225727,-5.970805178808224e-05,0.023002973579562557},{-0.014070424184452182,-0.014101738708901398,0.2653350866272367,0.0005098524653366541,0.019389013251685776,0.021013279344744795},{-0.024587973442701718,-0.026361048064225727,0.0005098524653366539,0.2766114367218398,0.018301393927047414,0.017605191669716636},{0.01819607019670323,-5.970805178808269e-05,0.01938901325168576,0.01830139392704742,0.28687071027910804,-0.0230562120398611},{-0.001298283417840573,0.023002973579562564,0.021013279344744795,0.01760519166971663,-0.023056212039861104,0.27919713286119147}}; +this->tensor[0][1] = {{-0.0620271235493209,0.002209685384227346,0.006992821454510288,0.001152484196274659,-0.025114091434387538,0.00027867799122898975},{0.0022096853842273464,-0.0019897882957640245,0.004705721624235655,0.0024542816299525354,0.0009972617911226866,-0.017360767315254384},{0.006992821454510287,0.004705721624235656,-0.047177442820274106,-0.0010573938579017856,-0.026554568088807518,-0.017649797868105263},{0.0011524841962746583,0.002454281629952532,-0.0010573938579017856,-0.02751329456346748,-0.015978658443241953,-0.022476384815457003},{-0.025114091434387534,0.0009972617911226868,-0.02655456808880751,-0.015978658443241953,-0.04488336805905352,-0.00029359526356803606},{0.00027867799122899045,-0.017360767315254384,-0.017649797868105256,-0.022476384815457003,-0.00029359526356803996,-0.0109574107707489}}; +this->tensor[0][2] = {{0.01175527657698454,0.004475992515084525,-9.69302880027457e-05,0.015644628906104116,0.015722694300839397,0.0015238152597699837},{0.004475992515084525,-0.07706289441887454,0.0009211837533800304,0.015039313850310015,-0.0011541345604388694,-0.01964527406963307},{-9.693028800274575e-05,0.0009211837533800304,-0.021433367273559923,-0.00021217016342831854,0.0151047801739754,-0.019899119914936304},{0.015644628906104116,0.015039313850310015,-0.0002121701634283177,-0.02806893453406208,-0.015768072487044416,0.012355953834429148},{0.0157226943008394,-0.001154134560438869,0.015104780173975403,-0.01576807248704442,-0.0031770439120824634,0.014064477434198624},{0.0015238152597699844,-0.01964527406963307,-0.019899119914936297,0.012355953834429147,0.01406447743419862,-0.0596741871323028}}; +this->tensor[0][3] = {{-0.019797977170881838,0.0007146960630374346,0.0018312633881750454,-0.0004576529586678317,-0.010732952100253152,0.0006572235993014263},{0.0007146960630374354,-0.0059180766174602075,-0.0006055102072873932,-5.512851457004361e-05,0.00025316023070300184,-0.0010717433112548587},{0.0018312633881750454,-0.0006055102072873933,-0.05634220737994188,0.0023751154616119354,-0.01057616527485346,-0.0013000390457893936},{-0.0004576529586678283,-5.5128514570042586e-05,0.0023751154616119354,-0.013944546861511498,0.00012120377808188703,-0.009567850755739914},{-0.010732952100253155,0.00025316023070300135,-0.010576165274853454,0.00012120377808188963,-0.04458312116946762,0.004236833159355484},{0.0006572235993014258,-0.0010717433112548559,-0.001300039045789396,-0.009567850755739914,0.0042368331593554825,-0.04182791705508593}}; +this->tensor[0][4] = {{-0.043191898052452125,0.002361017194459817,-0.003205745666291233,0.00553506625610064,-0.01012161511957544,-0.0006686339986836053},{0.002361017194459817,0.0014346839223125026,-0.00035750404424051265,0.005658526931416076,0.0021701068744304623,0.00277869785747359},{-0.0032057456662912343,-0.00035750404424051313,-0.02815581677983071,0.0017760989973157949,-0.009252102458852898,0.003568892061964044},{0.005535066256100646,0.005658526931416076,0.0017760989973157962,-0.02234358524558217,0.0017314942252142941,-0.005040865286175045},{-0.010121615119575439,0.0021701068744304614,-0.009252102458852903,0.0017314942252142946,-0.05691528667568073,0.008625754819319674},{-0.0006686339986836054,0.002778697857473589,0.003568892061964042,-0.005040865286175045,0.008625754819319672,-0.019568921033701996}}; +this->tensor[0][5] = 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{{-0.06334787265938091,0.005178037743896586,0.002439130644676401,-0.012738074333829359,-0.00046499596313505023,0.0003373416811108396},{0.0051780377438965875,-0.006804309372082451,-0.0019188633092193169,-0.01073205334258786,-0.0007970796759336139,-0.002104749040592177},{0.002439130644676401,-0.0019188633092193175,0.005385870964096991,0.00047831150308716246,0.00020344055130628235,-0.0014458985033511207},{-0.012738074333829355,-0.01073205334258786,0.00047831150308716165,-0.02916115065101712,-0.0010376937298428343,-0.0016262862542365478},{-0.00046499596313505083,-0.0007970796759336137,0.00020344055130628382,-0.0010376937298428334,-0.028338116024816888,-0.010162011470598337},{0.0003373416811108398,-0.0021047490405921784,-0.0014458985033511226,-0.0016262862542365472,-0.010162011470598338,-0.002263724377006281}}; +this->tensor[9][7] = {{-0.06675117386212435,0.000997014269070293,0.003430538235704945,0.050527044236857575,-0.010226557703158494,0.0009308195615036885},{0.0009970142690702924,-0.02790733151855076,-0.0011606576514911887,0.05029386704829369,0.0003367009752670085,0.001296406758866702},{0.003430538235704945,-0.0011606576514911887,-0.010795152795127971,-0.003148759612398522,-0.010146658836370424,-7.328183495471497e-05},{0.050527044236857575,0.050293867048293674,-0.0031487596123985226,-0.058269035634078,0.002331756815958504,-0.008969136932204363},{-0.0102265577031585,0.00033670097526700875,-0.010146658836370422,0.002331756815958502,-0.0403715192407652,0.0415900753054162},{0.0009308195615036882,0.001296406758866702,-7.328183495471646e-05,-0.008969136932204363,0.0415900753054162,-0.026718813377571822}}; +this->tensor[9][8] = {{-0.009466005286256796,0.0023000706505253085,-0.0022562492198719025,-0.01675922989907903,-0.0032875942326463306,-0.0029254807417638286},{0.0023000706505253085,-0.0461154574322506,0.004233902059687461,-0.017537379456424636,0.0016975014516113513,0.01642678274481848},{-0.0022562492198719033,0.004233902059687461,-0.03275825836343588,-0.0001377790580415511,-0.000701612440823074,0.017627463822524097},{-0.016759229899079034,-0.01753737945642464,-0.00013777905804155082,-0.02806897108404415,0.010536986395359943,0.0013203093731126848},{-0.00328759423264633,0.0016975014516113513,-0.0007016124408230775,0.010536986395359946,-0.0313143580258928,-0.016427375381312902},{-0.002925480741763829,0.01642678274481849,0.017627463822524097,0.0013203093731126887,-0.016427375381312902,-0.03844025604439335}}; +this->tensor[9][9] = {{0.25498484251437725,-0.017967266715297976,-0.013823779385231905,-0.0030043586003689377,-0.015682361380134697,0.0008768468797798391},{-0.017967266715297973,0.2642793125922961,-0.014802851738787561,-0.003915869598284668,0.0014730706492970685,0.012836608472605673},{-0.013823779385231903,-0.014802851738787558,0.2400756857026656,0.0023151660127956005,-0.01722645417223965,0.013098859856170372},{-0.003004358600368933,-0.0039158695982846785,0.0023151660127956005,0.26720079360409665,0.013879495351696207,-0.012735715771174995},{-0.015682361380134697,0.0014730706492970674,-0.017226454172239655,0.013879495351696207,0.26211434189120086,0.0011032920415035},{0.0008768468797798383,0.012836608472605678,0.013098859856170365,-0.012735715771174997,0.0011032920415035006,0.26569979566702}}; +}}; + +#endif /* LIB_TFEL_MATERIAL_TENSORS_HXX */ diff --git a/generic-behaviours/homogenization/MassonAffineFormulation/polycrystal.csv b/generic-behaviours/homogenization/MassonAffineFormulation/polycrystal.csv new file mode 100644 index 0000000..f7317e9 --- /dev/null +++ b/generic-behaviours/homogenization/MassonAffineFormulation/polycrystal.csv @@ -0,0 +1,10 @@ +-149.06000 18.01000 194.06000 0.0713 +-119.06000 18.01000 194.06000 0.1111 +-89.06000 18.01000 194.06000 0.1015 +-59.06000 18.01000 194.06000 0.1042 +-29.06000 18.01000 194.06000 0.0964 +0.94000 18.01000 194.06000 0.094 +30.94000 18.01000 194.06000 0.0711 +60.94000 18.01000 194.06000 0.132 +90.94000 18.01000 194.06000 0.1063 +120.94000 18.01000 194.06000 0.1118 diff --git a/generic-behaviours/homogenization/MassonAffineFormulation/references/Affine_tensors.ref b/generic-behaviours/homogenization/MassonAffineFormulation/references/Affine_tensors.ref new file mode 100644 index 0000000..e7b5b29 --- /dev/null +++ b/generic-behaviours/homogenization/MassonAffineFormulation/references/Affine_tensors.ref @@ -0,0 +1,177 @@ +# first column: time +# 2 column: 1th component of the strain (EXX) +# 3 column: 2th component of the strain (EYY) +# 4 column: 3th component of the strain (EZZ) +# 5 column: 4th component of the strain (EXY) +# 6 column: 5th component of the strain (EXZ) +# 7 column: 6th component of the strain (EYZ) +# 8 column: 1th component of the stress (SXX) +# 9 column: 2th component of the stress (SYY) +# 10 column: 3th component of the stress (SZZ) +# 11 column: 4th component of the stress (SXY) +# 12 column: 5th component of the stress (SXZ) +# 13 column: 6th component of the stress (SYZ) +# 14 column: first component of internal variable 'PhaseReferenceStress[0]' (PhaseReferenceStress[0]XX) +# 15 column: second component of internal variable 'PhaseReferenceStress[0]' (PhaseReferenceStress[0]YY) +# 16 column: third component of internal variable 'PhaseReferenceStress[0]' (PhaseReferenceStress[0]ZZ) +# 17 column: fourth component of internal variable 'PhaseReferenceStress[0]' (PhaseReferenceStress[0]XY) +# 18 column: fifth component of internal variable 'PhaseReferenceStress[0]' (PhaseReferenceStress[0]XZ) +# 19 column: sixth component of internal variable 'PhaseReferenceStress[0]' (PhaseReferenceStress[0]YZ) +# 20 column: first component of internal variable 'PhaseReferenceStress[1]' (PhaseReferenceStress[1]XX) +# 21 column: second component of internal variable 'PhaseReferenceStress[1]' (PhaseReferenceStress[1]YY) +# 22 column: third component of internal variable 'PhaseReferenceStress[1]' (PhaseReferenceStress[1]ZZ) +# 23 column: fourth component of internal variable 'PhaseReferenceStress[1]' (PhaseReferenceStress[1]XY) +# 24 column: fifth component of internal variable 'PhaseReferenceStress[1]' (PhaseReferenceStress[1]XZ) +# 25 column: sixth component of internal variable 'PhaseReferenceStress[1]' (PhaseReferenceStress[1]YZ) +# 26 column: first component of internal variable 'PhaseReferenceStress[2]' (PhaseReferenceStress[2]XX) +# 27 column: second component of internal variable 'PhaseReferenceStress[2]' (PhaseReferenceStress[2]YY) +# 28 column: third component of internal variable 'PhaseReferenceStress[2]' (PhaseReferenceStress[2]ZZ) +# 29 column: fourth component of internal variable 'PhaseReferenceStress[2]' (PhaseReferenceStress[2]XY) +# 30 column: fifth component of internal variable 'PhaseReferenceStress[2]' (PhaseReferenceStress[2]XZ) +# 31 column: sixth component of internal variable 'PhaseReferenceStress[2]' (PhaseReferenceStress[2]YZ) +# 32 column: first component of internal variable 'PhaseReferenceStress[3]' (PhaseReferenceStress[3]XX) +# 33 column: second component of internal variable 'PhaseReferenceStress[3]' (PhaseReferenceStress[3]YY) +# 34 column: third component of internal variable 'PhaseReferenceStress[3]' (PhaseReferenceStress[3]ZZ) +# 35 column: fourth component of internal variable 'PhaseReferenceStress[3]' (PhaseReferenceStress[3]XY) +# 36 column: fifth component of internal variable 'PhaseReferenceStress[3]' (PhaseReferenceStress[3]XZ) +# 37 column: sixth component of internal variable 'PhaseReferenceStress[3]' (PhaseReferenceStress[3]YZ) +# 38 column: first component of internal variable 'PhaseReferenceStress[4]' (PhaseReferenceStress[4]XX) +# 39 column: second component of internal variable 'PhaseReferenceStress[4]' (PhaseReferenceStress[4]YY) +# 40 column: third component of internal variable 'PhaseReferenceStress[4]' (PhaseReferenceStress[4]ZZ) +# 41 column: fourth component of internal variable 'PhaseReferenceStress[4]' (PhaseReferenceStress[4]XY) +# 42 column: fifth component of internal variable 'PhaseReferenceStress[4]' (PhaseReferenceStress[4]XZ) +# 43 column: sixth component of internal variable 'PhaseReferenceStress[4]' (PhaseReferenceStress[4]YZ) +# 44 column: first component of internal variable 'PhaseReferenceStress[5]' (PhaseReferenceStress[5]XX) +# 45 column: second component of internal variable 'PhaseReferenceStress[5]' (PhaseReferenceStress[5]YY) +# 46 column: third component of internal variable 'PhaseReferenceStress[5]' (PhaseReferenceStress[5]ZZ) +# 47 column: fourth component of internal variable 'PhaseReferenceStress[5]' (PhaseReferenceStress[5]XY) +# 48 column: fifth component of internal variable 'PhaseReferenceStress[5]' (PhaseReferenceStress[5]XZ) +# 49 column: sixth component of internal variable 'PhaseReferenceStress[5]' (PhaseReferenceStress[5]YZ) +# 50 column: first component of internal variable 'PhaseReferenceStress[6]' (PhaseReferenceStress[6]XX) +# 51 column: second component of internal variable 'PhaseReferenceStress[6]' (PhaseReferenceStress[6]YY) +# 52 column: third component of internal variable 'PhaseReferenceStress[6]' (PhaseReferenceStress[6]ZZ) +# 53 column: fourth component of internal variable 'PhaseReferenceStress[6]' (PhaseReferenceStress[6]XY) +# 54 column: fifth component of internal variable 'PhaseReferenceStress[6]' (PhaseReferenceStress[6]XZ) +# 55 column: sixth component of internal variable 'PhaseReferenceStress[6]' (PhaseReferenceStress[6]YZ) +# 56 column: first component of internal variable 'PhaseReferenceStress[7]' (PhaseReferenceStress[7]XX) +# 57 column: second component of internal variable 'PhaseReferenceStress[7]' (PhaseReferenceStress[7]YY) +# 58 column: third component of internal variable 'PhaseReferenceStress[7]' (PhaseReferenceStress[7]ZZ) +# 59 column: fourth component of internal variable 'PhaseReferenceStress[7]' (PhaseReferenceStress[7]XY) +# 60 column: fifth component of internal variable 'PhaseReferenceStress[7]' (PhaseReferenceStress[7]XZ) +# 61 column: sixth component of internal variable 'PhaseReferenceStress[7]' (PhaseReferenceStress[7]YZ) +# 62 column: first component of internal variable 'PhaseReferenceStress[8]' (PhaseReferenceStress[8]XX) +# 63 column: second component of internal variable 'PhaseReferenceStress[8]' (PhaseReferenceStress[8]YY) +# 64 column: third component of internal variable 'PhaseReferenceStress[8]' (PhaseReferenceStress[8]ZZ) +# 65 column: fourth component of internal variable 'PhaseReferenceStress[8]' (PhaseReferenceStress[8]XY) +# 66 column: fifth component of internal variable 'PhaseReferenceStress[8]' (PhaseReferenceStress[8]XZ) +# 67 column: sixth component of internal variable 'PhaseReferenceStress[8]' (PhaseReferenceStress[8]YZ) +# 68 column: first component of internal variable 'PhaseReferenceStress[9]' (PhaseReferenceStress[9]XX) +# 69 column: second component of internal variable 'PhaseReferenceStress[9]' (PhaseReferenceStress[9]YY) +# 70 column: third component of internal variable 'PhaseReferenceStress[9]' (PhaseReferenceStress[9]ZZ) +# 71 column: fourth component of internal variable 'PhaseReferenceStress[9]' (PhaseReferenceStress[9]XY) +# 72 column: fifth component of internal variable 'PhaseReferenceStress[9]' (PhaseReferenceStress[9]XZ) +# 73 column: sixth component of internal variable 'PhaseReferenceStress[9]' (PhaseReferenceStress[9]YZ) +# 74 column: ne +# 75 column: stored energy +# 76 column: disspated energy +0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 +0.01 1 -1 0 0 0 0 0.9762584724436 -0.9424157188117 -0.033822989907908 -0.0028533997118791 -0.019322202740486 0.092955130381976 0.95157580064751 -0.97032140566343 -0.037961593676859 -0.040915816015817 -0.19804202921015 -0.087412964583443 0.85435605784775 -1.0669388537073 -0.23748942412712 -0.035134706291713 -0.20249955196327 0.011107466244197 1.0618519869417 -0.95916460204932 -0.035043158174723 -0.049730535378054 -0.12702000264143 0.030108942827893 0.90906625879632 -0.99338996125484 -0.14570436571301 0.062038927141734 -0.13297897289315 0.13842059553905 0.95111818535086 -0.94292908487788 0.011184085175195 0.01112430952399 -0.16161129442337 0.25031792589824 0.94212422094632 -0.94218063284295 0.065451156379419 0.054939540523913 0.05824960230128 0.22058152176083 1.0141174032343 -0.89021308509149 0.089031415785124 -0.013847502805269 0.020721809535664 0.31731506705577 0.99504844125014 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std::pow(max(e_0+de_0,real(1e-10)),0.5*(n_-1)); const auto mu0 = sig0/3.*po; //second moments///////////////////////////////// -const auto em2 = tfel::math::trace(eto+deto)/3.; +const auto em = tfel::math::trace(eto+deto)/3.; const auto ed = tfel::math::deviator(eto+deto); +const auto em2 = em*em; const auto eeq2 = 2./3.*(ed|ed); using namespace tfel::material; const auto kg0 = KGModuli(k_m,mu0);