Publications

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This report is a collection of documents written as part of the Laboratory Directed Research and Development (LDRD) project A Mathematical Framework for Multiscale Science and Engineering: The Variational Multiscale Method and Interscale Transfer Operators. We present developments in two categories of multiscale mathematics and analysis. The first, continuum-to-continuum (CtC) multiscale, includes problems that allow application of the same continuum model at all scales with the primary barrier to simulation being computing resources. The second, atomistic-to-continuum (AtC) multiscale, represents applications where detailed physics at the atomistic or molecular level must be simulated to resolve the small scales, but the effect on and coupling to the continuum level is frequently unclear.

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This paper presents constitutive models for the anisotropic, finite-deformation viscoelastic behavior of soft fiber-reinforced composites. An essential assumption of the models is that both the fiber reinforcements and matrix can exhibit distinct time-dependent behavior. As such, the constitutive formulation attributes a different viscous stretch measure and free energy density to the matrix and fiber phases. Separate flow rules are specified for the matrix and the individual fiber families. The flow rules for the fiber families then are combined to give an anisotropic flow rule for the fiber phase. This is in contrast to many current inelastic models for soft fiber-reinforced composites which specify evolution equations directly at the composite level. The approach presented here allows key model parameters of the composite to be related to the properties of the matrix and fiber constituents and to the fiber arrangement. An efficient algorithm is developed for the implementation of the constitutive models in a finite-element framework, and examples are presented examining the effects of the viscoelastic behavior of the matrix and fiber phases on the time-dependent response of the composite.

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The primary goals of the present study are to: (1) determine how and why MEMS-scale friction differs from friction on the macro-scale, and (2) to begin to develop a capability to perform finite element simulations of MEMS materials and components that accurately predicts response in the presence of adhesion and friction. Regarding the first goal, a newly developed nanotractor actuator was used to measure friction between molecular monolayer-coated, polysilicon surfaces. Amontons law does indeed apply over a wide range of forces. However, at low loads, which are of relevance to MEMS, there is an important adhesive contribution to the normal load that cannot be neglected. More importantly, we found that at short sliding distances, the concept of a coefficient of friction is not relevant; rather, one must invoke the notion of 'pre-sliding tangential deflections' (PSTD). Results of a simple 2-D model suggests that PSTD is a cascade of small-scale slips with a roughly constant number of contacts equilibrating the applied normal load. Regarding the second goal, an Adhesion Model and a Junction Model have been implemented in PRESTO, Sandia's transient dynamics, finite element code to enable asperity-level simulations. The Junction Model includes a tangential shear traction that opposes the relative tangential motion of contacting surfaces. An atomic force microscope (AFM)-based method was used to measure nano-scale, single asperity friction forces as a function of normal force. This data is used to determine Junction Model parameters. An illustrative simulation demonstrates the use of the Junction Model in conjunction with a mesh generated directly from an atomic force microscope (AFM) image to directly predict frictional response of a sliding asperity. Also with regards to the second goal, grid-level, homogenized models were studied. One would like to perform a finite element analysis of a MEMS component assuming nominally flat surfaces and to include the effect of roughness in such an analysis by using a homogenized contact and friction models. AFM measurements were made to determine statistical information on polysilicon surfaces with different roughnesses, and this data was used as input to a homogenized, multi-asperity contact model (the classical Greenwood and Williamson model). Extensions of the Greenwood and Williamson model are also discussed: one incorporates the effect of adhesion while the other modifies the theory so that it applies to the case of relatively few contacting asperities.

This report is a collection of documents written by the group members of the Engineering Sciences Research Foundation (ESRF), Laboratory Directed Research and Development (LDRD) project titled 'A Robust, Coupled Approach to Atomistic-Continuum Simulation'. Presented in this document is the development of a formulation for performing quasistatic, coupled, atomistic-continuum simulation that includes cross terms in the equilibrium equations that arise due to kinematic coupling and corrections used for the calculation of system potential energy to account for continuum elements that overlap regions containing atomic bonds, evaluations of thermo-mechanical continuum quantities calculated within atomistic simulations including measures of stress, temperature and heat flux, calculation used to determine the appropriate spatial and time averaging necessary to enable these atomistically-defined expressions to have the same physical meaning as their continuum counterparts, and a formulation to quantify a continuum 'temperature field', the first step towards constructing a coupled atomistic-continuum approach capable of finite temperature and dynamic analyses.

An effort is underway at Sandia National Laboratories to develop a library of algorithms to search for potential interactions between surfaces represented by analytic and discretized topological entities. This effort is also developing algorithms to determine forces due to these interactions for transient dynamics applications. This document describes the Application Programming Interface (API) for the ACME (Algorithms for Contact in a Multiphysics Environment) library.

An effort is underway at Sandia National Laboratories to develop a library of algorithms to search for potential interactions between surfaces represented by analytic and discretized topological entities. This effort is also developing algorithms to determine forces due to these interactions for transient dynamics applications. This document describes the Application Programming Interface (API) for the ACME (Algorithms for Contact in a Multiphysics Environment) library.

An effort is underway at Sandia National Laboratories to develop a library of algorithms to search for potential interactions between surfaces represented by analytic and discretized topological entities. This effort is also developing algorithms to determine forces due to these interactions for transient dynamics applications. This document describes the Application Programming Interface (API) for the ACME (Algorithms for Contact in a Multiphysics Environment) library.

An effort is underway at Sandia National Laboratories to develop a library of algorithms to search for potential interactions between surfaces represented by analytic and discretized topological entities. This effort is also developing algorithms to determine forces due to these interactions for transient dynamics applications. This document describes the Application Programming Interface (API) for the ACME (Algorithms for Contact in a Multiphysics Environment) library.