fedoo.constitutivelaw.ElastoPlasticity

class ElastoPlasticity(young_modulus, poisson_ratio, yield_stress, name='')

Elasto-plastic constitutive law with isotropic hardening.

The stress integration uses a vectorized radial-return algorithm for the von Mises yield criterion. The finite-element lifecycle is provided by fedoo.core.mechanical3d.MechanicalUMAT; the scalar accumulated plastic strain P and plastic-strain tensor EP are exposed as labelled components of the private Statev array.

In a geometrically nonlinear updated-Lagrangian analysis, this law is a corotational extension of the same additive small-strain model. Tensorial history is transported with the objective rotation increment before each return mapping. This makes the response objective under finite rotations, but it is not a multiplicative finite-plasticity model (there is no decomposition F = Fe @ Fp).

The returned elastoplastic tangent is the continuum tangent evaluated at the updated stress. It is not the algorithmically consistent tangent of the discrete radial-return integration. Consequently, global Newton convergence is not guaranteed to be quadratic for finite plastic increments or non-proportional loading paths.

Warning

This Python implementation is intended only for pedagogical use and as a readable reference implementation. For computational analyses, prefer fedoo.constitutivelaw.Simcoon, which provides optimized constitutive updates and algorithmically consistent tangent options.

Parameters:

• young_modulus (float) – Young modulus.

• poisson_ratio (float) – Poisson ratio.

• yield_stress (float) – Initial yield stress.

• name (str, optional) – Name of the constitutive law.

__init__(young_modulus, poisson_ratio, yield_stress, name='')

Methods

ElastoPlasticity.compute_stress(total_strain)	Integrate a material-point state without an assembly.
ElastoPlasticity.get_H_plane_stress(H)	Convert a full 3D tangent matrix H in an equivalent behavior in 2D with the plane stress assumption.
ElastoPlasticity.get_all()	Return a dict with all the known ConstitutiveLaw (with a name).
ElastoPlasticity.get_current_local_frame([...])	Return the trial material frame in global coordinates.
ElastoPlasticity.get_elastic_matrix([dimension])	Return the isotropic elastic matrix in engineering Voigt form.
ElastoPlasticity.get_local_frame([assembly])	Return material frames, resolved at assembly Gauss points.
ElastoPlasticity.get_local_rotation([...])	Return a Simcoon rotation for the requested material frame.
ElastoPlasticity.get_plastic_strain()	Return plastic strain from the most recent integration.
ElastoPlasticity.get_plasticity()	Return plasticity from the most recent integration.
ElastoPlasticity.get_stress()	Return stress from the most recent integration.
ElastoPlasticity.get_tangent_matrix([...])	Return the current tangent, or the elastic tangent initially.
ElastoPlasticity.get_temp_gp(assembly, pb)	Return the current temperature field at Gauss points, if any.
ElastoPlasticity.global2local_H(H[, ...])	Rotate a global stiffness to material axes using Simcoon.
ElastoPlasticity.global2local_rotation_increment(DR)	Express a finite rotation increment in the initial material basis.
ElastoPlasticity.global2local_strain(strain)	Express engineering-strain vector(s) from global to material axes.
ElastoPlasticity.global2local_stress(stress)	Express stress Voigt vector(s) from global to material axes.
ElastoPlasticity.global2local_tensor(tensor)	Change both axes of 3x3 tensor fields to the initial material basis.
ElastoPlasticity.hardening_function(plasticity)	Evaluate the isotropic hardening stress.
ElastoPlasticity.hardening_function_derivative(...)	Evaluate the derivative of the isotropic hardening stress.
ElastoPlasticity.initialize(assembly, pb)	Initialize the constitutive law for the current problem.
ElastoPlasticity.local2global_H(H[, ...])	Rotate a material stiffness to global axes using Simcoon.
ElastoPlasticity.local2global_strain(strain)	Express engineering-strain vector(s) from material to global axes.
ElastoPlasticity.local2global_stress(stress)	Express stress Voigt vector(s) from material to global axes.
ElastoPlasticity.reset()	Reset cached results; assembly history is managed by Fedoo.
ElastoPlasticity.set_density(density)	Set the mass density associated with this mechanical material.
ElastoPlasticity.set_hardening_function(...)	Define the isotropic hardening function.
ElastoPlasticity.set_initial_statev(...)	Set a labeled initial state-variable field on an assembly.
ElastoPlasticity.set_local_frame(local_frame)	Define the material coordinate frame.
ElastoPlasticity.set_return_mapping_tolerance(...)	Set the absolute tolerance used by the local return mapping.
ElastoPlasticity.set_start(assembly, pb)	Begin a new time iteration.
ElastoPlasticity.to_start(assembly, pb)	Restart the current time iteration.
ElastoPlasticity.update(assembly, pb)	Update the constitutive law for the current problem state.
ElastoPlasticity.yield_function(stress, ...)	Evaluate the von Mises yield function.
ElastoPlasticity.yield_function_derivative(stress)	Differentiate the yield function with respect to stress.

ElastoPlasticity.is_isotropic
ElastoPlasticity.manages_material_frame
ElastoPlasticity.name	Name of the constitutive law.
ElastoPlasticity.required_corate
ElastoPlasticity.shear_modulus	Shear modulus.
ElastoPlasticity.is_initialized	Tag set to True once the law is intialized.