Micromechanics based second gradient continuum theory for shear band modeling in cohesive granular materials following damage elasticity

By Yang Yang, Anil Misra. 2012

160 citations recorded by the source corpus.

Abstract Gradient theories, as a regularized continuum mechanics approach, have found wide applications for modeling strain localization failure process. This paper presents a second gradient stress–strain damage elasticity theory based upon the method of virtual power. The theory considers the strain gradient and its conjugated double stresses. Instead of introducing an intrinsic material length scale into the constitutive law in an ad hoc fashion, a microstructural granular mechanics approach is applied to derive the higher-order constitutive coefficients such that the internal length scale parameter reflects the natural granularity of the underlying material microstructure. The derivations of the required damage constitutive relationships, the strong form governing equations as well as its weak form for the second gradient model are described. The recently popularized Element-Free Galerkin (EFG) method is then employed to discretize the weak form equilibrium equation for accommodating the resultant higher-order continuity requirements and further handling the mesh sensitivity problem. Numerical examples for shear band simulations show that the proposed second gradient continuum model can produce stable, accurate as well as mesh-size independent solutions without a priori assumption of the shear band path.

Subfields: Materials Chemistry, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/be24d1eb77b8e99be647a345b14e5ff40c479687

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In Materials Chemistry

In Mechanics of Materials

Citations in the corpus

Exegesis of the Introduction and Sect. I from “Fundamentals of the Mechanics of Continua”** by E. Hellinger (2017, background): “The literature in the subject is becoming immense: we quote here [20, 78] among the most interesting papers obtaining first gradient continua as continuous limit while, for what concerns the papers where a higher gradient continuum limit is obtained, we cite [4] and [5, 21, 89] (see also the effort ”
Analytical continuum mechanics à la Hamilton–Piola least action principle for second gradient continua and capillary fluids (2013, background): “[128], Misra and Chang [107], Yang and Misra [169][170], Yang et al.”
Strain gradient and generalized continua obtained by homogenizing frame lattices (2018, background): “(see for instance [81], [69], [3], [4], [55], [75], [85]).”
At the origins and in the vanguard of peridynamics, non-local and higher-gradient continuum mechanics: An underestimated and still topical contribution of Gabrio Piola (2013, background): “Many important applications can be conceived for higher gradient materials, as for instance those involving the phenomena described for instance in [1], [27], [30], [51], [71], [72], [103], [112], [113], [114], [115], [116], [117], [118], [119], [141], [142], [143], [144].”
Second-gradient continua as homogenized limit of pantographic microstructured plates: a rigorous proof (2015, methodology): “, [42–52]), no general method or technique is available yet for characterizing the discrete microstructures which must be modeled in the homogenized limit by means of generalized continua.”