Daniel J. Segalman

A model for viscoelastic fluid behavior which allows non-affine deformation

Abstract A continuum theory of viscoelasticity is developed which allows non-affine deformation, defined in an appropriate manner. The constitutive equation is a generalization of that obtained from molecular theory with the addition of one scalar parameter which becomes important for large deformations. The theory is applied to simple shear flows, the scalar parameter being determined to match certain experimental data. The theory shows good agreement with all data examined. The paper concludes with the development of a general non-affine thermodynamic theory.

A four-parameter Iwan model for lap-type joints

The constitutive behavior of mechanical joints is largely responsible for the energy dissipation and vibration damping in built-up structures. For reasons arising from the dramatically different length scales associated with those dissipative mechanisms and the length scales characteristic of the overall structure, this physics cannot be captured through direct numerical simulation (DNS) of the contact mechanics within a structural dynamics analysis. The difficulties of DNS manifest themselves either in terms of Courant times that are orders of magnitude smaller than that necessary for structural dynamics analysis or as intractable conditioning problems. The only practical method for accommodating the nonlinear nature of joint mechanisms within structural dynamic analysis is through constitutive models employing degrees of freedom natural to the scale of structural dynamics. In this way, development of constitutive models for joint response is a prerequisite for a predictive structural dynamics capability. A four-parameter model, built on a framework developed by Iwan, is used to reproduce the qualitative and quantitative properties of lap-type joints. In the development presented here, the parameters are deduced by matching joint stiffness under low load, the force necessary to initiate macroslip, and experimental values of energy dissipation in harmonic loading. All the necessary experiments can be performed on real hardware or virtually via fine-resolution, nonlinear quasistatic finite elements. The resulting constitutive model can then be used to predict the force/displacement results from arbitrary load histories.

Stable Galerkin reduced order models for linearized compressible flow

The Galerkin projection procedure for construction of reduced order models of compressible flow is examined as an alternative discretization of the governing differential equations. The numerical stability of Galerkin models is shown to depend on the choice of inner product for the projection. For the linearized Euler equations, a symmetry transformation leads to a stable formulation for the inner product. Boundary conditions for compressible flow that preserve stability of the reduced order model are constructed. Preservation of stability for the discrete implementation of the Galerkin projection is made possible using a piecewise-smooth finite element basis. Stability of the reduced order model using this approach is demonstrated on several model problems, where a suitable approximation basis is generated using proper orthogonal decomposition of a transient computational fluid dynamics simulation.

A Dynamic Model of a Linear Actuator Based on Polymer Hydrogel

The design and analysis of a series of linear actuators based on polymer hydrogel is presented. The actuators use arrays of pH sensitive gel fibers together with a fluid irrigation system to locally and rapidly regulate the composition of the solution. A dynamic model is constructed for one of the linear actuators, which includes the polymer gel, fluidic system, and transmission mechanics. Emphasis in the design and mechanical modeling of the actuators is placed on the com plete system including not only the polymer gel, but also on the containment system, irrigation scheme, and servo valving system.

Smooth spline-like finite-element differentiation of full-field experimental data over arbitrary geometry

A new smooth two-dimensional numerical method is presented for representing and differentiating discrete fullfield experimental information. The method involves minimizing a positive definite functional by use of finite-elements to ‘best-fit’ the data. Experimental data points may occur in any configuration, boundary derivatives need not be specified, and arbitrarily shaped regions can be handled readily. The method is demonstrated by photomechanical strain analysis.

Theory and application of electrically controlled polymeric gels

Presents several applications of ionizable polymeric gels that are capable of undergoing substantial expansions and contractions when subjected to changing pH environments, temperature, electric field or solvent. Conceptual designs for smart, electrically activated devices exploiting this phenomenon are discussed. These devices have the possibility of being manipulated via active computer control as large-displacement actuators for use in adaptive structures. The technology enabling these novel devices is the use of compliant containers for the gels and their solvents, removing the difficulties associated with maintaining a bath for the gels. Though most of these devices are designed using properties discussed in the literature, some presented near the end of this paper make use of conclusions that the authors have drawn from the literature and their own experimental work. Those conclusions about the basic mechanisms of electromechanical gels are discussed in the third part of this paper and a complete set of governing equations describing these mechanisms is presented in the fourth section. This paper concludes with a discussion of some of the ramifications of the above system of equations and a discussion on gel-driven devices and the control of such devices.

Using Series-Series Iwan-Type Models for Understanding Joint Dynamics

In mechanical assemblies, the energy loss induced by joints and interfaces can account for a significant portion of the overall structural dissipation. This work considers the dynamical behavior of an elastic rod on a frictional foundation as a model for the dissipation introduced by micro-slip in mechanical joints. In a quasi-static loading limit, the deformation of the rod and hence the frictional dissipation can be solved in closed form. The resulting model is a continuum model of series arrangements of parallel Jenkins elements. For a general class of normal load distributions, the resulting energy loss per forcing cycle follows a power-law and is qualitatively similar to observed experimental findings. Finally, these results are compared with those obtained from a discrete formulation of the rod including inertial effects. For loading conditions that are consistent with mechanical joints, the numerical results from the discrete model are consistent with the closed form predictions obtained in the quasistatic limit.

Handbook on dynamics of jointed structures.

The problem of understanding and modeling the complicated physics underlying the action and response of the interfaces in typical structures under dynamic loading conditions has occupied researchers for many decades. This handbook presents an integrated approach to the goal of dynamic modeling of typical jointed structures, beginning with a mathematical assessment of experimental or simulation data, development of constitutive models to account for load histories to deformation, establishment of kinematic models coupling to the continuum models, and application of finite element analysis leading to dynamic structural simulation. In addition, formulations are discussed to mitigate the very short simulation time steps that appear to be required in numerical simulation for problems such as this. This handbook satisfies the commitment to DOE that Sandia will develop the technical content and write a Joints Handbook. The content will include: (1) Methods for characterizing the nonlinear stiffness and energy dissipation for typical joints used in mechanical systems and components. (2) The methodology will include practical guidance on experiments, and reduced order models that can be used to characterize joint behavior. (3) Examples for typical bolted and screw joints will be provided.

A Method for Calculating the Dynamics of Rotating Flexible Structures, Part 1: Derivation

The problem of calculating the vibrations of rotating structures has challenged analysts since it was observed that the use of traditional modal approaches may incorrectly lead to the prediction of infinite deformation when rotation rates exceed the first natural frequency. Much recently published work on beams has shown that such predictions are artifacts of incorporating incomplete kinematics into the analysis, but only simple structures such as individual beams and plates are addressed. The authors present a new approach to analyzing rotating flexible structures that applies to the rotation of general linear (unjointed) structures, using a system of nonlinearly coupled deformation modes. This technique, tentatively named a Method of Quadratic Components, utilizes a nonlinear configuration space in which all kinematic constraints are satisfied up to second order.

Suppression of regenerative chatter via impedance modulation

A new technique for the suppression of machine tool chatter in turning based on modulation of the system impedance is analyzed. The modulation frequency is selected as half the spindle frequency. Using the method of harmonic balance and a numerical root finding scheme on the transcendental characteristic equation, stability diagrams arc computed for a variety of modulation amplitudes. The stability boundaries are verified by using the Nyquist stability criterion and growth exponents computed from transient simulations of the vibratory response. It is shown in this way that the impedance modulation technique successfully scrambles the regenerative process that leads to chatter and widens the stability region (by increasing the maximum allowed cutting depth), particularly for low values of the spindle speed.