The Contimech Library

simcoon.simmit.dev(input: Annotated[numpy.typing.ArrayLike, numpy.float64], copy: bool = True) → numpy.typing.NDArray[numpy.float64]

Returns the deviatoric part of a 3x3 matrix.

Parameters:: m (pybind11::array_t<double>) – Input 3x3 matrix.
Returns:: Deviatoric part of the input matrix.
Return type:: pybind11::array_t<double>

Examples

import numpy as np
import simcoon as sim

# Example for dev
m = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
dev_m = sim.dev(m)
print(dev_m)

simcoon.simmit.sph(input: Annotated[numpy.typing.ArrayLike, numpy.float64], copy: bool = True) → numpy.typing.NDArray[numpy.float64]

Returns the spherical part of a 3x3 matrix.

Parameters:: m (pybind11::array_t<double>) – Input 3x3 matrix.
Returns:: Spherical part of the input matrix.
Return type:: pybind11::array_t<double>

Examples

import numpy as np
import simcoon as sim

# Example for sph
m = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
sph_m = sim.sph(m)
print(sph_m)

simcoon.simmit.tr(input: Annotated[numpy.typing.ArrayLike, numpy.float64]) → float

Returns the trace of a tensor expressed in Voigt notation.

Parameters:: v (pybind11::array_t<double>) – Input tensor in Voigt notation.
Returns:: Trace of the input tensor.
Return type:: pybind11::array_t<double>

Examples

import numpy as np
import simcoon as sim

# Example for tr
v = np.array([1, 1, 1, 0, 0, 0])
trace = sim.tr(v)
print(trace)

simcoon.simmit.Mises_stress(input: Annotated[numpy.typing.ArrayLike, numpy.float64]) → float

Provides the Von Mises stress of a second-order stress tensor written as a vector in Voigt notation.

Parameters:: v (pybind11::array_t<double>) – Input stress tensor in Voigt notation.
Returns:: Von Mises stress of the input tensor.
Return type:: pybind11::array_t<double>

Examples

import numpy as np
import simcoon as sim

# Example for Mises_stress
v = np.array([1, 1, 1, 0, 0, 0])
stress = sim.Mises_stress(v)
print(stress)

simcoon.simmit.eta_stress(input: Annotated[numpy.typing.ArrayLike, numpy.float64], copy: bool = True) → numpy.typing.NDArray[numpy.float64]

Provides the stress flow of a second-order stress tensor written as a vector in Voigt notation.

Parameters:: v (pybind11::array_t<double>) – Input stress tensor in Voigt notation.
Returns:: Stress flow of the input tensor.
Return type:: pybind11::array_t<double>

Examples

import numpy as np
import simcoon as sim

# Example for eta_stress
v = np.array([1, 1, 1, 0, 0, 0])
flow = sim.eta_stress(v)
print(flow)

simcoon.simmit.Mises_strain(input: Annotated[numpy.typing.ArrayLike, numpy.float64]) → float

Provides the Von Mises strain of a second-order strain tensor.

Parameters:: v (pybind11::array_t<double>) – Input strain tensor in Voigt notation.
Returns:: Von Mises strain of the input tensor.
Return type:: pybind11::array_t<double>

Examples

import numpy as np
import simcoon as sim

# Example for Mises_strain
v = np.array([1, 1, 1, 0, 0, 0])
strain = sim.Mises_strain(v)
print(strain)

simcoon.simmit.eta_strain(input: Annotated[numpy.typing.ArrayLike, numpy.float64], copy: bool = True) → numpy.typing.NDArray[numpy.float64]

Provides the strain flow of a second-order strain tensor written as a vector in Voigt notation.

Parameters:: v (pybind11::array_t<double>) – Input strain tensor in Voigt notation.
Returns:: Strain flow of the input tensor.
Return type:: pybind11::array_t<double>

Examples

import numpy as np
import simcoon as sim

# Example for eta_strain
v = np.array([1, 1, 1, 0, 0, 0])
flow = sim.eta_strain(v)
print(flow)

simcoon.simmit.J2_stress(input: Annotated[numpy.typing.ArrayLike, numpy.float64]) → float

Provides the second invariant of the deviatoric part of a second-order stress tensor, written as a vector in Voigt notation.

Parameters:: v (pybind11::array_t<double>) – Input stress tensor in Voigt notation.
Returns:: Second invariant of the deviatoric part of the input tensor.
Return type:: pybind11::array_t<double>

Examples

import numpy as np
import simcoon as sim

# Example for J2_stress
v = np.array([1, 1, 1, 0, 0, 0])
invariant = sim.J2_stress(v)
print(invariant)

simcoon.simmit.J2_strain(input: Annotated[numpy.typing.ArrayLike, numpy.float64]) → float

Provides the second invariant of the deviatoric part of a second-order strain tensor, written as a vector in Voigt notation.

Parameters:: v (pybind11::array_t<double>) – Input strain tensor in Voigt notation.
Returns:: Second invariant of the deviatoric part of the input tensor.
Return type:: pybind11::array_t<double>

Examples

import numpy as np
import simcoon as sim

# Example for J2_strain
v = np.array([1, 1, 1, 0, 0, 0])
invariant = sim.J2_strain(v)
print(invariant)

simcoon.simmit.J3_stress(input: Annotated[numpy.typing.ArrayLike, numpy.float64]) → float

Provides the third invariant of the deviatoric part of a second-order stress tensor, written as a vector in Voigt notation.

Parameters:: v (pybind11::array_t<double>) – Input stress tensor in Voigt notation.
Returns:: Third invariant of the deviatoric part of the input tensor.
Return type:: pybind11::array_t<double>

Examples

import numpy as np
import simcoon as sim

# Example for J3_stress
v = np.array([1, 1, 1, 0, 0, 0])
invariant = sim.J3_stress(v)
print(invariant)

simcoon.simmit.J3_strain(input: Annotated[numpy.typing.ArrayLike, numpy.float64]) → float

Provides the third invariant of the deviatoric part of a second-order strain tensor, written as a vector in Voigt notation.

Parameters:: v (pybind11::array_t<double>) – Input strain tensor in Voigt notation.
Returns:: Third invariant of the deviatoric part of the input tensor.
Return type:: pybind11::array_t<double>

Examples

import numpy as np
import simcoon as sim

# Example for J3_strain
v = np.array([1, 1, 1, 0, 0, 0])
invariant = sim.J3_strain(v)
print(invariant)

simcoon.simmit.Macaulay_p(value: SupportsFloat) → float

Provides the results of the MacCaulay brackets operator <>+.

Parameters:: d (pybind11::array_t<double>) – Input tensor.
Returns:: Result of the MacCaulay brackets operator <>+.
Return type:: pybind11::array_t<double>

Examples

import numpy as np
import simcoon as sim

# Example for Macaulay_p
d = np.array([1, -1, 0])
result = sim.Macaulay_p(d)
print(result)

simcoon.simmit.Macaulay_n(value: SupportsFloat) → float

Provides the results of the MacCaulay brackets operator <>-.

Parameters:: d (pybind11::array_t<double>) – Input tensor.
Returns:: Result of the MacCaulay brackets operator <>-.
Return type:: pybind11::array_t<double>

Examples

import numpy as np
import simcoon as sim

# Example for Macaulay_n
d = np.array([1, -1, 0])
result = sim.Macaulay_n(d)
print(result)

simcoon.simmit.sign(value: SupportsFloat) → float

Provides the results of the sign operator.

Parameters:: d (pybind11::array_t<double>) – Input tensor.
Returns:: Result of the sign operator.
Return type:: pybind11::array_t<double>

Examples

import numpy as np
import simcoon as sim

# Example for sign
d = np.array([1, -1, 0])
result = sim.sign(d)
print(result)

simcoon.simmit.normal_ellipsoid(u: SupportsFloat, v: SupportsFloat, a1: SupportsFloat, a2: SupportsFloat, a3: SupportsFloat, copy: bool = True) → numpy.typing.NDArray[numpy.float64]

Provides the normalized vector normal to an ellipsoid with semi-principal axes of length a1, a2, a3.

Parameters:

u (pybind11::array_t<double>) – Input vector u.
v (pybind11::array_t<double>) – Input vector v.
a1 (pybind11::array_t<double>) – Length of semi-principal axis a1.
a2 (pybind11::array_t<double>) – Length of semi-principal axis a2.
a3 (pybind11::array_t<double>) – Length of semi-principal axis a3.

Returns:

Normalized vector normal to the ellipsoid.

Return type:

pybind11::array_t<double>

Examples

import numpy as np
import simcoon as sim

# Example for normal_ellipsoid
u = np.array([1, 0, 0])
v = np.array([0, 1, 0])
a1 = np.array([1])
a2 = np.array([1])
a3 = np.array([1])
normal = sim.normal_ellipsoid(u, v, a1, a2, a3)
print(normal)

simcoon.simmit.curvature_ellipsoid(u: SupportsFloat, v: SupportsFloat, a1: SupportsFloat, a2: SupportsFloat, a3: SupportsFloat) → float

Provides the curvature of an ellipsoid with semi-principal axes of length a1, a2, a3 at the angle u,v.

Parameters:

u (pybind11::array_t<double>) – Input vector u.
v (pybind11::array_t<double>) – Input vector v.
a1 (pybind11::array_t<double>) – Length of semi-principal axis a1.
a2 (pybind11::array_t<double>) – Length of semi-principal axis a2.
a3 (pybind11::array_t<double>) – Length of semi-principal axis a3.

Returns:

Curvature of the ellipsoid.

Return type:

pybind11::array_t<double>

Examples

import numpy as np
import simcoon as sim

# Example for curvature_ellipsoid
u = np.array([1, 0, 0])
v = np.array([0, 1, 0])
a1 = np.array([1])
a2 = np.array([1])
a3 = np.array([1])
curvature = sim.curvature_ellipsoid(u, v, a1, a2, a3)
print(curvature)

simcoon.simmit.sigma_int(input: Annotated[numpy.typing.ArrayLike, numpy.float64], u: SupportsFloat, v: SupportsFloat, a1: SupportsFloat, a2: SupportsFloat, a3: SupportsFloat, copy: bool = True) → numpy.typing.NDArray[numpy.float64]

Provides the normal and tangent components of the traction vector in the normal direction n to an ellipsoid with axes a1, a2, a3 from an input inside stress.

Parameters:

sigma_in (pybind11::array_t<double>) – Input stress tensor.
u (pybind11::array_t<double>) – Input vector u.
v (pybind11::array_t<double>) – Input vector v.
a1 (pybind11::array_t<double>) – Length of semi-principal axis a1.
a2 (pybind11::array_t<double>) – Length of semi-principal axis a2.
a3 (pybind11::array_t<double>) – Length of semi-principal axis a3.

Returns:

Normal and tangent components of the traction vector.

Return type:

pybind11::array_t<double>

Examples

import numpy as np
import simcoon as sim

# Example for sigma_int
sigma_in = np.array([1, 1, 1, 0, 0, 0])
u = np.array([1, 0, 0])
v = np.array([0, 1, 0])
a1 = np.array([1])
a2 = np.array([1])
a3 = np.array([1])
result = sim.sigma_int(sigma_in, u, v, a1, a2, a3)
print(result)

simcoon.simmit.p_ikjl(normal: Annotated[numpy.typing.ArrayLike, numpy.float64], copy: bool = True) → numpy.typing.NDArray[numpy.float64]

Computes the Hill interfacial operator according to a normal a.

Parameters:: a (pybind11::array_t<double>) – Input normal vector.
Returns:: Hill interfacial operator.
Return type:: pybind11::array_t<double>

Examples

import numpy as np
import simcoon as sim

# Example for p_ikjl
a = np.array([1, 0, 0])
result = sim.p_ikjl(a)
print(result)

simcoon.simmit.auto_sym_dyadic(input: Annotated[numpy.typing.ArrayLike, numpy.float64], copy: bool = True) → numpy.typing.NDArray[numpy.float64]

Provides the dyadic product of a symmetric tensor with itself.

Parameters:: a (pybind11::array_t<double>) – Input symmetric tensor.
Returns:: Dyadic product of the input tensor with itself.
Return type:: pybind11::array_t<double>

Examples

import numpy as np
import simcoon as sim

# Example for auto_sym_dyadic
a = np.random.rand(3, 3)
a = (a + a.T) / 2  # Make a symmetric
result = sim.auto_sym_dyadic(a)
print(result)

simcoon.simmit.sym_dyadic(a: Annotated[numpy.typing.ArrayLike, numpy.float64], b: Annotated[numpy.typing.ArrayLike, numpy.float64], copy: bool = True) → numpy.typing.NDArray[numpy.float64]

Provides the dyadic product of two symmetric tensors.

Parameters:

a (pybind11::array_t<double>) – Input symmetric tensor a.
b (pybind11::array_t<double>) – Input symmetric tensor b.

Returns:

Dyadic product of the input tensors.

Return type:

pybind11::array_t<double>

Examples

import numpy as np
import simcoon as sim

# Example for sym_dyadic
a = np.random.rand(3, 3)
a = (a + a.T) / 2  # Make a symmetric
b = np.random.rand(3, 3)
b = (b + b.T) / 2  # Make a symmetric
result = sim.sym_dyadic(a, b)
print(result)

simcoon.simmit.auto_dyadic(input: Annotated[numpy.typing.ArrayLike, numpy.float64], copy: bool = True) → numpy.typing.NDArray[numpy.float64]

Provides the dyadic product of a tensor with itself.

Parameters:: a (pybind11::array_t<double>) – Input tensor.
Returns:: Dyadic product of the input tensor with itself.
Return type:: pybind11::array_t<double>

Examples

import numpy as np
import simcoon as sim

# Example for auto_dyadic
a = np.random.rand(3, 3)
a = (a + a.T) / 2  # Make a symmetric
result = sim.auto_dyadic(a)
print(result)

simcoon.simmit.dyadic_4vectors_sym(n_a: Annotated[numpy.typing.ArrayLike, numpy.float64], n_b: Annotated[numpy.typing.ArrayLike, numpy.float64], conv: str, copy: bool = True) → numpy.typing.NDArray[numpy.float64]

Provides the dyadic product of four vectors to provide a symmetric 4th order tensor.

Parameters:

a (pybind11::array_t<double>) – Input vector n_a.
b (pybind11::array_t<double>) – Input vector n_b.
conv (std::string) – Convention for the dyadic product.

Returns:

Symmetric 4th order tensor.

Return type:

pybind11::array_t<double>

Examples

import numpy as np
import simcoon as sim

# Example for dyadic_4vectors_sym
a = np.array([1, 0, 0])
b = np.array([0, 1, 0])
conv = "aabb"  # or "abab"
result = sim.dyadic_4vectors_sym(a, b, conv)
print(result)

simcoon.simmit.auto_sym_dyadic_operator(input: Annotated[numpy.typing.ArrayLike, numpy.float64], copy: bool = True) → numpy.typing.NDArray[numpy.float64]

Provides the symmetric 4th-order dyadic product of a symmetric tensor with itself.

Parameters:: a (pybind11::array_t<double>) – Input symmetric tensor.
Returns:: Symmetric 4th-order dyadic product of the input tensor with itself.
Return type:: pybind11::array_t<double>

Examples

import numpy as np
import simcoon as sim

# Example for auto_sym_dyadic_operator
a = np.random.rand(3, 3)
a = (a + a.T) / 2  # Make a symmetric
result = sim.auto_sym_dyadic_operator(a)
print(result)

simcoon.simmit.sym_dyadic_operator(a: Annotated[numpy.typing.ArrayLike, numpy.float64], b: Annotated[numpy.typing.ArrayLike, numpy.float64], copy: bool = True) → numpy.typing.NDArray[numpy.float64]

Provides the symmetric 4th-order dyadic product of two symmetric tensors.

Parameters:

a (pybind11::array_t<double>) – Input symmetric tensor a.
b (pybind11::array_t<double>) – Input symmetric tensor b.

Returns:

Symmetric 4th-order dyadic product of the input tensors.

Return type:

pybind11::array_t<double>

Examples

import numpy as np
import simcoon as sim

# Example for sym_dyadic_operator
a = np.random.rand(3, 3)
a = (a + a.T) / 2  # Make a symmetric
b = np.random.rand(3, 3)
b = (b + b.T) / 2  # Make b symmetric
result = sim.sym_dyadic_operator(a, b)
print(result)