Continuous softening up to the onset of failure: a hyperelastic modelling approach with intrinsic softening for isotropic incompressible soft solids

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This paper seeks to put forward an alternative notion for modelling the continuous softening in the finite deformation of incompressible isotropic rubber-like materials, up to the onset of failure. Based on the proposition that ‘there is no fundamental reason as to why the basic constitutive parameters of the (hyper)elastic state of a material cannot determine the natural evolution of softening and failure in that material’, the concept of hyperelasticity with intrinsic softening is posited. In contrast to the currently available theories of continuum damage mechanics and energy limiters, which superpose external parameters onto the basic hyperelastic model, the alternative approach presented here postulates that if a hyperelastic strain energy function accommodates a comprehensive set of constitutive parameters and has an appropriate functional form, it will intrinsically capture the observed continuous softening in the stress–deformation curves of soft solids, up to the onset of failure. Examples of this notion are presented using a specific hyperelastic model previously proposed by the author, applied here to extant datasets of a wide variety of isotropic incompressible soft solids, ranging from soft tissues to protein gels and 3D printed biomaterials, that include the softening behaviour. The favourable modelling results obtained via this approach are demonstrated. It is conferred that these results portend a versatile modelling tool for application to the whole-range deformation of soft solids, up to the onset of failure, and make the case for devising a unified theory for modelling both continuous and discontinuous softening in the finite deformation of rubber-like materials.
Original languageEnglish
Article number104183
Number of pages6
JournalMechanics Research Communications
Early online date10 Aug 2023
Publication statusPublished - 1 Oct 2023


  • continuous softening
  • constitutive modelling
  • hyperelasticity with intrinsic softening
  • finite deformations
  • soft solids

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