page_title: Viscoplasticity
section_title: Elastic perfectly viscoplastic solid (Bingham–Norton model)
hierarchical_section_title: Viscoplasticity / Rheological models of viscoplasticity / Elastic perfectly viscoplastic solid (Bingham–Norton model)
caption_attribution_description: English: This was performed using Power Point Presentation.
context_page_description: Viscoplasticity is a theory in continuum mechanics that describes the rate-dependent inelastic behavior of solids. Rate-dependence in this context means that the deformation of the material depends on the rate at which loads are applied. The inelastic behavior that is the subject of viscoplasticity is plastic deformation which means that the material undergoes unrecoverable deformations when a load level is reached. Rate-dependent plasticity is important for transient plasticity calculations. The main difference between rate-independent plastic and viscoplastic material models is that the latter exhibit not only permanent deformations after the application of loads but continue to undergo a creep flow as a function of time under the influence of the applied load.
  The elastic response of viscoplastic materials can be represented in one-dimension by Hookean spring elements. Rate-dependence can be represented by nonlinear dashpot elements in a manner similar to viscoelasticity. Plasticity can be accounted for by adding sliding frictional elements as shown in Figure 1.
context_section_description: Two types of elementary approaches can be used to build up an elastic-perfectly viscoplastic mode.  In the first situation, the sliding friction element and the dashpot are arranged in parallel and then connected in series to the elastic spring as shown in Figure 7.  This model is called the Bingham–Maxwell model (by analogy with the Maxwell model and the Bingham model) or the Bingham–Norton model.  In the second situation, all three elements are arranged in parallel.  Such a model is called a Bingham–Kelvin model by analogy with the Kelvin model.
  For elastic-perfectly viscoplastic materials, the elastic strain is no longer considered negligible but the rate of plastic strain is only a function of the initial yield stress and there is no influence of hardening.  The sliding element represents a constant yielding stress when the elastic limit is exceeded irrespective of the strain.  The model can be expressed as
  where  is the viscosity of the dashpot element.  If the dashpot element has a response that is of the Norton form
  we get the Bingham–Norton model
  Other expressions for the strain rate can also be observed in the literature with the general form
  The responses for strain hardening, creep, and relaxation tests of such material are shown in Figure 8.
caption: Figure 8. The response of elastic perfectly viscoplastic solid to hardening, creep and relaxation tests.
exif: {}