Polycrystalline materials consist of grains (crystals) oriented at different angles resulting in a heterogeneous and anisotropic mechanical behavior at that micro-length scale. In this study, a novel method is proposed for the first time to determine the [Formula: see text] crystal orientations of grains in a [Formula: see text] domain, using solely [Formula: see text] deformation fields. The grain boundaries are assumed to be unknown and delineated from the reconstructed changes in the crystallographic orientation. Further, the constitutive equations that describe the mechanical behavior of the domain in [Formula: see text] under plane stress conditions are derived, assuming that the material is transversely isotropic in 3D. Finite element based algorithms are utilized to discretize the inverse problem. The in-house written inverse problem solver is coupled with Matlab-based optimization scripts to solve for the mechanical property distributions. The performance of this method is tested at different noise levels with synthetic displacements that were used as measured data. The reconstructions deteriorate as the noise level is increased. This work presents a first milestone in the verification of this novel technology with synthetic data.
more »
« less
General Finite-Element Framework of the Virtual Fields Method in Nonlinear Elasticity
Abstract This paper presents a method to derive the virtual fields for identifying constitutive model parameters using the Virtual Fields Method (VFM). The VFM is an approach to identify unknown constitutive parameters using deformation fields measured across a given volume of interest. The general principle for solving identification problems with the VFM is first to derive parametric stress field, where the stress components at any point depend on the unknown constitutive parameters, across the volume of interest from the measured deformation fields. Applying the principle of virtual work to the parametric stress fields, one can write scalar equations of the unknown parameters and solve the obtained system of equations to deduce the values of unknown parameters. However, no rules have been proposed to select the virtual fields in identification problems related to nonlinear elasticity and there are multiple strategies possible that can yield different results. In this work, we propose a systematic, robust and automatic approach to reconstruct the systems of scalar equations with the VFM. This approach is well suited to finite-element implementation and can be applied to any problem provided that full-field deformation data are available across a volume of interest. We also successfully demonstrate the feasibility of the novel approach by multiple numerical examples. Potential applications of the proposed approach are numerous in biomedical engineering where imaging techniques are commonly used to observe soft tissues and where alterations of material properties are markers of diseased states.
more »
« less
- Award ID(s):
- 1727104
- NSF-PAR ID:
- 10310601
- Date Published:
- Journal Name:
- Journal of Elasticity
- Volume:
- 145
- Issue:
- 1-2
- ISSN:
- 0374-3535
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
more » « less
Abstract This paper explores the use of autonomous underwater vehicles (AUVs) equipped with sensors to construct water quality models to aid in the assessment of important environmental hazards, for instance related to point‐source pollutants or localized hypoxic regions. Our focus is on problems requiring the autonomous discovery and dense sampling of critical areas of interest in real‐time, for which standard (e.g., grid‐based) strategies are not practical due to AUV power and computing constraints that limit mission duration. To this end, we consider adaptive sampling strategies on Gaussian process (GP) stochastic models of the measured scalar field to focus sampling on the most promising and informative regions. Specifically, this study employs the GP upper confidence bound as the optimization criteria to adaptively plan sampling paths that balance a trade‐off between exploration and exploitation. Two informative path planning algorithms based on (i) branch‐and‐bound techniques and (ii) cross‐entropy optimization are presented for choosing future sampling locations while considering the motion constraints of the sampling platform. The effectiveness of the proposed methods are explored in simulated scalar fields for identifying multiple regions of interest within a three‐dimensional environment. Field experiments with an AUV using both virtual measurements on a known scalar field and in situ dissolved oxygen measurements for studying hypoxic zones validate the approach's capability to quickly explore the given area, and then subsequently increase the sampling density around regions of interest without sacrificing model fidelity of the full sampling area.
-
Blasch, Erik ; Ravela, Sai (Ed.)A coupled path-planning and sensor configuration method is proposed. The path-planning objective is to minimize exposure to an unknown, spatially-varying, and temporally static scalar field called the threat field. The threat field is modeled as a weighted sum of several scalar fields, each representing a mode of threat. A heterogeneous sensor network takes noisy measurements of the threat field. Each sensor in the network observes one or more threat modes within a circular field of view (FoV). The sensors are configurable, i.e., parameters such as location and size of field of view can be changed. The measurement noise is assumed to be normally distributed with zero mean and a variance that monotonically increases with the size of the FoV, emulating the FoV v/s resolution trade-off in most sensors. Gaussian Process regression is used to estimate the threat field from these measurements. The main innovation of this work is that sensor configuration is performed by maximizing a so-called task-driven information gain (TDIG) metric, which quantifies uncertainty reduction in the cost of the planned path. Because the TDIG does not have any convenient structural properties, a surrogate function called the self-adaptive mutual information (SAMI) is considered. Sensor configuration based on the TDIG or SAMI introduces coupling with path-planning in accordance with the dynamic data-driven application systems paradigm. The benefit of this approach is that near-optimal plans are found with a relatively small number of measurements. In comparison to decoupled path-planning and sensor configuration based on traditional information-driven metrics, the proposed CSCP method results in near-optimal plans with fewer measurements.more » « less
-
more » « less
Abstract Estimating soil properties from the mechanical reaction to a displacement is a common strategy, used not only in in situ soil characterization (e.g., pressuremeter and dilatometer tests) but also by biological organisms (e.g., roots, earthworms, razor clams), which sense stresses to explore the subsurface. Still, the absence of analytical solutions to predict the stress and deformation fields around cavities subject to geostatic stress, has prevented the development of characterization methods that resemble the strategies adopted by nature. We use the finite element method (FEM) to model the displacement-controlled expansion of cavities under a wide range of stress conditions and soil properties. The radial stress distribution at the cavity wall during expansion is extracted. Then, methods are proposed to prepare, transform and use such stress distributions to back-calculate the far field stresses and the mechanical parameters of the material around the cavity (Mohr-Coulomb friction angle
$$\phi $$ E ). Results show that: (i) The initial stress distribution around the cavity can be fitted to a sum of cosines to estimate the far field stresses; (ii) By encoding the stress distribution as intensity images, in addition to certain scalar parameters, convolutional neural networks can consistently and accurately back-calculate the friction angle and Young’s modulus of the soil. -
Granular flows occur in a wide range of situations of practical interest to industry, in our natural environment and in our everyday lives. This paper focuses on granular flow in the so-called inertial regime, when the rheology is independent of the very large particle stiffness. Such flows have been modelled with the $\unicode[STIX]{x1D707}(I),\unicode[STIX]{x1D6F7}(I)$ -rheology, which postulates that the bulk friction coefficient $\unicode[STIX]{x1D707}$ (i.e. the ratio of the shear stress to the pressure) and the solids volume fraction $\unicode[STIX]{x1D719}$ are functions of the inertial number $I$ only. Although the $\unicode[STIX]{x1D707}(I),\unicode[STIX]{x1D6F7}(I)$ -rheology has been validated in steady state against both experiments and discrete particle simulations in several different geometries, it has recently been shown that this theory is mathematically ill-posed in time-dependent problems. As a direct result, computations using this rheology may blow up exponentially, with a growth rate that tends to infinity as the discretization length tends to zero, as explicitly demonstrated in this paper for the first time. Such catastrophic instability due to ill-posedness is a common issue when developing new mathematical models and implies that either some important physics is missing or the model has not been properly formulated. In this paper an alternative to the $\unicode[STIX]{x1D707}(I),\unicode[STIX]{x1D6F7}(I)$ -rheology that does not suffer from such defects is proposed. In the framework of compressible $I$ -dependent rheology (CIDR), new constitutive laws for the inertial regime are introduced; these match the well-established $\unicode[STIX]{x1D707}(I)$ and $\unicode[STIX]{x1D6F7}(I)$ relations in the steady-state limit and at the same time are well-posed for all deformations and all packing densities. Time-dependent numerical solutions of the resultant equations are performed to demonstrate that the new inertial CIDR model leads to numerical convergence towards physically realistic solutions that are supported by discrete element method simulations.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/s10659-021-09842-8
