UMAT: DDSDDE in large strain hyperelasticity - Constitutive Models
https://polymerfem.com/community/constitutive-models/umat-ddsdde-in-large-strain-hyperelasticity/
PolymerFEM.com Discussion Boarden-USWed, 19 Jun 2024 11:39:35 +0000wpForo60
https://polymerfem.com/community/constitutive-models/umat-ddsdde-in-large-strain-hyperelasticity/#post-11033
Fri, 16 Aug 2013 06:07:09 +0000MatsHello,thanks to this forum, I already found a lot about the correct definition of the tangent modulus in Umat subroutines. I am testing my subroutines on a simple cube and unfortunately, my subroutines only work for normal tension. It seems that I am still doing some systematic error.Following the user subroutine reference manual, the material jacobian matrix is DDSDDE = (delta sigma)/(delta epsilon)So this is Cauchy stress derived to logarithmic strain. On the same site, there is also the definition: For rate form constitutive laws the tangent moduli is given as DDSDDE = 1/J (partial delta (J sigma)) / (partial delta epsilon)with J = Det(F). So this is the Kirchhoff stress derived to the logarithmic strain. Further I found out that Abaqus needs the tangent modulus with Jaumann stress rate.As I am doing large strain analysis, I do not use the logarithmic strain, but the deformation gradient DFGRD1 to compute strain and stresses at the end of the increment. Second my constitutive law is pure elastic, so far I do not use a rate formulation. The material is defined by a strain energy potential Psi(C), with Cauchy Green deformation tensor C = DFGRD1transpose DFGRD1.I tried two approaches so far to compute DDSDDE:Analytic:Tangent modulus in spatial frame: DDSDDEspatial = 4 dd Psi(C) / dC dCThen push forward to material frame: DDSDDEmaterial = 1/J DFGRD1 DFGRD1 DDSDDEspatial DFGRD1transpose DFGRD1transposeConvert to Jaumann: DDSDDE = DDSDDEmaterial + h Numeric:I implemented a numerical approximation of DDSDDE as proposed in . The algorithm estimates the tangent moduli by a forward differentiation of the stress.Unfortunately, both approaches do only work for normal tension, shear or combined loading fails.What does Abaqus need? Cauchy or Kirchhoff tangent moduli?Is there anything in the .inp file I need to consider? Element types etc.Thanks in advance any hints how to get my UMAT working!BestChris Belytschko 2001: Nonlinear Finite Elements for Continua and Structures Sun 2008: Numerical approximation of tangent moduli for finite element implementations of nonlinear hyperelastic material models]]>Constitutive Modelszhaiyshttps://polymerfem.com/community/constitutive-models/umat-ddsdde-in-large-strain-hyperelasticity/#post-11033UMAT works for single element and fails for multiple elements
https://polymerfem.com/community/constitutive-models/umat-ddsdde-in-large-strain-hyperelasticity/#post-11023
Sun, 28 Jul 2013 09:17:02 +0000Perfect, in the document is amongst other usefull information the correct definition of the Jacobian. Thanks!Hi Chrichri, I am facing the same problem. I am using the SUN (2008) paper to solve my problem. The UMAT works for the single element and fails for multiple elements. How did u obtain the basis vectors in the spatial description from the ABAQUS. I assumed them to be {1,0,0} {0,1,0} and {0,0,1}. This way it worked for single element. How did you finally fix this issue.Thanks a LOT-Ravi]]>Constitutive Modelsreal_madridhttps://polymerfem.com/community/constitutive-models/umat-ddsdde-in-large-strain-hyperelasticity/#post-11023
https://polymerfem.com/community/constitutive-models/umat-ddsdde-in-large-strain-hyperelasticity/#post-10985
Fri, 28 Jun 2013 09:21:49 +0000Constitutive Modelspetermorrisonhttps://polymerfem.com/community/constitutive-models/umat-ddsdde-in-large-strain-hyperelasticity/#post-10985
https://polymerfem.com/community/constitutive-models/umat-ddsdde-in-large-strain-hyperelasticity/#post-10979
Wed, 26 Jun 2013 11:58:58 +0000Constitutive ModelsFrankMonkeyhttps://polymerfem.com/community/constitutive-models/umat-ddsdde-in-large-strain-hyperelasticity/#post-10979UMAT: DDSDDE in large strain hyperelasticity
https://polymerfem.com/community/constitutive-models/umat-ddsdde-in-large-strain-hyperelasticity/#post-28799
Tue, 25 Jun 2013 06:04:14 +0000thanks to this forum, I already found a lot about the correct definition of the tangent modulus in Umat subroutines. I am testing my subroutines on a simple cube and unfortunately, my subroutines only work for normal tension. It seems that I am still doing some systematic error.Following the user subroutine reference manual, the material jacobian matrix is DDSDDE = (delta sigma)/(delta epsilon)So this is Cauchy stress derived to logarithmic strain. On the same site, there is also the definition: For rate form constitutive laws the tangent moduli is given as DDSDDE = 1/J (partial delta (J sigma)) / (partial delta epsilon)with J = Det(F). So this is the Kirchhoff stress derived to the logarithmic strain. Further I found out that Abaqus needs the tangent modulus with Jaumann stress rate.As I am doing large strain analysis, I do not use the logarithmic strain, but the deformation gradient DFGRD1 to compute strain and stresses at the end of the increment. Second my constitutive law is pure elastic, so far I do not use a rate formulation. The material is defined by a strain energy potential Psi(C), with Cauchy Green deformation tensor C = DFGRD1transpose DFGRD1.I tried two approaches so far to compute DDSDDE:Analytic:Tangent modulus in spatial frame: DDSDDEspatial = 4 dd Psi(C) / dC dCThen push forward to material frame: DDSDDEmaterial = 1/J DFGRD1 DFGRD1 DDSDDEspatial DFGRD1transpose DFGRD1transposeConvert to Jaumann: DDSDDE = DDSDDEmaterial + h Numeric:I implemented a numerical approximation of DDSDDE as proposed in . The algorithm estimates the tangent moduli by a forward differentiation of the stress.Unfortunately, both approaches do only work for normal tension, shear or combined loading fails.What does Abaqus need? Cauchy or Kirchhoff tangent moduli?Is there anything in the .inp file I need to consider? Element types etc.Thanks in advance any hints how to get my UMAT working!BestChris Belytschko 2001: Nonlinear Finite Elements for Continua and Structures Sun 2008: Numerical approximation of tangent moduli for finite element implementations of nonlinear hyperelastic material models]]>Constitutive Modelspetermorrisonhttps://polymerfem.com/community/constitutive-models/umat-ddsdde-in-large-strain-hyperelasticity/#post-28799