17.1.1 Elastic behavior: overview

The material library in ABAQUS includes several models of elastic behavior:

Linear elasticity: Linear elasticity (Linear elastic behavior, Section 17.2.1) is the simplest form of elasticity available in ABAQUS. The linear elastic model can define isotropic, orthotropic, or anisotropic material behavior and is valid for small elastic strains.

Plane stress orthotropic failure: Failure theories are provided (Plane stress orthotropic failure measures, Section 17.2.3) for use with linear elasticity. They can be used to obtain postprocessed output requests.

Porous elasticity: The porous elastic model in ABAQUS/Standard (Elastic behavior of porous materials, Section 17.3.1) is used for porous materials in which the volumetric part of the elastic strain varies with the logarithm of the equivalent pressure stress. This form of nonlinear elasticity is valid for small elastic strains.

Hypoelasticity: The hypoelastic model in ABAQUS/Standard (Hypoelastic behavior, Section 17.4.1) is used for materials in which the rate of change of stress is defined by an elasticity matrix multiplying the rate of change of elastic strain, where the elasticity matrix is a function of the total elastic strain. This general, nonlinear elasticity is valid for small elastic strains.

Rubberlike hyperelasticity: For rubberlike material at finite strain the hyperelastic model (Hyperelastic behavior of rubberlike materials, Section 17.5.1) provides a general strain energy potential to describe the material behavior for nearly incompressible elastomers. This nonlinear elasticity model is valid for large elastic strains.

Foam hyperelasticity: The hyperfoam model (Hyperelastic behavior in elastomeric foams, Section 17.5.2) provides a general capability for elastomeric compressible foams at finite strains. This nonlinear elasticity model is valid for large strains (especially large volumetric changes). The foam plasticity model should be used for foam materials that undergo permanent deformation (Crushable foam plasticity models, Section 18.3.5).

Viscoelasticity: The viscoelastic model is used to specify time-dependent material behavior (Time domain viscoelasticity, Section 17.7.1). In ABAQUS/Standard it is also used to specify frequency-dependent material behavior (Frequency domain viscoelasticity, Section 17.7.2). It must be combined with linear elasticity, rubberlike hyperelasticity, or foam hyperelasticity.

Hysteresis: The hysteresis model in ABAQUS/Standard (Hysteresis in elastomers, Section 17.8.1) is used to specify rate-dependent behavior of elastomers. It is used in conjunction with hyperelasticity.

Mullins effect: The Mullins effect model (Mullins effect in rubberlike materials, Section 17.6.1) is used to specify stress softening of filled rubber elastomers due to damage, a phenomenon referred to as Mullins effect. The model can also be used to include permanent energy dissipation and stress softening effects in elastomeric foams (Energy dissipation in elastomeric foams, Section 17.6.2). It is used in conjunction with rubberlike hyperelasticity or foam hyperelasticity.

No compression or no tension elasticity: The no compression or no tension models in ABAQUS/Standard (No compression or no tension, Section 17.2.2) can be used when compressive or tensile principal stresses should not be generated. These options can be used only with linear elasticity.

Equation of state: The equation of state in ABAQUS/Explicit provides a hydrostatic material model in which the pressure is defined as a function of the density and the internal energy (Equation of state, Section 17.9.1). The material modeled by an equation of state may have no deviatoric strength or may have either isotropic elastic or Newtonian viscous deviatoric behavior. This model can be used by itself or in conjunction with the Mises or the Johnson-Cook plasticity models to model elastic-plastic hydrodynamic materials.

Thermal strain

Thermal expansion can be introduced for any of the elasticity models (Thermal expansion, Section 20.1.2) except the equation of state model.

Elastic strain magnitude

Except in the hyperelasticity, the stresses are always assumed to be small compared to the tangent modulus of the elasticity relationship; that is, the elastic strain must be small (less than 5%). The total strain can be arbitrarily large if inelastic response such as metal plasticity is included in the material definition.

For finite-strain calculations where the large strains are purely elastic, the hyperelastic model (for rubberlike behavior), or the foam hyperelasticity model (for elastomeric foams) should be used. In ABAQUS/Standard the linear or porous elasticity models are appropriate in other cases where the large strains are inelastic. In ABAQUS/Explicit the hyperelasticity is the only model that gives realistic predictions of actual material behavior at large elastic strains.

In ABAQUS/Standard the linear elastic, porous elastic, and hypoelastic models will exhibit poor convergence characteristics if the stresses reach levels of 50% or more of the elastic moduli; this limitation is not serious in practical cases because these material models are not valid for the resulting large strains.