Multiscale Modeling of Epoxies and Epoxy-Based Composites
273
example, Mortazavi et al. studied graphene reinforced DGEBA epoxy composites
to understand their thermal conduction and dependence on geometry and volume
fraction of the fiber reinforcements [55, 74]. Subramanian et al. simulated the
damage and fracture of CNT/epoxy nanocomposites using MD and FEM models
[53]. In these studies, the MD simulation predictions were upscaled into FEM
simulations to develop homogenized properties based on microscale representative
volume elements (RVEs). Additionally, Choi et al. studied the size effects of carbon
nanotubes in SWNT/epoxy systems using a combined MD/FEM model [81]. In
this approach, the interphase geometric boundaries and mechanical response were
predicted from FEM through matching of homogenization and deformation energy
from MD simulations [82].
It should be noted that the MD and FEM models are at the nano- and microscales,
respectively; thus, there is a need for developing homogenization methods to bridge
the length-scale gap between both models. The CG-MD models provide such an
approach. Since CG-MD models can simulate large-scale domains (i.e., up to
the microscale), it is feasible to explicitly simulate the fiber/matrix regions with
dynamically created CG epoxy structures, and the resulting material properties can
be directly upscaled to FEM models, which will enable a one-way information flow.
In particular, CG-based bridging methods can be beneficial to epoxy and epoxybased composite modeling.
3 Multiscale Simulations of Epoxies and Their Properties
3.1 Modeling the Curing Process of Epoxies
A first step in any epoxy molecular modeling simulation is to create a structure that
represents a true epoxy material. Many simulations have been devoted to simulate
the dynamic curing process of highly cross-linked epoxies [27, 40, 65, 83, 84]. The
creation of an epoxy system is highly dependent on the epoxy resin, the crosslinker, and the force field employed to describe the system dynamics. Generally, a
mixture of monomers and curing agents are placed in a simulation cell with periodic
boundary conditions in all directions. The functional groups on the prepolymers
are allowed to form covalent bonds according to a pre-defined distance-based bond
creation rule [85]. The cross-linking process is considered complete when a certain
degree of conversion is achieved or there are no more bonds to create in the system.
This general curing process is adopted in both MD and CG simulations with a few
modifications to achieve a good epoxy structures. The main modification occurs
in the cross-linking step. Wu and Xu [40] developed an algorithm that employed
repeated MD and molecular mechanics (MM) simulation steps during the curing
process and were able to achieve an epoxy network with conversion up to 93.7%
with less computing time and much flexibility. Additionally, Varshney et al. [51]
proposed a multistep robust procedure that includes a relaxation period during the
polymer network buildup and noted that the relaxation time between each step of
273
example, Mortazavi et al. studied graphene reinforced DGEBA epoxy composites
to understand their thermal conduction and dependence on geometry and volume
fraction of the fiber reinforcements [55, 74]. Subramanian et al. simulated the
damage and fracture of CNT/epoxy nanocomposites using MD and FEM models
[53]. In these studies, the MD simulation predictions were upscaled into FEM
simulations to develop homogenized properties based on microscale representative
volume elements (RVEs). Additionally, Choi et al. studied the size effects of carbon
nanotubes in SWNT/epoxy systems using a combined MD/FEM model [81]. In
this approach, the interphase geometric boundaries and mechanical response were
predicted from FEM through matching of homogenization and deformation energy
from MD simulations [82].
It should be noted that the MD and FEM models are at the nano- and microscales,
respectively; thus, there is a need for developing homogenization methods to bridge
the length-scale gap between both models. The CG-MD models provide such an
approach. Since CG-MD models can simulate large-scale domains (i.e., up to
the microscale), it is feasible to explicitly simulate the fiber/matrix regions with
dynamically created CG epoxy structures, and the resulting material properties can
be directly upscaled to FEM models, which will enable a one-way information flow.
In particular, CG-based bridging methods can be beneficial to epoxy and epoxybased composite modeling.
3 Multiscale Simulations of Epoxies and Their Properties
3.1 Modeling the Curing Process of Epoxies
A first step in any epoxy molecular modeling simulation is to create a structure that
represents a true epoxy material. Many simulations have been devoted to simulate
the dynamic curing process of highly cross-linked epoxies [27, 40, 65, 83, 84]. The
creation of an epoxy system is highly dependent on the epoxy resin, the crosslinker, and the force field employed to describe the system dynamics. Generally, a
mixture of monomers and curing agents are placed in a simulation cell with periodic
boundary conditions in all directions. The functional groups on the prepolymers
are allowed to form covalent bonds according to a pre-defined distance-based bond
creation rule [85]. The cross-linking process is considered complete when a certain
degree of conversion is achieved or there are no more bonds to create in the system.
This general curing process is adopted in both MD and CG simulations with a few
modifications to achieve a good epoxy structures. The main modification occurs
in the cross-linking step. Wu and Xu [40] developed an algorithm that employed
repeated MD and molecular mechanics (MM) simulation steps during the curing
process and were able to achieve an epoxy network with conversion up to 93.7%
with less computing time and much flexibility. Additionally, Varshney et al. [51]
proposed a multistep robust procedure that includes a relaxation period during the
polymer network buildup and noted that the relaxation time between each step of