Jeong-Hoon Song

Dynamic Fracture of Shells Subjected to Impulsive Loads

lation or in the vicinity of the crack tip 14. In related work, Armero and Ehrlich 15 used embedded discontinuity elements to model hinge lines in plates. The development of a fracture criterion that is computationally efficient and is easily applied in terms of available data poses a significant difficulty. Fracture criteria for quasibrittle materials, such as aluminum, are usually expressed in terms of the critical maximum principal tensile strain. However, in low order finite element models solved by explicit time integration, the maximum principal tensile strain tends to be quite noisy, so that crack paths computed by direct application of such a criterion tend to be erratic and do not conform to experimentally observed crack paths. Here, we propose a nonlocal form of a strain-based fracture criterion. The nonlocal form is obtained by a kernel-weighted average over a sector in front of the crack tip. In addition, we describe a combination of this kernel-weighted average with an angular component that can be used to indicate crack branching. The methodology is applied to the fracture of shell experiments performed by Chao and Shepherd 16. Although these experiments are very interesting, they do not provide enough experimental data for a validation of the methodology. Nevertheless, we show that the method is able to reproduce the change in failure mode that occurs for longer notches as compared with shorter notches and that the overall final configuration agrees reasonably well with that observed in the experiments.

A method for growing multiple cracks without remeshing and its application to fatigue crack growth

A numerical model to analyse the growth and the coalescence of cracks in a quasibrittle cell containing multiple cracks is presented. The method is based on the extended finite element method in which discontinuous enrichment functions are added to the finite element approximation to take into account the presence of the cracks, so that it requires no remeshing. In order to describe the discontinuities only the tip enrichment and the step enrichment are used. The method does not require a special enrichment for the junction of two cracks and the junction is automatically captured by the combination of the step enrichments. The geometry of the cracks which is described implicitly by the level set method is independent of the finite element mesh. In the numerical example, linear elastic fracture mechanics is adopted to describe the behaviour of the cracks along with the Paris fatigue law and the intact bulk material is assumed to be elastic. The numerical results show that cracks can grow and interconnect with each other without remeshing as fatigue progresses and that the pattern of fatigue crack development converges with mesh refinement.

On computing stress in polymer systems involving multi-body potentials from molecular dynamics simulation.

Hardy stress definition has been restricted to pair potentials and embedded-atom method potentials due to the basic assumptions in the derivation of a symmetric microscopic stress tensor. Force decomposition required in the Hardy stress expression becomes obscure for multi-body potentials. In this work, we demonstrate the invariance of the Hardy stress expression for a polymer system modeled with multi-body interatomic potentials including up to four atoms interaction, by applying central force decomposition of the atomic force. The balance of momentum has been demonstrated to be valid theoretically and tested under various numerical simulation conditions. The validity of momentum conservation justifies the extension of Hardy stress expression to multi-body potential systems. Computed Hardy stress has been observed to converge to the virial stress of the system with increasing spatial averaging volume. This work provides a feasible and reliable linkage between the atomistic and continuum scales for multi-body potential systems.

Bridging the multi phase-field and molecular dynamics models for the solidification of nano-crystals

Abstract We present a computational analysis of the multi-grain solidification behavior of a crystal-melt nickel (Ni) system at a moderate undercooling degree via both a molecular dynamics (MD) and a phase field model (PFM). The required simulation parameters for the PFM analysis are extracted from the MD analysis employing embedded atom (EAM) potentials thus leveraging the dual approach. The good agreement of the solidification dynamics as predicted by both the PFM and MD approaches at the nano- temporal and spatial length scales, indicates the feasibility of bridging the MD and PFM simulations in the statistical mean sense. This is achieved by parameterizing the PFM by materials properties obtained from MD and by characterizing the contribution of individual physical quantities through the PFM approach. Throughout this approach, we can more closely relate MD and PFM analysis, which can potentially enable better predictions of the themodynamic and kinetic processes of solidification, melting, and phase transformation processes with the PFM approach when is based on MD simulations.

Heat flux expressions that satisfy the conservation laws in atomistic system involving multibody potentials

Heat flux expressions are derived for multibody potential systems by extending the original Hardys methodology and modifying Admal & Tadmors formulas. The continuum thermomechanical quantities obtained from these two approaches are easy to compute from molecular dynamics (MD) results, and have been tested for a constant heat flux model in two distinctive systems: crystalline iron and polyethylene (PE) polymer. The convergence criteria and affecting parameters, i.e. spatial and temporal window size, and specific forms of localization function are found to be different between the two systems. The conservation of mass, momentum, and energy are discussed and validated within this atomistic-continuum bridging.

Explicit Dynamic Finite Element Method for Predicting Implosion/Explosion Induced Failure of Shell Structures

A simplified implementation of the conventional extended finite element method (XFEM) for dynamic fracture in thin shells is presented. Though this implementation uses the same linear combination of the conventional XFEM, it allows for considerable simplifications of the discontinuous displacement and velocity fields in shell finite elements. The proposed method is implemented for the discrete Kirchhoff triangular (DKT) shell element, which is one of the most popular shell elements in engineering analysis. Numerical examples for dynamic failure of shells under impulsive loads including implosion and explosion are presented to demonstrate the effectiveness and robustness of the method.

On Investigating the Thermomechanical Properties of Cross-linked Epoxy Via Molecular Dynamics Analysis

ABSTRACT In this work, we demonstrate the feasibility of a computational approach based on first principles for estimating various thermomechanical quantities of a cross-linked epoxy resin. In particular, this work is focused on determining estimated values of the variation in glass transition temperature, coefficient of thermal expansion, volume shrinkage due to curing, Young’s modulus, Poisson’s ratio, yield strength, and viscosity as a function of temperature and degree of curing via molecular dynamics simulations. In most cases it has been demonstrated that the values predicted by the proposed approach are in good agreement with the respective experimentally measured values. In addition, the validity of the proposed models describing the dependence of the thermomechanical quantities on temperature and curing degree is examined. Throughout this study, we demonstrate that the molecular dynamics–based computational predictive framework can serve as an excellent infrastructure that can enable numerical prediction of materials properties and thereby can reduce the costs of associated with physical experimentation. In addition, we demonstrate that insightful information can be generated at the molecular and microscopic scales that is not easily extractable from experiments.

Computational modeling of material deterioration at various length scales

In the past decade, a dominant theme in computational fracture mechanics has been to obtain a more fundamental understanding ofmaterial deterioration process, rather than relying on phenomenological or empirical approaches to make predictions. This is driven by a growing need to make predictions of the failure behavior of materials across length scales starting from first principles and going up to the continuum scale. In order to predict such material response, the development of rigorous computational models for modeling material deterioration process at various time and length scales has been of importance to the computational mechanics community. Several interesting approaches have thus been proposed to increase our understanding of the inter-related materials deterioration processes at disparate length scales. While experimental fracture mechanics is important for identifying the physical

Explicit Dynamic Finite Element Method for Failure with Smooth Fracture Energy Dissipations

A numerical method for dynamic failure analysis through the phantom node method is further developed. A distinct feature of this method is the use of the phantom nodes with a newly developed correction force scheme. Through this improved approach, fracture energy can be smoothly dissipated during dynamic failure processes without emanating noisy artifact stress waves. This method is implemented to the standard 4-node quadrilateral finite element; a single quadrature rule is employed with an hourglass control scheme in order to decrease computational cost and circumvent difficulties associated with the subdomain integration schemes for cracked elements. The effectiveness and robustness of this method are demonstrated with several numerical examples. In these examples, we showed the effectiveness of the described correction force scheme along with the applicability of this method to an interesting class of structural dynamic failure problems.

Towards Computational Synthesis of Microstructural Crystalline Morphologies for Additive Manufacturing Applications

Powder-based additive manufacturing technologies introduce severe variations in microstructure in terms of grain size and aspect ratio that, coupled with porosity, can result in dramatic effects on the functional (mechanical, thermal, fatigue, fracture etc.) performance of as-produced parts. In the context of Integrated Computational Materials Engineering (ICME), it is essential develop a computationally efficient approach for generating synthetic microstructural morphologies that reflect these process-induced features. In the present paper, we employ two methodologies for computing the evolution of metal solidification at the microstructural level as a function of process parameters associated with additive manufacturing. The first method is the Continuum Diffuse Interface Model (CDM) applied to an arbitrary material system, and the second, the Multi-Phase Field Model (MPFM) applied to pure nickel (Ni). We present examples of microstructures generated by these methods within the context of additive manufacturing.