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Thermomechanics-based nonlinear rate-dependent coupled damage-plasticity granular micromechanics model

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Abstract

Thermomechanics and granular micromechanics approaches are combined to derive constitutive equations for modeling rate-dependent granular materials with damage and plasticity. The derivation is motivated by the recognition that the effect of micro-scale mechanisms upon the macro-scale behavior is known to be significant for granular materials. A general thermomechanical framework applicable to rate-dependent granular materials with damage and plasticity is developed. Based upon this framework, an expression for macro-scale Cauchy stress tensor is obtained in terms of the micro-scale grain interaction forces and the relationship between micro- and macro-scale kinematics. In addition, a Clausius–Duhem type inequality applicable to inter-granular interaction is derived, which is used to establish micro-scale constitutive relations for particular type of inter-granular interactions. The expression for Cauchy stress tensor and the micro-scale constitutive relations is then combined under a mean field kinematic assumption to obtain evolution-type macro-scale constitutive equations. The advantage of the granular micromechanics approach is that the damage and plasticity are defined using simple 1d functions at micro-scale, and complicated plastic potentials, damage functions and rules for their evolution are not required. The resultant model is applied to investigate primary, secondary and tertiary creep, creep-recovery as well as rate-dependent response under uniaxial compressive loading. Model applicability is also demonstrated for asymmetric tensile-compressive response under creep-recovery loading. The model is used to evaluate the evolution of elastic energy, and viscous, plastic and damage dissipation at the macro- and micro-scale with respect to creep time and loading level. The results show the development of loading-induced anisotropy due to damage and plasticity in these materials.

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Correspondence to Anil Misra.

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Communicated by Francesco dell’Isola and Giuseppe Piccardo.

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Misra, A., Singh, V. Thermomechanics-based nonlinear rate-dependent coupled damage-plasticity granular micromechanics model. Continuum Mech. Thermodyn. 27, 787–817 (2015). https://doi.org/10.1007/s00161-014-0360-y

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Keywords

  • Thermomechanics
  • Rate dependence
  • Damage-plasticity
  • Granular materials
  • Micromechanics
  • Time integration