Material

This class is provided as a demonstration example.

Material class methods

method	input	returns	description
__init__(…)	parameters as {‘E’:10.0}		constructor. Sets parameters for this material and initializes all internal variables
getArea()		$A$	return cross section area from parameters[‘A’]
getStress()		$\sigma$	request axial stress
getStiffness		$E_t$	request axial stiffness
setStrain(eps)	strain $\epsilon$		update state for a user provided axial strain value

Element class variables

name	type	description
params	dict	default parameters: {‘E’:100., ‘nu’:0.0, ‘fy:1.0e30} Holds user provided parameters (MOE, Poisson’s ratio, yield stress)
plastic_strain	float	internal state variable.
sig	float	holds current stress
Et	float	holds current materil tangent modulus

Equations

1. Elastic trial state:

   1.1 $\sigma =E\ast (\epsilon -{\epsilon }_P)$

   1.2 $E_t=E$

2. Yield check: $f=||\sigma ||-f_y$

3. IF $f\ge 0$:

   3.1. $\mathrm{\Delta }{\epsilon }_P=\text{sign}(\sigma )\ast \frac{f}{E}$

   3.2. $\sigma =\sigma -E\ast \mathrm{\Delta }{\epsilon }_P$

   3.3. $E_t=E_t-E$