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 \(\varepsilon\)		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 \(\sigma = E * (\varepsilon - \varepsilon_P)\)

   1.2 \(E_t = E\)

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

3. IF \(f \ge 0\):

   3.1. \(\Delta\varepsilon_P = \text{sign}(\sigma) * \frac{f}{E}\)

   3.2. \(\sigma = \sigma - E * \Delta\varepsilon_P\)

   3.3. \(E_t = E_t - E\)