Developing Multiscale Simulations with Coupled Molecular Dynamics and the Finite Element Method: Polymers and Gecko Adhesion

Many problems in materials science and engineering are fundamentally multiscale, where localized molecular processes govern, constrain, or trigger the macroscopic behavior of much larger bodies. Only a few regions of interest—for example, the neighborhood of a crack tip during fracture or an adhesive contact—require molecular resolution to capture mechanisms like bond breaking, chain disentanglement, or interfacial physics. The surrounding bulk contributes primarily through load transfer and boundary conditions, and can therefore be modeled at lower fidelity without sacrificing accuracy for the observables of interest. This thesis develops and applies a concurrent coupling between molecular dynamics (MD) and the finite element (FE) method within the Capriccio framework to realize the above strategy. Molecular dynamics is used precisely where molecular mechanisms matter, while FE carries the global response. The two descriptions overlap in a bridging domain where energetic contributions are blended and kinematic constraints synchronize boundary displacements. A staggered workflow alternates MD substeps (with FE and parts of the coupling frozen) and quasi-static FE substeps (with MD and complementary parts of the coupling frozen). Information is exchanged via anchor points (APs): virtual particles that transmit time-averaged forces from MD to FE and impose updated FE displacements back on MD. The first contribution addresses two systematic interface errors that arise when a finite MD region is carved from a periodic bulk and embedded in a continuum: (i) boundary-layer bias (density and stress mismatches) from chain cutting and (ii) a surface-tension–like contraction due to the loss of long-range nonbonded neighbors. A passive fur layer—retained molecular segments just outside the MD boundary that move affinely with the local FE deformation—restores the missing configurational environment while adding essentially no MD cost. All traction transfer remains through anchor points (APs), as in the standard coupling scheme; the fur is kinematically driven, not time-integrated. With this correction, the MD interior recovers the density and stress of fully periodic reference simulations, and the coupled response becomes markedly less sensitive to the precise profile of energy-blending weights in the overlap. The second contribution extends the framework into the large-strain and fracture regime for a glassy polymer—specifically, a coarse-grained model of atactic polystyrene. On the continuum side, a nonlinear viscoelastic–viscoplastic constitutive law is calibrated from slow, large-strain MD data to represent the response beyond linear elasticity. On the molecular side, a bond-breaking criterion allows covalent scission once a bond-energy threshold is exceeded, enabling a realistic competition between disentanglement and scission under load. Hybrid boundary conditions—nonperiodic along the coupling directions and periodic along the third—permit crack growth with appropriate lateral constraints. The resulting simulations capture craze initiation, crack propagation, and the evolving balance between molecular mechanisms that were previously inaccessible. The third contribution generalizes Capriccio to many MD domains coupled in parallel to a single FE body within the same staggered algorithm. This capability is essential for systems comprising several spatially separated molecular regions of interest (e.g., multiple adhesive contacts, failure sites, or embedded nanoparticles) that interact through a shared structure. The extension is demonstrated in a gecko adhesion study, where multiple spatula–substrate contacts evolve simultaneously while the common seta shaft applies and redistributes load. Furthermore, simple design choices during modeling (e.g., co-locating anchor points with FE nodes) eliminate interpolation/extrapolation at the interface and enable accurate scaling to many parallel MD domains. This illustrates that the method can be adapted beyond bulk polymer problems to a broader class of applications. Taken together, these developments advance Capriccio from a tool primarily suited to small-strain bulk polymers into a versatile method for problems that combine localized molecular physics with global mechanics, enabling high-fidelity simulations exactly where they are most informative.