Multiscale Simulation from Atomistic to Continuum -- Coupling Molecular Dynamics (MD) with Material Point Method (MPM)

Failure in single crystals and polycrystalline materials usually involve processes such as dislocation, cleavage, macrocrack initiation and growth as well as coalescence until final fracture. Multiscale modeling is necessary to understand the mechanical behavior of materials from atomistic to continuum scales. MPM has been used for continuum simulation. The use of material points at the continuum level provides a natural connection with the atoms in the lattice at the atomistic scale. A hierarchical mesh refinement technique in MPM is presented to scale down the continuum level to the atomistic level, so that material points at the fine level in MPM are allowed to directly couple with the atoms in the MD. A one-to-one correspondence of MD atoms and MPM points is used in the transition region, and non-local elastic theory is used to assure compatibility between MD and MPM regions, so that seamless coupling between MD and MPM can be accomplished. A single crystal silicon workmaterial under uniaxial tension is used in demonstrating the viability of the technique. A Tersoff-type, three-body potential was used in the MD simulations. Further, elastic plastic constitutive material model is integrated with three-dimensional MPM to aid simulation of nanocrystalline material behavior at continuum scale. A new multiscale simulation approach is introduced that couples atomistic scale simulations using MD with continuum scale simulations using MPM. The coupled MD/MPM simulations show that the silicon under nanometric tension experiences with increasing elongation in elasticity, dislocation generation and plasticity by slip, void formation and propagation, formation of amorphous structure, necking, and final rupture. Results are presented in terms of stress - strain relationships at several strain rates, as well as the rate dependence of uniaxial material properties. This new multiscale computational method has potential for use in cases where a detailed atomistic-level analysis is necessary in localized spatially separated regions whereas continuum mechanics is adequate in rest of the material.Mechanical & Aerospace Engineerin

Twin boundary stability

Ideas from continuum mechanics are used to derive an elastic stability inequality for a contact plane between two different materials under quasi-static, homogeneous conditions. The terms in this inequality are interpreted for the case of an ideal twinning plane between two variants of a face-centered cubic material. High quality potentials for Ni and Cu are used in molecular dynamics calculations to calibrate relevant energies and displacements near the twinning plane. It is found that in comparison with direct molecular dynamics calculations the inequality predicts the critical stress in Ni within 1.9% and within 1.3% for Cu. Although the critical and calculated critical stresses are only upper bounds for the more realistic case of an imperfect boundary, the calculations give considerable insight into the interplay of energies that lead to boundary motion

Modeling and simulation of dynamic problems in solid mechanics using material point method

Scope and Method of Study: A relatively new computational method, namely Material Point Method (MPM), developed by Prof. Sulsky^1 of University of New Mexico , from the Particle-In-Cell (PIC) method in computational fluid mechanics, was used for simulations of dynamic problems. In this regard, various dynamic and material simulations have been carried out, which include dynamic crack growth using cohesive zone model, microstructure evolution of closed-cell polymer foam in compression and simulation of granular materials. In this process the MPM algorithm was developed by, either implementing completely newer capabilities of simulation or refining the older versions for increased robustness and versatility.Findings and Conclusions: The incorporation of a characteristic length scale in MPM through cohesive zone model allowed investigation of physics-based dynamic crack propagation. The simulations are capable of handling crack growth with crack-tip velocities in both sub-Rayleigh and intersonic regimes. Crack initiation and propagation are the natural outcome of the simulations incorporating the cohesive zone model. Good qualitative agreement was observed between numerical results presented here and the experimental results in terms of the photoelastic stress patterns ahead of the crack-tip.MPM will allow prediction of material properties for microstructures driving the optimization of processing and performance in foam materials through simulation of real microstructures. The simulations are able to capture the various stages of deformations in foam compression. The stress-strain curve simulated from MPM compares reasonably with the experimental results. Based on the results from µ-CT and MPM simulations, it was found that elastic buckling of cell-walls occur even in the elastic regime of compression. Within the elastic region, less than 35% of the cell-wall material carries majority of the compressive load.The particle nature in MPM was found suitable for simulation of granular materials. Contact algorithm has been implemented in MPM to allow MPM to handle slip and friction between bodies in contact. Nanoindentation was carried out on sand grains to determine its properties at granular level, which can be used along with µ-CT to carry out granular simulations of sand

Simulation of the Evolution of the Nanostructure of Crosslinked Silica-Aerogels under Compression

Silica-aerogels are ultra-low-density assemblies of silica nanoparticles, and possess superior acoustic, specific energy absorption and thermal insulation properties. A new class of aerogels encapsulated with polymer is classified as crosslinked silica-aerogels. Manufacturing of such crosslinked silica-aerogel structures, depending on the type and shape of the nanoparticles, the polymer cross-linker and the chemistry in use, yields structures with vastly different morphologies and a wide range of mechanical behavior. With this, it has become necessary to understand the nanostructure / macroscopic properties relationship. Modeling of the aerogel material properties from mesoscale and up approach is needed, which is not considered by the current phenomenological models based on continuum material assumption. Most of the existing simulation methodologies face difficulties mainly due to complex nanostructures, large distortions, and extensive contact. A relatively new numerical method called Material Point Method (MPM) can circumvent these problems. For example, MPM has been used effectively in modeling the microstructural evolution of the bulk metallic glass foam with 70% porosity, where 3D X-Ray microtomography was used first to obtain the representative volume element (RVE) of the closed-cell foam . Due to the particle description of matter, MPM is a very suitable for silica-aerogel simulations. In this regard, an approach based on X-Ray nano-computed tomography (n-CT) will be used to model cross-linked aerogel mesostructure. The voxel information from the 3D tomography will be used to generate material points in MPM. The parallel version (using Structured Adaptive Mesh Refinement Application Infrastructure) of MPM code will be used to simulate the response of the model under compression. In this paper, the MPM is used to model a crosslinked templated silicaaerogel (X-MP4-T045) in compression, and the simulation results are compared with the compressive stress-strain curve obtained experimentally. This work will focus on the deformation mechanisms in crosslinked templated silica-aerogel such as the elastic buckling, compaction and densification, as well as the dependence of mechanical properties on the porosity effect for this crosslinked templated silica-aerogel

Kinetics of a fast moving twinning dislocation

Constitutive models for plastic deformation in materials subjected to high rate loading conditions require kinetic descriptions of moving dislocations and moving interfaces. In materials that exhibit twinning, the velocities with which a twinning dislocation and a twin boundary can propagate has implications on the material behavior at high strain rates‑specifically the rate of plastic deformation and the rate sensitivity. In this study, we focus our attention on motion of a twinning dislocation in a face-centered cubic nickel. We use molecular dynamics simulations to simulate a moving twinning dislocation and investigate the effects of changing shear stress. Results suggest the material speeds have an influence on the velocities with which a twinning dislocation can propagate. Velocities from simulations will be related to observations from impact experiments

The Importance of Structural Anisotropy in Computational Models of Traumatic Brain Injury

Understanding the mechanisms of injury might prove useful in assisting the development of methods for the management and mitigation of traumatic brain injury (TBI). Computational head models can provide valuable insight into the multi-length-scale complexity associated with the primary nature of diffuse axonal injury. It involves understanding how the trauma to the head (at the cm length scale) translates to the white matter tissue (at the millimeter length scale), and even further down to the axonal-length scale, where physical injury to axons (e.g. axon separation) may occur. However, to accurately represent the development of TBI, the biofidelity of these computational models is of utmost importance. There has been a focused effort to improve the biofidelity of computational models by including more sophisticated material definitions and implementing physiologically relevant measures of injury. This paper summarizes recent computational studies that have incorporated structural anisotropy in both the material definition of the white matter and the injury criterion as a means to improve the predictive capabilities of computational models for TBI. We discuss the role of structural anisotropy on both the mechanical response of the brain tissue and on the development of injury. We also outline future directions in the computational modeling of TBI

Simulation of dynamic crack growth using the generalized interpolation material point (GIMP) method

Dynamic crack growth is simulated by implementing a cohesive zone model in the generalized interpolation material point (GIMP) method. Multiple velocity fields are used in GIMP to enable handling of discrete discontinuity on either side of the interface. Multilevel refinement is adopted in the region around the crack-tip to resolve higher strain gradients. Numerical simulations of crack growth in a homogeneous elastic solid under mode-II plane strain conditions are conducted with the crack propagating along a weak interface. A parametric study is conducted with respect to varying impact speeds ranging from 5 m/s to 60 rn/s and cohesive strengths from 4 to 35 MPa. Numerical results are compared qualitatively with the dynamic fracture experiments of Rosakis et al. [(1999) Science 284:1337-1340]. The simulations are capable of handling crack growth with crack-tip velocities in both sub-Rayleigh and intersonic regimes. Crack initiation and propagation are the natural outcome of the simulations incorporating the cohesive zone model. For various impact speeds, the sustained crack-tip velocity falls either in the sub-Rayleigh regime or in the region between root 2c(S) (c(S) is the shear wave speed) and C-D (C-D is the dilatational wave speed) of the bulk material. The Burridge-Andrews mechanism for transition of the crack-tip velocity from sub-Rayleigh to intersonic speed of the bulk material is observed for impact speeds ranging from 9.5 to 60 m/s (for normal and shear cohesive strengths of 24 MPa). Within the intersonic regime, sustained crack-tip velocities between 1.66 cS (or 0.82 C-D) and 1.94 cS (or 0.95 C-D) were obtained. For the cases simulated in this work, within the stable intersonic regime, the lowest intersonic crack-tip velocity obtained was 1.66 cS (or 0.82 C-D)