Inverse problems arise in a wide range of applications, whenever unknown model parameters cannot be measured directly. Instead, the unknown parameters are estimated using experimental data and forward simulations. Thermal inverse problems, such as material characterization problems, are often large-scale and transient. Therefore, they require intrusive adjoint-based gradient implementations in order to be solved efficiently. The capability to solve large-scale transient thermal inverse problems using an adjoint-based approach was recently implemented in SNL Sierra Mechanics, a massively parallel capable multiphysics code suite. This report outlines the theory, optimization formulation, and path taken to implement thermal inverse capabilities in Sierra within a unit test framework. The capability utilizes Sierra/Aria and Sierra/Fuego data structures, the Rapid Optimization Library, and an interface to the Sierra/InverseOpt library. The existing Sierra/Aria time integrator is leveraged to implement a time-dependent adjoint solver.
Residual stress is a common result of manufacturing processes, but it is one that is often overlooked in design and qualification activities. There are many reasons for this oversight, such as lack of observable indicators and difficulty in measurement. Traditional relaxation-based measurement methods use some type of material removal to cause surface displacements, which can then be used to solve for the residual stresses relieved by the removal. While widely used, these methods may offer only individual stress components or may be limited by part or cut geometry requirements. Diffraction-based methods, such as X-ray or neutron, offer non-destructive results but require access to a radiation source. With the goal of producing a more flexible solution, this LDRD developed a generalized residual stress inversion technique that can recover residual stresses released by all traction components on a cut surface, with much greater freedom in part geometry and cut location. The developed method has been successfully demonstrated on both synthetic and experimental data. The project also investigated dislocation density quantification using nonlinear ultrasound, residual stress measurement using Electronic Speckle Pattern Interferometry Hole Drilling, and validation of residual stress predictions in Additive Manufacturing process models.
The concept of total-internal-reflection elastic metasurface (TIR-MS)was recently proposed [1]and employed within flexible planar waveguides in order to create highly subwavelength sound-hard barriers impenetrable to low frequency elastic waves. The underlying physical mechanism relies on the design of engineered interfaces exhibiting extreme phase gradients such that any incoming wave at, approximately, any incidence will experience total-internal-reflection conditions. At the design frequency, the metasurface exhibits a large phase gradient such that, in accordance with the generalized Snell's law, the first critical angle is virtually always exceeded. It is worth noting that in practical realizations, the actual total reflection performance might vary depending on the angle of incidence. This dependence is due to the discrete implementation of the metasurface which results in diffraction effects. This paper presents the results of an experimental study that explores the vibration isolation performance of TIR-MS when applied to structures made of complex combinations of different elastic waveguides (e.g. bolted assemblies of beams, plates, and shells). Such system can be seen as a prototypical structure emulating mechanical assemblies of practical interest for many engineering applications. Experimental results confirm that, when the TIR-MS is embedded in the host waveguide, significant vibration isolation capabilities are achieved under quasi-omnidirectional incidence and highly subwavelength excitation conditions (i.e. the ratio of the operating wavelength to the width of the TIR-MS is approximately 5.25). These experimental results suggest new interesting directions to achieve vibration isolation and mechanical energy filtering for practical engineering systems.
The integrity of engineering structures is often compromised by embedded surfaces that result from incomplete bonding during the manufacturing process, or initiation of damage from fatigue or impact processes. Examples include delaminations in composite materials, incomplete weld bonds when joining two components, and internal crack planes that may form when a structure is damaged. In many cases the areas of the structure in question may not be easily accessible, thus precluding the direct assessment of structural integrity. In this paper, we present a gradient-based, partial differential equation (PDE)-constrained optimization approach for solving the inverse problem of interface detection in the context of steady-state dynamics. An objective function is defined that represents the difference between the model predictions of structural response at a set of spatial locations, and the experimentally measured responses. One of the contributions of our work is a novel representation of the design variables using a density field that takes values in the range [0,1]andraised and raised to an integer exponent that promotes solutions to be near the extrema of the range. The density field is combined with the penalty method for enforcing a zero gap condition and realizing partially bonded surfaces. The use of the penalty method with a density field representation leads to objective functions that are continuously differentiable with respect to the unknown parameters, enabling the use of efficient gradient-based optimization algorithms. Numerical examples of delaminated plates are presented to demonstrate the feasibility of the approach.
In computational structural dynamics problems, the ability to calibrate numerical models to physical test data often depends on determining the correct constraints within a structure with mechanical interfaces. These interfaces are defined as the locations within a built-up assembly where two or more disjointed structures are connected. In reality, the normal and tangential forces arising from friction and contact, respectively, are the only means of transferring loads between structures. In linear structural dynamics, a typical modeling approach is to linearize the interface using springs and dampers to connect the disjoint structures, then tune the coefficients to obtain sufficient accuracy between numerically predicted and experimentally measured results. This work explores the use of a numerical inverse method to predict the area of the contact patch located within a bolted interface by defining multi-point constraints. The presented model updating procedure assigns contact definitions (fully stuck, slipping, or no contact) in a finite element model of a jointed structure as a function of contact pressure computed from a nonlinear static analysis. The contact definitions are adjusted until the computed modes agree with experimental test data. The methodology is demonstrated on a C-shape beam system with two bolted interfaces, and the calibrated model predicts modal frequencies with <3% total error summed across the first six elastic modes.
Differences in impedance are usually observed when components are tested in fixtures at lower levels of assembly from those in which they are fielded. In this work, the Kansas City National Security Campus (KCNSC) test bed hardware geometry is used to explore the sensitivity of the form of the objective function on the adequate reproduction of relevant response characteristics at the next level of assembly. Inverse methods within Sandia National Laboratories’ Sierra/SD code suite along with the Rapid Optimization Library (ROL) are used for identifying an unknown material (variable shear and bulk modulus) distributed across a predefined fixture volume. Comparisons of the results between time-domain based objective functions are presented. The development of the objective functions, solution sensitivity, and solution convergence will be discussed in the context of the practical considerations required for creating a realizable set of test hardware based on the variable-modulus optimized solutions.
This letter presents the concept of the Total Internal Reflection metasurface (TIR-MS) which supports the realization of structure-embedded subwavelength acoustic shields for elastic waves propagating in thin waveguides. The proposed metasurface design exploits extreme phase gradients, implemented via locally resonant elements, in order to achieve operating conditions that are largely beyond the critical angle. Such artificial discontinuity is capable of producing complete reflection of the incoming waves regardless of the specific angle of incidence. From a practical perspective, the TIR-MS behaves as a sound hard barrier that is impenetrable to long-wavelength modes at a selected frequency. The TIR metasurface concept is first conceived for a flat interface embedded in a rectangular waveguide and designed to block longitudinal S0-type guided modes. Then, it is extended to circular plates in order to show how enclosed areas can be effectively shielded by incoming waves. Given the same underlying physics, an equivalent dynamic behavior was also numerically and experimentally illustrated for flexural A0-type guided modes. This study shows numerical and experimental evidence that, when the metasurface is excited at the target frequency, significant vibration isolation can be achieved in the presence of waves having any arbitrary angle of incidence. These results open interesting paths to achieve vibration isolation and energy filtering in certain prototypical structures of interest for practical engineering applications.
Exterior acoustic problems occur in a wide range of applications, making the finite element analysis of such problems a common practice in the engineering community. Various methods for truncating infinite exterior domains have been developed, including absorbing boundary conditions, infinite elements, and more recently, perfectly matched layers (PML). PML are gaining popularity due to their generality, ease of implementation, and effectiveness as an absorbing boundary condition. PML formulations have been developed in Cartesian, cylindrical, and spherical geometries, but not ellipsoidal. In addition, the parallel solution of PML formulations with iterative solvers for the solution of the Helmholtz equation, and how this compares with more traditional strategies such as infinite elements, has not been adequately investigated. In this paper, we present a parallel, ellipsoidal PML formulation for acoustic Helmholtz problems. To faciliate the meshing process, the ellipsoidal PML layer is generated with an on-the-fly mesh extrusion. Though the complex stretching is defined along ellipsoidal contours, we modify the Jacobian to include an additional mapping back to Cartesian coordinates in the weak formulation of the finite element equations. This allows the equations to be solved in Cartesian coordinates, which is more compatible with existing finite element software, but without the necessity of dealing with corners in the PML formulation. Herein we also compare the conditioning and performance of the PML Helmholtz problem with infinite element approach that is based on high order basis functions. On a set of representative exterior acoustic examples, we show that high order infinite element basis functions lead to an increasing number of Helmholtz solver iterations, whereas for PML the number of iterations remains constant for the same level of accuracy. This provides an additional advantage of PML over the infinite element approach.
This letter demonstrates the design of continuously graded elastic cylinders to achieve passive cloaking from harmonic acoustic excitation, both at single frequencies and over extended bandwidths. The constitutive parameters in a multilayered, constant-density cylinder are selected in a partial differential equation-constrained optimization problem, such that the residual between the pressure field from an unobstructed spreading wave in a fluid and the pressure field produced by the cylindrical inclusion is minimized. The radial variation in bulk modulus appears fundamental to the cloaking behavior, while the shear modulus distribution plays a secondary role. Such structures could be realized with functionally-graded elastic materials.
Simulation of the response of a system to an acoustic environment is desirable in the assessment of aerospace structures in flight-like environments. In simulating a laboratory acoustic test a large challenge is modeling the as-tested acoustic field. Acoustic source inversion capabilities in Sandia’s Sierra/SD structural dynamics code have allowed for the determination of an acoustic field based on measured microphone responses—given measured pressures, source inversion optimization algorithms determine the input parameters of a set of acoustic sources defined in an acoustic finite element model. Inherently, the resulting acoustic field is dependent on the target microphone data. If there are insufficient target points, then the as-tested field may not be recreated properly. Here, the question of number of microphones is studied using synthetic data, that is, target data taken from a previous simulation which allows for comparison of the full pressure field—an important benefit not available with test data. By exploring a range of target points distributed throughout the domain, a rate of convergence to the true field can be observed. Results will be compared with the goal of developing guidelines for the number of sensors required to aid in the design of future laboratory acoustic tests to be used for model assessment.
In this report we formulate eigenvalue-based methods for model calibration using a PDE-constrained optimization framework. We derive the abstract optimization operators from first principles and implement these methods using Sierra-SD and the Rapid Optimization Library (ROL). To demon- strate this approach, we use experimental measurements and an inverse solution to compute the joint and elastic foam properties of a low-fidelity unit (LFU) model.
In this report we derive frequency-domain methods for inverse characterization of the constitutive parameters of viscoelastic materials. The inverse problem is cast in a PDE-constrained optimization framework with efficient computation of gradients and Hessian vector products through matrix free operations. The abstract optimization operators for first and second derivatives are derived from first principles. Various methods from the Rapid Optimization Library (ROL) are tested on the viscoelastic inversion problem. The methods described herein are applied to compute the viscoelastic bulk and shear moduli of a foam block model, which was recently used in experimental testing for viscoelastic property characterization.