An optimization method for stochastic reconstruction from empirical data - A limestone rock strain fields study-case using digital image correlation data.

Stochastic field reconstruction is a crucial technique to improve the accuracy of modern rock simulation. It allows explicit modelling of field conditions, often employed in uncertainty quantification analysis and upsampling and upscaling procedures. This paper presents a case-study of a framework for the stochastic reconstruction of rock's strain field using experimental data. The proposed framework is applied to a limestone outcrop in which the strain field is measured using Digital Image Correlation (DIC). Assuming that the strain fields of these rocks are well-represented by Gaussian random fields, we capitalize on the algorithms used for training Gaussian processes to estimate the correlation family and the parameters that best represent these fields. Although the spherical and exponential kernels often correspond to the best fit, our results depict that each field shall be analyzed separately and no general rule can be defined. We show that the method is versatile and can be employed in any measurable field reasonably represented by a Gaussian random field. Therefore, the present work aims to highlight the following topics:•A study-case of stochastic strain field reconstruction aims to contribute to uncertainty quantification of rock experimental procedures.•A stochastic minimization algorithm is presented to solve the maximum likelihood estimation to define the most suitable hyper-parameter: correlation length.•The calculated hyper-parameters of a set correlation functions are presented to best reproduce the strain fields of a rock sample.

Publisher Correction: Non-cuttable material created through local resonance and strain rate effects.

An amendment to this paper has been published and can be accessed via a link at the top of the paper.

Non-cuttable material created through local resonance and strain rate effects.

We have created a new architected material, which is both highly deformable and ultra-resistant to dynamic point loads. The bio-inspired metallic cellular structure (with an internal grid of large ceramic segments) is non-cuttable by an angle grinder and a power drill, and it has only 15% steel density. Our architecture derives its extreme hardness from the local resonance between the embedded ceramics in a flexible cellular matrix and the attacking tool, which produces high-frequency vibrations at the interface. The incomplete consolidation of the ceramic grains during the manufacturing also promoted fragmentation of the ceramic spheres into micron-size particulate matter, which provided an abrasive interface with increasing resistance at higher loading rates. The contrast between the ceramic segments and cellular material was also effective against a waterjet cutter because the convex geometry of the ceramic spheres widened the waterjet and reduced its velocity by two orders of magnitude. Shifting the design paradigm from static resistance to dynamic interactions between the material phases and the applied load could inspire novel, metamorphic materials with pre-programmed mechanisms across different length scales.

Damping of selectively bonded 3D woven lattice materials.

The objective of this paper is to unveil a novel damping mechanism exhibited by 3D woven lattice materials (3DW), with emphasis on response to high-frequency excitations. Conventional bulk damping materials, such as rubber, exhibit relatively low stiffness, while stiff metals and ceramics typically have negligible damping. Here we demonstrate that high damping and structural stiffness can be simultaneously achieved in 3D woven lattice materials by brazing only select lattice joints, resulting in a load-bearing lattice frame intertwined with free, 'floating' lattice members to generate damping. The produced material samples are comparable to polymers in terms of damping coefficient, but are porous and have much higher maximum use temperature. We shed light on a novel damping mechanism enabled by an interplay between the forcing frequency imposed onto a load-bearing lattice frame and the motion of the embedded, free-moving lattice members. This novel class of damping metamaterials has potential use in a broad range of weight sensitive applications that require vibration attenuation at high frequencies.