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@ -14,7 +14,7 @@ from . import _rotation
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def deformation_Cauchy_Green_left(F: _np.ndarray) -> _np.ndarray:
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def deformation_Cauchy_Green_left(F: _np.ndarray) -> _np.ndarray:
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"""
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r"""
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Calculate left Cauchy-Green deformation tensor (Finger deformation tensor).
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Calculate left Cauchy-Green deformation tensor (Finger deformation tensor).
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Parameters
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Parameters
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@ -27,12 +27,18 @@ def deformation_Cauchy_Green_left(F: _np.ndarray) -> _np.ndarray:
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B : numpy.ndarray, shape (...,3,3)
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B : numpy.ndarray, shape (...,3,3)
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Left Cauchy-Green deformation tensor.
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Left Cauchy-Green deformation tensor.
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Notes
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-----
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.. math::
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\vb{B} = \vb{F} \vb{F}^{T}
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"""
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"""
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return _np.matmul(F,_tensor.transpose(F))
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return _np.matmul(F,_tensor.transpose(F))
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def deformation_Cauchy_Green_right(F: _np.ndarray) -> _np.ndarray:
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def deformation_Cauchy_Green_right(F: _np.ndarray) -> _np.ndarray:
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"""
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r"""
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Calculate right Cauchy-Green deformation tensor.
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Calculate right Cauchy-Green deformation tensor.
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Parameters
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Parameters
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@ -45,6 +51,12 @@ def deformation_Cauchy_Green_right(F: _np.ndarray) -> _np.ndarray:
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C : numpy.ndarray, shape (...,3,3)
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C : numpy.ndarray, shape (...,3,3)
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Right Cauchy-Green deformation tensor.
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Right Cauchy-Green deformation tensor.
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Notes
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-----
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.. math::
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\vb{C} = \vb{F}^{T} \vb{F}
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"""
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"""
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return _np.matmul(_tensor.transpose(F),F)
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return _np.matmul(_tensor.transpose(F),F)
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@ -65,12 +77,15 @@ def equivalent_strain_Mises(epsilon: _np.ndarray) -> _np.ndarray:
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Notes
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Notes
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-----
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-----
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The von Mises equivalent of a deviatoric strain tensor is defined as:
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The von Mises equivalent of a strain tensor is defined as:
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.. math::
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.. math::
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\epsilon_\text{vM} = \sqrt{2/3 \epsilon^\prime_{ij} \epsilon^\prime_{ij}}
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\epsilon_\text{vM} = \sqrt{2/3 \epsilon^\prime_{ij} \epsilon^\prime_{ij}}
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where :math:`\vb{\epsilon}^\prime` is the deviatoric part
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of the strain tensor.
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"""
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"""
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return _equivalent_Mises(epsilon,2.0/3.0)
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return _equivalent_Mises(epsilon,2.0/3.0)
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@ -91,12 +106,15 @@ def equivalent_stress_Mises(sigma: _np.ndarray) -> _np.ndarray:
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Notes
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Notes
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-----
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-----
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The von Mises equivalent of a deviatoric stress tensor is defined as:
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The von Mises equivalent of a stress tensor is defined as:
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.. math::
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.. math::
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\sigma_\text{vM} = \sqrt{3/2 \sigma^\prime_{ij} \sigma^\prime_{ij}}
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\sigma_\text{vM} = \sqrt{3/2 \sigma^\prime_{ij} \sigma^\prime_{ij}}
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where :math:`\vb{\sigma}^\prime` is the deviatoric part
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of stress tensor.
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"""
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"""
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return _equivalent_Mises(sigma,3.0/2.0)
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return _equivalent_Mises(sigma,3.0/2.0)
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