FEM-03. FINITE ELEMENT MODELS – PLASTICITY

In this third post on practical finite element modelling, we will outline some of the common ways of creating finite element models with metallic materials and plasticity using the Abaqus code (although the concepts can be easily applied to any other finite element code).

Plasticity in metallic materials

The plasticity of a metallic material occurs when we subject the material to a sufficient stress state to cause dislocations in the internal structure of the material and consequently permanent deformations.

The picture below shows a typical stress-strain curve of a metallic material for a uniaxial test:

Finite Element Modelling - Plasticity

On a practical level, the creation of finite element models with plasticity has its main use in the analysis of structures under ultimate load, where the different structural codes and regulations allow the ultimate strength of the materials used to be used.

In these cases, the acting load can be considered monotonic, and it is not necessary to define a hardening law that allows for the updating of the plasticising surface that would apply in the case of cyclic loads. This situation greatly simplifies the non-linear calculation of the structure, since we only need to have the stress-strain curve, or otherwise calculate it from the basic mechanical properties of the material.

It should be pointed out that in the case of wanting to evaluate the behaviour of the material under cyclic loads (such as the wheel-rail contact of a railway vehicle), with complete cycles of compression and traction, it is necessary to correctly define the type of hardening of the material, the most common being: isotropic hardening, kinematic hardening and combined hardening. In a future post, we will talk about these constitutive models and how to implement them in Abaqus.

Perfect elasto-plastic

Perfect Elasto-Plastic Stress-Strain Curve
Stress-strain curve with perfect elasto-plastic behaviour
*****************************************
** FEM Abaqus Entry
** E = Young's module
** v = Poisson coefficient
** Fty = Yield stress
** e = maximum elongation
*****************************************
** Elastic behavior
*****************************************
*Material, name=material_name
*Elastic
E, ν
*****************************************
** Plastic behavior
*****************************************
*Plastic
Fty·(1+Fty/E), 0.0
Fty·(1+Fty/E), ln(1+e)-Fty,true/E
*****************************************

Elasto-plastic with linear hardening

Elasto-Plastic stress-strain curve with hardening
Stress-strain curve with elasto-plastic behaviour with linear hardening
      *****************************************
      **   Entrada en código FEM Abaqus
      **   E = módulo elástico
      **   v = coeficiente de Poisson
      **   Fty = tensión límite elástico
      **   Ftu = tensión última
      **   e = elongación máxima de rotura
      *****************************************
      ** Elastic behavior
      *****************************************
      *Material, name=material_name 
      *Elastic 
      E, ν
      *****************************************
      ** Plastic behavior
      *****************************************
      *Plastic
      Fty·(1+Fty/E), 0.0
      Ftu,true, ln(1+e)-Fty/E
      *****************************************

Ramberg-Osgood

Finite Element Models. Plasticity. Ramberg-Osgood stress-strain curve.
Idealised stress-strain curve according to Ramberg-Osgood formulation

In our download section you can download our procedure “ISM2006 Metallic Plasticity Modelling – ABAQUS FEM Code”. This procedure provides detailed information on the definition of the parameters necessary to model the plasticity of metallic materials in Abaqus, including a free tool to automatically obtain the Ramberg-Osgood curves from the usual parameters of the mechanical properties of the material.

      *****************************************
      **   FEM Abaqus Entry
      **   E = Young's module
      **   v = Poisson coefficient
      **   Fty = yield stress
      **   Ftu = ultimate stress
      **   e = maximum elongation
      *****************************************
      ** Elastic behavior
      *****************************************
      *Material, name=material_name 
      *Elastic 
      E, ν
      *****************************************
      ** Plastic behavior
      *****************************************
      *Plastic
      Fty·(1+Fty/E), 0.0
      Ftu,true, ln(1+e)-Fty/E
      *****************************************
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