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Multiscale Modeling of Random Nano- and Micro-Fiber Reinforced Cementitious Composites

Research Sponsor:

  • Vanderbilt University Grant Research Program
  • Vanderbilt University Institute for Software Integrated Systems (ISIS)
  • Investigators:

    Matthew G. Pike and Caglar Oskay

    Research Goals and Methods


  • To gain a fundamental understanding of the interactions between the fibers and the cement matrix in carbon nano- and micro-fiber reinforced cement composites
  • To evaluate the effects of the chemical structure of the interface on the macroscopic mechanical failure properties
  • Multiscale Computational Framework:

  • Composite response controlled at the molecular scale through the chemical and mechanical interactions
  • Nanoscale investigations and nanoscopically informed embedded cohesive law
  • Link the material microstructure to the composite mesoscale: based on the overall response of the RVE
  • Computational Design of Carbon Nano- and Micro-Fiber Reinforced Cementitious Composites:

  • Random short fiber reinforced composite material
  • The inter-facial interaction between the matrix and the reinforcement has significant effect on the overall response of the composite structure
  • Use of the extended finite element method (X-FEM)to model the fibers in the matrix

  • Modeling Short Fibers Reinforced Composites Using XFEM

    Representative Volume Element (RVE):

  • Constitutive response of the cohesive zone model for interdependent damage-plasticity modeling of the cement phase
  • Random short-fiber reinforced matrix idealization
  • XFEM framework to evaluate the response of the RVE
  • Extended Finite Element Method (XFEM):

  • Fibers accounted for by using additional enrichment functions
  • Enrichment of the finite element approximation by additional functions that model the internal boundaries
  • Fibers can be modeled as rigid or flexible

  • Complex finite element discretizations that require resolution of fibers are eliminated
  • N(x): nodal enrichment function, : nodal value, ψ(x): enrichment function, : additional degree of freedom nodal value

  • XFEM Element Types

    Nodal Enrichment Function:

  • Enrichment function of fiber inclusion comprised of level set functions
  • Level set functions for fiber interface and fiber tips separately

  • Φα(x)=(xxit : level set function at fiber tip, i – tracks the motion of each fiber tip
  • Φc(x)=min ||xxr|| : level set function at interface – tracks the motion of the fiber interface

  • Enrichment Function

    Enriched Nodal Basis Functions

    Fiber Response

    Rigid Fibers:

  • Assume each fiber moves as a rigid body as does not deform
  • Described through rotation and translation
  • Penalty method applied to fiber constraint at fiber/matrix interface

  • Flexible Fibers:

  • Assume each fiber is flexible and do not bend but stretch under loading
  • Flexibility of fiber decrease the strength of the matrix
  • The energy from the stretch is added to the system

  • Fiber De-Bonding and Cohesive Embedded Laws

    Fiber De-Bonding:

  • Fibers will de-bond from the matrix once the loading reaches a critical stress
  • Additional term added to discretization at account for the de-bonding:

  • De-Bonding Enrichment Function

    Cohesive Embedded Law:

  • Energy based, nanoscopically informed cohesive embedded law
  • Separation over the interface of the fiber and matrix, resisted by cohesive tractions
  • Non linear constitutive relationship between cohesive tractions and the displacement jumps along the fiber cement interface as a function of the molecular structure

  • Cohesive Traction relationship and Fiber De-Bonding Motion


    Multiscale Computational Framework for Modeling the Mechanical Response of Nano- and Micro-Fiber Reinforced Cementitious Composites:

  • An efficient XFEM approach is proposed to evaluate the RVE response
  • Nano- and micro-fibers modeled for rigid, flexibility and de-bonding of fibers
  • Nanoscale response with the nanoscopically informed cohesive embedded law
  • Future Potential:

  • Pathway to achieve simulation based molecular scale engineering of cementitious composites
  • Aid in the composite material design process