TensorUtils (Artisynth API documentation)

java.lang.Object
- artisynth.core.materials.TensorUtils

public class TensorUtils
extends java.lang.Object

Constructor Summary

Constructors
Constructor and Description

TensorUtils()

Constructors
Constructor and Description
`TensorUtils()`

Method Summary

All Methods Static Methods Concrete Methods
Modifier and Type	Method and Description
`static void`	`addScaled4thPowerProduct(Matrix6d D, double s, Vector3d a)` Adds the scaled tensor product
`static void`	`addScaledIdentity(Matrix6d D, double s)` Adds a scaled identity to a 4th order constitutive tensor represented as a 6 x 6 matrix.
`static void`	`addScaledIdentityProduct(Matrix6d D, double s)` Adds the scaled tensor product
`static void`	`addSymmetricIdentityDot(Matrix6d D, double s, Matrix6d A)` Adds the scale symmetric tensor product
`static void`	`addSymmetricIdentityProduct(Matrix6d D, double s, Matrix3dBase S)` Adds the scale symmetric tensor product
`static void`	`addSymmetricIdentityProduct(Matrix6d D, Matrix3dBase S)` Adds the symmetric tensor product
`static void`	`addSymmetricTensorDot(Matrix6d D, Matrix6d A, Matrix6d B)` Adds the symmetric tensor product
`static void`	`addSymmetricTensorProduct(Matrix6d D, double s, Matrix3dBase A, Matrix3dBase B)` Adds a scaled symmetric tensor product
`static void`	`addSymmetricTensorProduct(Matrix6d D, Matrix3dBase A, Matrix3dBase B)` Adds the symmetric tensor product
`static void`	`addSymmetricTensorProduct4(Matrix6d D, double s, Matrix3dBase A, Matrix3dBase B)` Adds the scaled symmetric tensor product
`static void`	`addTensorProduct(Matrix6d D, double s, Matrix3dBase A)` Adds the scaled tensor product
`static void`	`addTensorProduct(Matrix6d D, double s, Matrix3dBase A, Matrix3dBase B)` Adds the scaled tensor product
`static void`	`addTensorProduct(Matrix6d D, Matrix3dBase A)` Adds the tensor product
`static void`	`addTensorProduct4(Matrix6d D, double s, Matrix3dBase A)` Adds the scaled symmetric tensor product
`static Matrix6d`	`brownToRegular()`
`static void`	`createElasticityRotation(Matrix6d T, Matrix3dBase R)` Creates a 6x6 rotation matrix for transforming the elasticity tensor From Brown University Notes
`static void`	`createElasticityRotationBrown(Matrix6d T, Matrix3dBase R)`
`static void`	`createElasticityRotationOld(Matrix6d T, Matrix3dBase R)` Creates a 6x6 rotation matrix for transforming the elasticity tensor From Brown University Notes
`static void`	`createElasticityUnrotation(Matrix6d T, Matrix3dBase R)` Creates a 6x6 "unrotation" matrix for transforming the elasticity tensor (i.e.
`static double`	`dot(Matrix3dBase A, Matrix3dBase B)` Compute the dot product of two matrics, given by
`static void`	`main(java.lang.String[] args)`
`static void`	`mulTangent(SymmetricMatrix3d sig, Matrix6d D, SymmetricMatrix3d eps)`
`static Matrix6d`	`regularToBrown()`
`static void`	`rotateTangent(Matrix6d DR, Matrix6d D1, Matrix3dBase R)` Rotates a 6x6 material tangent matrix into a new coordinate system.
`static void`	`rotateTangentOld(Matrix6d DR, Matrix6d D1, Matrix3dBase R)` Rotates a 6x6 material tangent matrix into a new coordinate system.
`static double`	`symmetricTrace(Matrix6d D)` Returns the trace of D interpretted as a symmetric 4d tensor.
`static void`	`unrotateTangent(Matrix6d DR, Matrix6d D1, Matrix3dBase R)` Rotates a 6x6 material tangent matrix into a new coordinate system.
`static void`	`v3DotTens4sDotv3(Matrix3d out, Vector3d a, Matrix6d T, Vector3d b)` Computes the following formula: v3a .

Methods inherited from class java.lang.Object
equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

- Constructor Detail
  - TensorUtils
```
public TensorUtils()
```
- Method Detail
  - addSymmetricIdentityProduct
```
public static void addSymmetricIdentityProduct(Matrix6d D,
                                               Matrix3dBase S)
```
    Adds the symmetric tensor product
```
  S (X) I + I (X) S
 
```
    to a symmetric 4th order constitutive tensor represented as a 6 x 6 matrix. Here, S is a symmetric 3 x 3 matrix, I is the 3 x 3 identity matrix, and X denotes a tensor product.
    With respect to FEBio, this corresponds to the operation tens4ds.dyad1s(A, I).
    Parameters:
    
    D - 6 x 6 matrix representation of the tensor to which the product is added
    
    S - matrix for forming the product. This is assumed to be symmetric and only the upper triangular components are used.
  - addSymmetricIdentityProduct
```
public static void addSymmetricIdentityProduct(Matrix6d D,
                                               double s,
                                               Matrix3dBase S)
```
    Adds the scale symmetric tensor product
```
  s (S (X) I + I (X) S)
 
```
    to a symmetric 4th order constitutive tensor represented as a 6 x 6 matrix. Here, S is a symmetric 3 x 3 matrix, I is the 3 x 3 identity matrix, and X denotes a tensor product.
    With respect to FEBio, this corresponds to the operation tens4ds.dyad1s(A, I) when s = 1.
    Parameters:
    
    D - 6 x 6 matrix representation of the tensor to which the product is added
    
    s - scale factor
    
    S - matrix for forming the product. This is assumed to be symmetric and only the upper triangular components are used.
  - addSymmetricTensorProduct
```
public static void addSymmetricTensorProduct(Matrix6d D,
                                             Matrix3dBase A,
                                             Matrix3dBase B)
```
    Adds the symmetric tensor product
```
  A (X) B + B (X) A
 
```
    to a symmetric 4th order constitutive tensor represented as a 6 x 6 matrix. Here, A and B are 3 x 3 matrices (assumed to be symmetric), and (X) denotes a tensor product.
    With respect to FEBio, this corresponds to the operation tens4ds.dyad1s(A,B).
    Note that this method sets only the upper triangular components of D.
    Parameters:
    
    D - 6 x 6 matrix representation of the tensor to which the product is added
    
    A - first matrix for forming the product, assumed to be symmetric with only the upper triangular components used.
    
    B - second matrix for forming the product, assumed to be symmetric with only the upper triangular components used.
  - addSymmetricTensorProduct
```
public static void addSymmetricTensorProduct(Matrix6d D,
                                             double s,
                                             Matrix3dBase A,
                                             Matrix3dBase B)
```
    Adds a scaled symmetric tensor product
```
  s (A (X) B + B (X) A)
 
```
    to a symmetric 4th order constitutive tensor represented as a 6 x 6 matrix. Here, A and B are 3 x 3 matrices (assumed to be symmetric), and (X) denotes a tensor product.
    With respect to FEBio, this corresponds to the operation tens4ds.dyad1s(A,B) when s = 1.
    Note that this method sets only the upper triangular components of D.
    Parameters:
    
    D - 6 x 6 matrix representation of the tensor to which the product is added
    
    s - scale factor
    
    A - first matrix for forming the product, assumed to be symmetric with only the upper triangular components used.
    
    B - second matrix for forming the product, assumed to be symmetric with only the upper triangular components used.
  - addTensorProduct
```
public static void addTensorProduct(Matrix6d D,
                                    Matrix3dBase A)
```
    Adds the tensor product
```
 A (X) A 
```
    to a symmetric 4th order constitutive tensor represented as a 6 x 6 matrix. Here, A is a 3 x 3 matrix (assumed to be symmetric), and (X) denotes a tensor product.
    With respect to FEBio, this corresponds to the operation tens4ds.dyad1s(A).
    Note that this method sets only the upper triangular components of D.
    Parameters:
    
    D - 6 x 6 matrix representation of the tensor to which the product is added
    
    A - matrix for forming the product, assumed to be symmetric with only the upper triangular components used.
  - addTensorProduct
```
public static void addTensorProduct(Matrix6d D,
                                    double s,
                                    Matrix3dBase A)
```
    Adds the scaled tensor product
```
  s (A (X) A)
 
```
    to a symmetric 4th order constitutive tensor represented as a 6 x 6 matrix. Here, A is a 3 x 3 matrix (assumed to be symmetric), and (X) denotes a tensor product.
    With respect to FEBio, this corresponds to the operation tens4ds.dyad1s(A) when s = 1.
    Note that this method sets only the upper triangular components of D.
    Parameters:
    
    D - 6 x 6 matrix representation of the tensor to which the product is added
    
    s - scale factor
    
    A - matrix for forming the product, assumed to be symmetric with only the upper triangular components used.
  - addTensorProduct
```
public static void addTensorProduct(Matrix6d D,
                                    double s,
                                    Matrix3dBase A,
                                    Matrix3dBase B)
```
    Adds the scaled tensor product
```
  s (A (X) B)
 
```
    to a 4th order constitutive tensor represented as a 6 x 6 matrix. Here, A and B are 3 x 3 matrices (assumed to be symmetric), and (X) denotes a tensor product.
    Parameters:
    
    D - 6 x 6 matrix representation of the tensor to which the product is added
    
    s - scale factor
    
    A - matrix for forming the product, assumed to be symmetric with only the upper triangular components used.
    
    B - matrix for forming the product, assumed to be symmetric with only the upper triangular components used.
  - addScaledIdentityProduct
```
public static void addScaledIdentityProduct(Matrix6d D,
                                            double s)
```
    Adds the scaled tensor product
```
  s ( I (X) I )
 
```
    to a symmetric 4th order constitutive tensor represented as a 6 x 6 matrix. Here, s is a scalar, I is the 3 x 3 identity matrix, and X denotes a tensor product.
    Parameters:
    
    D - 6 x 6 matrix representation of the tensor to which the product is added
    
    s - scaling factor for the product
  - addScaledIdentity
```
public static void addScaledIdentity(Matrix6d D,
                                     double s)
```
    Adds a scaled identity to a 4th order constitutive tensor represented as a 6 x 6 matrix.
    
    Parameters:
    
    s - scaling factor for the identity
  - addScaled4thPowerProduct
```
public static void addScaled4thPowerProduct(Matrix6d D,
                                            double s,
                                            Vector3d a)
```
    Adds the scaled tensor product
```
  s ( a X a X a X a )
 
```
    to a symmetric 4th order constitutive tensor represented as a 6 x 6 matrix. Here, s is a scalar, a is a 3-vector, and X denotes a tensor product.
    Parameters:
    
    D - 6 x 6 matrix representation of the tensor to which the product is added
    
    s - scaling factor for the product
    
    a - vector defining the product
  - addTensorProduct4
```
public static void addTensorProduct4(Matrix6d D,
                                     double s,
                                     Matrix3dBase A)
```
    Adds the scaled symmetric tensor product
```
  s (A_ik A_jl + A_il A_jk)/2 
 
```
    to a symmetric 4th order constitutive tensor represented as a 6 x 6 matrix. Here, s is a scalar and A is a 3 x 3 matrix (assumed to be symmetric).
    With respect to FEBio, this corresponds to the operation tens4ds.dyad4snv(A) if the scaling is 1.
    Note that this method sets only the upper triangular components of D.
    Parameters:
    
    D - 6 x 6 matrix representation of the tensor to which the product is added
    
    s - scaling factor for the product
    
    A - matrix used to form the product (assumed symmetric with only the upper triangular part used)
  - addSymmetricTensorProduct4
```
public static void addSymmetricTensorProduct4(Matrix6d D,
                                              double s,
                                              Matrix3dBase A,
                                              Matrix3dBase B)
```
    Adds the scaled symmetric tensor product
```
 s (A_ik B_jl + A_il B_jk)/2 + (B_ik A_jl + B_il A_jk)/2
 
```
    to a symmetric 4th order constitutive tensor represented as a 6 x 6 matrix. Here, s is a scalar and A is a 3 x 3 matrix (assumed to be symmetric).
    With respect to FEBio, this corresponds to the operation tens4ds.dyad4s(A,B) if the scaling is 1.
    Note that this method sets only the upper triangular components of D.
    Parameters:
    
    D - 6 x 6 matrix representation of the tensor to which the product is added
    
    s - scaling factor for the product
    
    A - first matrix in the product (assumed symmetric with only the upper triangular part used)
    
    B - second matrix in the product (assumed symmetric with only the upper triangular part used)
  - rotateTangentOld
```
public static void rotateTangentOld(Matrix6d DR,
                                    Matrix6d D1,
                                    Matrix3dBase R)
```
    Rotates a 6x6 material tangent matrix into a new coordinate system. The rotation is specified by a rotation matrix R that transforms from the new coordinate system into the current one. The transformation is based on the general 4th order elasticity tensor rotation formula
    A'_ijkl = sum R_ai R_bj R_ck R_dl A_abcd
    but is optimized and also accomodates the fact that the 6x6 tangent matrix is a reduced version of the general elasticity tensor. It also assumes that the elasticity tensor is symmetric. Each entry in the tangent matrix corresponds to ijkl indices of the elasticity tensor as follows:
    [ 0000 0011 0022 0001 0012 0002 1100 1111 1122 1101 1112 1102 2200 2211 2222 2201 2212 2202 0100 0111 0122 0101 0112 0102 1200 1211 1222 1201 1212 1202 0200 0211 0222 0201 0212 0202 ]
    Note that this indexing convention follows that used in FEBio but is not standard; in particular, the lower and right entries are sometimes interchanged depending on how the stress/strain tensors are vectorized.
    
    Parameters:
    
    DR - result is returned here
    
    D1 - original tangent matrix to rotate
    
    R - rotation matrix
  - createElasticityRotationOld
```
public static void createElasticityRotationOld(Matrix6d T,
                                               Matrix3dBase R)
```
    Creates a 6x6 rotation matrix for transforming the elasticity tensor From Brown University Notes
    
    Parameters:
    
    T - output 6x6 matrix
    
    R - 3D rotation matrix
  - createElasticityRotationBrown
```
public static void createElasticityRotationBrown(Matrix6d T,
                                                 Matrix3dBase R)
```
  - regularToBrown
```
public static Matrix6d regularToBrown()
```
  - brownToRegular
```
public static Matrix6d brownToRegular()
```
  - createElasticityRotation
```
public static void createElasticityRotation(Matrix6d T,
                                            Matrix3dBase R)
```
    Creates a 6x6 rotation matrix for transforming the elasticity tensor From Brown University Notes
    
    Parameters:
    
    T - output 6x6 matrix
    
    R - 3D rotation matrix
  - createElasticityUnrotation
```
public static void createElasticityUnrotation(Matrix6d T,
                                              Matrix3dBase R)
```
    Creates a 6x6 "unrotation" matrix for transforming the elasticity tensor (i.e. uses R') From Brown University Notes
    
    Parameters:
    
    T - output 6x6 matrix
    
    R - 3D rotation matrix
  - rotateTangent
```
public static void rotateTangent(Matrix6d DR,
                                 Matrix6d D1,
                                 Matrix3dBase R)
```
    Rotates a 6x6 material tangent matrix into a new coordinate system. The rotation is specified by a rotation matrix R that transforms from the new coordinate system into the current one.
    
    Parameters:
    
    DR - result is returned here
    
    D1 - original tangent matrix to rotate
    
    R - rotation matrix
  - unrotateTangent
```
public static void unrotateTangent(Matrix6d DR,
                                   Matrix6d D1,
                                   Matrix3dBase R)
```
    Rotates a 6x6 material tangent matrix into a new coordinate system. The rotation is specified by the transpose of rotation matrix R
    
    Parameters:
    
    DR - result is returned here
    
    D1 - original tangent matrix to rotate
    
    R - rotation to "unrotate"
  - mulTangent
```
public static void mulTangent(SymmetricMatrix3d sig,
                              Matrix6d D,
                              SymmetricMatrix3d eps)
```
  - main
```
public static void main(java.lang.String[] args)
```
  - v3DotTens4sDotv3
```
public static void v3DotTens4sDotv3(Matrix3d out,
                                    Vector3d a,
                                    Matrix6d T,
                                    Vector3d b)
```
    Computes the following formula: v3a . T4S . v3b where v3a and v3b are both vector-3, T4S is a symmetrical 4th order tensor, and . is the dot product symbol. FEBio: tens4ds::vdotTdotv
    
    Parameters:
    
    out - Result to be stored in. 3x3 matrix.
    
    a - Left vector3
    
    T - Symmetrical 4th order tensor. E.g. material stress matrix.
    
    b - Right vector3
  - addSymmetricTensorDot
```
public static void addSymmetricTensorDot(Matrix6d D,
                                         Matrix6d A,
                                         Matrix6d B)
```
    Adds the symmetric tensor product
```
 A_ijmn B_mnkl + B_ijmn A_mnkl
 
```
    to D. Equivalent to FEBio tens4ds.ddots (A,B)
  - addSymmetricIdentityDot
```
public static void addSymmetricIdentityDot(Matrix6d D,
                                           double s,
                                           Matrix6d A)
```
    Adds the scale symmetric tensor product
```
 s (A_ijmn IxI_mnkl + IxI_ijmn A_mnkl)
 
```
    to D, where IxI = I (X) I. Equivalent to FEBio tens4ds.ddots (A,IxI) when s = 1.
  - dot
```
public static double dot(Matrix3dBase A,
                         Matrix3dBase B)
```
    Compute the dot product of two matrics, given by
```
 A_ij B_ij
 
```
  - symmetricTrace
```
public static double symmetricTrace(Matrix6d D)
```
    Returns the trace of D interpretted as a symmetric 4d tensor. Equilavent to FEBio tens4ds::tr().

Class TensorUtils

Constructor Summary

Method Summary

Methods inherited from class java.lang.Object

Constructor Detail

TensorUtils

Method Detail

addSymmetricIdentityProduct

addSymmetricIdentityProduct

addSymmetricTensorProduct

addSymmetricTensorProduct

addTensorProduct

addTensorProduct

addTensorProduct

addScaledIdentityProduct

addScaledIdentity

addScaled4thPowerProduct

addTensorProduct4

addSymmetricTensorProduct4

rotateTangentOld

createElasticityRotationOld

createElasticityRotationBrown

regularToBrown

brownToRegular

createElasticityRotation

createElasticityUnrotation

rotateTangent

unrotateTangent

mulTangent

main

v3DotTens4sDotv3

addSymmetricTensorDot

addSymmetricIdentityDot

dot

symmetricTrace