Publications

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This report develops and documents nonlinear kinematic relations needed to implement piezoelectric constitutive models in ALEGRA-EMMA [5], where calculations involving large displacements and rotations are routine. Kinematic relationships are established using Gausss law and Faradays law; this presentation on kinematics goes beyond piezoelectric materials and is applicable to all dielectric materials. The report then turns to practical details of implementing piezoelectric models in an application code where material principal axes are rarely aligned with user defined problem coordinate axes. This portion of the report is somewhat pedagogical but is necessary in order to establish documentation for the piezoelectric implementation in ALEGRA-EMMA. This involves transforming elastic, piezoelectric, and permittivity moduli from material principal axes to problem coordinate axes. The report concludes with an overview of the piezoelectric implementation in ALEGRA-EMMA and small verification examples.

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A non-local, ordinary-state-based, peridynamics viscoelasticity model is developed. In this model, viscous effects are added to deviatoric deformations and the bulk response remains elastic. The model uses internal state variables and is conceptually similar to linearized isotropic viscolelasticity in the local theory. The modulus state, which is used to form the Jacobian matrix in Newton-Raphson algorithms, is presented. The model is shown to satisfy the 2nd law of thermodynamics and is applicable to problems in solid continuum mechanics where fracture and rate effects are important; it inherits all the advantages for modeling fracture associated with peridynamics. By combining this work with the previously published ordinary-state-based plasticity model, the model may be amenable to viscoplasticity problems where plasticity and rate effects are simultaneously important. Also, the model may be extended to include viscous effects for spherical deformations as well. The later two extensions are not presented and may be the subject of further work.

This report details efforts to deploy Agile Components for rapid development of a peridynamics code, Peridigm. The goal of Agile Components is to enable the efficient development of production-quality software by providing a well-defined, unifying interface to a powerful set of component-based software. Specifically, Agile Components facilitate interoperability among packages within the Trilinos Project, including data management, time integration, uncertainty quantification, and optimization. Development of the Peridigm code served as a testbed for Agile Components and resulted in a number of recommendations for future development. Agile Components successfully enabled rapid integration of Trilinos packages into Peridigm. A cost of this approach, however, was a set of restrictions on Peridigm's architecture which impacted the ability to track history-dependent material data, dynamically modify the model discretization, and interject user-defined routines into the time integration algorithm. These restrictions resulted in modifications to the Agile Components approach, as implemented in Peridigm, and in a set of recommendations for future Agile Components development. Specific recommendations include improved handling of material states, a more flexible flow control model, and improved documentation. A demonstration mini-application, SimpleODE, was developed at the onset of this project and is offered as a potential supplement to Agile Components documentation.

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An implicit time integration algorithm for a non-local, state-based, peridynamics plasticity model is developed. The flow rule was proposed in [3] without an integration strategy or yield criterion. This report addresses both of these issues and thus establishes the first ordinary, state-based peridynamics plasticity model. Integration of the flow rule follows along the lines of the classical theories of rate independent J{sub 2} plasticity. It uses elastic force state relations, an additive decomposition of the deformation state, an elastic force state domain, a flow rule, loading/un-loading conditions, and a consistency condition. Just as in local theories of plasticity (LTP), state variables are required. It is shown that the resulting constitutive model does not violate the 2nd law of thermodynamics. The report also develops a useful non-local yield criterion that depends upon the yield stress and horizon for the material. The modulus state for both the ordinary elastic material and aforementioned plasticity model is also developed and presented.

Progress in MEMS fabrication has enabled a wide variety of force and displacement sensing devices to be constructed. One device under intense development at Sandia is a passive shock switch, described elsewhere (Mitchell 2008). A goal of all MEMS devices, including the shock switch, is to achieve a high degree of reliability. This, in turn, requires systematic methods for validating device performance during each iteration of design. Once a design is finalized, suitable tools are needed to provide quality assurance for manufactured devices. To ensure device performance, measurements on these devices must be traceable to NIST standards. In addition, accurate metrology of MEMS components is needed to validate mechanical models that are used to design devices to accelerate development and meet emerging needs. Progress towards a NIST-traceable calibration method is described for a next-generation, 2D Interfacial Force Microscope (IFM) for applications in MEMS metrology and qualification. Discussed are the results of screening several suitable calibration methods and the known sources of uncertainty in each method.

This report summarizes design and modeling activities for the MEMS passive shock sensor. It provides a description of past design revisions, including the purposes and major differences between design revisions but with a focus on Revisions 4 through 7 and the work performed in fiscal year 2008 (FY08). This report is a reference for comparing different designs; it summarizes design parameters and analysis results, and identifies test structures. It also highlights some of the changes and or additions to models previously documented [Mitchell et al. 2006, Mitchell et al. 2008] such as the way uncertainty thresholds are analyzed and reported. It also includes dynamic simulation results used to investigate how positioning of hard stops may reduce vibration sensitivity.

This report summarizes the functional, model validation, and technology readiness testing of the Sandia MEMS Passive Shock Sensor in FY08. Functional testing of a large number of revision 4 parts showed robust and consistent performance. Model validation testing helped tune the models to match data well and identified several areas for future investigation related to high frequency sensitivity and thermal effects. Finally, technology readiness testing demonstrated the integrated elements of the sensor under realistic environments.

This report describes activities conducted in FY07 to mature the MEMS passive shock sensor. The first chapter of the report provides motivation and background on activities that are described in detail in later chapters. The second chapter discusses concepts that are important for integrating the MEMS passive shock sensor into a system. Following these two introductory chapters, the report details modeling and design efforts, packaging, failure analysis and testing and validation. At the end of FY07, the MEMS passive shock sensor was at TRL 4.