new_material.rst
No OneTemporary
Actions

Subscribers

None

File Metadata

	``New Materials``
	=================

	Extrinsic Bilinear
	-------------------------------
	The bilinear descending law is represented by the following equation:

	.. math::
	\label{eq:cl:coh_ext_bil}
	\boldsymbol{\sigma} = \begin{cases}
	\sigma_{h} + \dfrac{\delta_h-\delta}{\delta_h}(\sigma_c -\sigma_h) \text{ for opening } \delta=\delta_{max}\leq \delta_h\\
	\dfrac{\delta_c-\delta}{\delta_c-\delta_h}\sigma_h \text{ for opening } \delta=\delta_{max} > \delta_h\\
	\dfrac{\delta}{\delta_{max}}T_{max} \text{ for closing/reopening } \delta < \delta_{max}\\
	\end{cases}

	where :math:`\delta_c` represents the effecive separation upon which
	the cohesive element is totally damaged, :math:`\delta_{max}` is the
	current maximum effective separation, :math:`T_{max}` is the
	traction-separation at :math:`\delta=\delta_{max}`, :math:`\delta_h`
	and :math:`\sigma_h` indicate the position of the inflection point
	determined by :math:`h` and :math:`G_{cI}`

	.. math::
	h = \dfrac{\sigma_h}{\delta_h}, \quad G_{cI} = \dfrac{1}{2}(\sigma_h\delta_c+\sigma_c\delta_h)

	.. _fig:cohesive:extrinsic-bilinear:
	.. figure:: figures/cl/cohesive-extrinsic-bilinear.svg
	:align: center

	Bilinear traction-separation law for extrinsic type cohesive element