Mauricio Fernández

ACCESS e.V. · Multiscale and Data-driven Material Modeling

The Hashin-Shtrikman bounds accounting for eigenfields are represented in terms of tensorial texture coefficients for arbitrarily anisotropic materials and arbitrarily textured polycrystals. This requires a short review of the Hashin-Shtrikman bounds with eigenfields, an investigation of the polarization field determined by the stationarity conditi...

https://arxiv.org/abs/1902.07443 - A multi-fidelity surrogate model for highly nonlinear multiscale problems is proposed. It is based on the introduction of two different surrogate models and an adaptive on-the-fly switching. The two concurrent surrogates are built incrementally starting from a moderate set of evaluations of the full order model. T...

The present work aims at the identification of the effective constitutive behavior of Σ5 aluminum grain boundaries (GB) for proportional loading by using machine learning (ML) techniques. The input for the ML approach is high accuracy data gathered in challenging molecular dynamics (MD) simulations at the atomic scale for varying temperatures and l...

In the present work, two machine learning based constitutive models for finite deformations are proposed. Using input convex neural networks, the models are hyperelastic, anisotropic and fulfill the polyconvexity condition, which implies ellipticity and thus ensures material stability. The first constitutive model is based on a set of polyconvex, a...

Mechanical metamaterials such as open-and closed-cell lattice structures, foams, composites, etc. can often be parametrized in terms of their microstructural properties, e.g., relative densities, aspect ratios, material, shape or topological parameters. To model the effective constitutive behavior and facilitate efficient multiscale simulation, des...

A sequential nonlinear multiscale method for the simulation of elastic metamaterials subject to large deformations and instabilities is proposed. For the finite strain homogenization of cubic beam lattice unit cells, a stochastic perturbation approach is applied to induce buckling. Then, three variants of anisotropic effective constitutive models b...

Mechanical metamaterials such as open‐ and closed‐cell lattice structures, foams, composites, etc. can often be parametrized in terms of their microstructural properties, e.g., relative densities, aspect ratios, material, shape or topological parameters. To model the effective constitutive behavior and facilitate efficient multiscale simulation, de...

In the present work, two machine learning based constitutive models for finite deformations are proposed. Using input convex neural networks, the models are hyperelastic, anisotropic and fulfill the polyconvexity condition, which implies ellipticity and thus ensures material stability. The first constitutive model is based on a set of polyconvex, a...

A sequential nonlinear multiscale method for the simulation of elastic metamaterials subject to large deformations and instabilities is presented in this work. For the microscopic finite strain homogenization of a cubic beam lattice unit cell, a stochastic perturbation approach is applied to induce buckling. To identify the effective constitutive b...

This work investigates the capabilities of anisotropic theory-based, purely data-driven and hybrid approaches to model the homogenized constitutive behavior of cubic lattice metamaterials exhibiting large deformations and buckling phenomena. The effective material behavior is assumed as hyperelastic, anisotropic and finite deformations are consider...

Strategies for the generation of periodic discrete structures with identical two-point correlation—called 2PC-equivalent—are developed. It is shown that starting from a set of 2PC-equivalent root structures, 2PC-equivalent child structures of arbitrary resolution and number of phases (e.g. material phases) can be generated based on phase extension...

This work investigates the capabilities of anisotropic theory-based, purely data-driven and hybrid approaches to model the homogenized constitutive behavior of cubic lattice metamaterials exhibiting large deformations and buckling phenomena. The effective material behavior is assumed as hyperelastic, anisotropic and finite deformations are consider...

The Löwner partial order is taken into consideration in order to define Löwner majorants for a given finite set of symmetric matrices. A special class of Löwner majorants is analyzed based on two specific matrix parametrizations: a two-parametric form and a four-parametric form, which arise in the context of so-called zeroth-order bounds of the eff...

The present work continues the investigation first started by Lobos et al. (J. Elast. 128(1):17–60, 2017) concerning the orientation average of tensorial quantities connected to single-crystal physical quantities distributed in polycrystals. In Lobos et al. (J. Elast. 128(1):17–60, 2017), central orientation density functions were considered in the...

Strategies for the generation of periodic discrete structures with identical two-point correlation are developed. Starting from a pair of root structures, which are not related by translation, phase inversion or axis reflections, child structures of arbitrary resolution (i.e., pixel or voxel numbers) and number of phases (i.e., material phases/spec...

The present work continues the investigation first started by Lobos et al. (2017) concerning the orientation average of tensorial quantities connected to single crystal physical quantities distributed in polycrystals. In Lobos et al. (2017), central orientation density functions were considered in the orientation average for fourth-order tensors wi...

The Löwner partial order is taken into consideration in order to define Löwner majorants for a given finite set of symmetric matrices. A special class of Löwner majorants is analyzed based on two specific matrix parametrizations: a two-parametric form and a four-parametric form, which arise in the context of so-called zeroth-order bounds of the eff...

A multi-fidelity surrogate model for highly nonlinear multiscale problems is proposed. It is based on the introduction of two different surrogate models and an adaptive on-the-fly switching. The two concurrent surrogates are built incrementally starting from a moderate set of evaluations of the full order model. Therefore, a reduced order model (RO...

The present work generalizes the results of Böhlke and Lobos (Acta Mater. 67:324–334, 2014) by giving an explicit representation of the Hashin–Shtrikman (HS) bounds of linear elastic properties in terms of tensorial Fourier texture coefficients not only for cubic materials but for arbitrarily anisotropic linear elastic polycrystalline materials. Ba...

This work approaches the fields of homogenization and of materials design for the linear and nonlinear mechanical properties with prescribed properties-profile. The set of achievable properties is bounded by the zeroth-order bounds (which are material specific), the first-order bounds (containing volume fractions of the phases) and the second-order...

It is shown in the present work that for linear elastic multiphase materials the orientation average of a stiffness tensor can be given in a closed form if central model functions are taken into consideration for the description of the material orientation distribution. This holds for arbitrary numbers of material constituents and for arbitrary deg...

Zeroth-order bounds of elastic properties have been discussed by E. Kröner, Bounds for effective elastic moduli of disordered materials, J. Mech. Phys. Solids 25 (3) (1977) 137–155. and by Nadeau and Ferrari J. Nadeau, M. Ferrari, On optimal zeroth-order bounds with application to Hashin-Shtrikman bounds and anisotropy parameters, Int. J. Solids St...

For a chosen combination of materials for a multiphase polycrystalline composite, a crystallite orientation distribution function for each phase is formulated as a superposition of analytic central model von Mises-Fisher functions. The chosen central model functions allow the analytic integration of orientation averages of arbitrarily anisotropic f...

For polycrystals made of cubic materials like copper, aluminum, iron and other metals and ceramics, the macroscopic elastic behavior can be bounded using minimum energy principles. Böhlke and Lobos (Acta Mater. 67:324–334, 2014) have shown that not only the Voigt and the Reuss bound but also the Hashin–Shtrikman bounds can be represented explicitly...

For crystal aggregates, the orientation distribution of single crystals affects the anisotropic linear elastic properties. In the singular approximation for cubic materials, this influence is reflected by a fourth-order texture coefficient. From this approximation, the statistical bounds of Voigt, Reuss and Hashin-Shtrikman, and an isotropically se...

The possibility of using an additional sequentially connected friction spring element in order to reduce vibration amplitudes both for the self-excited oscillations and for the forced vibrations is discussed in the paper. The analysis is based on the averaging technique for systems with “slave variables” and demonstrates two main effects: damping d...

The Hashin–Shtrikman bounds of aggregates of cubic crystals are explicitly represented in terms of tensorial texture coefficients. The formula is valid for arbitrary crystallographic textures and isotropic two-point statistics. The isotropy of the two-point statistics implies that the grain shape is isotropic on average. The new explicit representa...