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UMAT for Superelasticity and Plasticity of Shape Memory Alloys Superelastic-plastic behavior is based on the uniaxial behavior shown here:

ToT

EL

SL

SU

EU LT

UT

ME EUt

SL t

EL t

SU t

SLc

AEL

1P1 , iPi ,

Copyright Dassault Systmes | www.3ds.com UMAT for Superelasticity Elastic-Plastic Model 2

Usage Superelastic only behavior MATERIAL, NAME=name USER MATERIAL, CONSTANTS=15 + NA

AE , Av , ME , Mv , L ,

LT

, SL , EL

OT , UT

, SU , EU , SCL , LV , AN , S1N , SNA...N

DEPVAR 24,

Superelastic-plastic behavior MATERIAL, NAME=name USER MATERIAL, CONSTANTS=16 + NA + 2NP

AE , Av , ME , Mv , L ,

LT

, SL , EL

OT , UT

, SU , EU , SCL , LV , AN , S1N , SNA...N , PN , NPPNP1P1 ,..., (8 values per line)

DEPVAR 31,

Note that for both the elastic and elastic-plastic behaviors, the name parameter on *MATERIAL must start with ABQ_SUPER_ELASTIC.

Copyright Dassault Systmes | www.3ds.com UMAT for Superelasticity Elastic-Plastic Model 3

Input to Superelasticity UMAT

AE Austenite elasticity

Av Austenite Poissons ratio

ME Martensite elasticity

Mv Martensite Poissons ratio

L Transformation strain

LT

T loading SL Start of transformation loading EL End of transformation loading OT Reference temperature

UT

T unloading SU Start of transformation unloading EU End of transformation unloading SCL Start of transformation stress during loading in compression, as a positive

value LV Volumetric transformation strain. If LV = L , an associated flow algorithm

is used, with LV computed based on SL and SCL . For all other cases, a nonassociated flow algorithm is used, which produces an unsymmetric Jacobian matrix. The USYMM parameter is thus required on the *USER MATERIAL keyword

AN Number of annealings to be performed during the analysis

S1N - SNAN Step numbers at which all state dependent variable are set to zero

PN Number of stress-strain pairs to define yield curve

NPPNP1

P1 ,..., Stress-strain points in the yield curve

Copyright Dassault Systmes | www.3ds.com UMAT for Superelasticity Elastic-Plastic Model 4

Output from Superelasticity UMAT

SDV1 6 Linear elastic strains

SDV7 12 Transformation strains

SDV19 Equivalent transformation strain

SDV20 Volumetric transformation strain

SDV21 Fraction of Martensite

SDV22 Equivalent uniaxial tensile stress

SDV23 Equivalent uniaxial tensile transformation strain

SDV24 Equivalent uniaxial tensile total strain

SDV26 31 Plastic strains1

SENER, ELSE, ALLSE Linear elastic strain energy variables2

PENER, ELPD, ALLPD Transformation strain energy variables2

1. Available for superelastic-plastic behavior

2. See the Output Table in ABAQUS Users Manual for definitions