arXiv subjects

Ricardo A. Lebensohn

Publications and source records attributed to Ricardo A. Lebensohn.

5 recordsLinked to original sources

arXiv2025

Microstructure-based Variational Neural Networks for Robust Uncertainty Quantification in Materials Digital Twins

Aleatoric uncertainties - irremovable variability in microstructure morphology, constituent behavior, and processing conditions - pose a major challenge to developing uncertainty-robust digital twins. We introduce the Variational Deep Material Network (VDMN), a physics-informed surrogate model that enables efficient and probabilistic forward and inverse predictions of material behavior. The VDMN captures microstructure-induced variability by embedding variational distributions within its hierarchical, mechanistic architecture. Using an analytic propagation scheme based on Taylor-series expansion and automatic differentiation, the VDMN efficiently propagates uncertainty through the network during training and prediction. We demonstrate its capabilities in two digital-twin-driven applications: (1) as an uncertainty-aware materials digital twin, it predicts and experimentally validates the nonlinear mechanical variability in additively manufactured polymer composites; and (2) as an inverse calibration engine, it disentangles and quantitatively identifies overlapping sources of uncertainty in constituent properties. Together, these results establish the VDMN as a foundation for uncertainty-robust materials digital twins.

cs.LG↗

arXiv2025

Micropolar elastoplasticity using a fast Fourier transform-based solver

This work presents a micromechanical spectral formulation for obtaining the full-field and homogenized response of elastoplastic micropolar composites. A closed-form radial-return mapping is derived from thermodynamics-based micropolar elastoplastic constitutive equations to determine the increment of plastic strain necessary to return the generalized stress state to the yield surface, and the algorithm implementation is verified using the method of numerically manufactured solutions. Then, size-dependent material response and micro-plasticity are shown as features that may be efficiently simulated in this micropolar elastoplastic framework. The computational efficiency of the formulation enables the generation of large datasets in reasonable computing times.

cs.CE↗

arXiv2021

Imposing equilibrium on measured 3-D stress fields using Hodge decomposition and FFT-based optimization

We present a methodology to impose micromechanical constraints, i.e. stress equilibrium at grain and sub-grain scale, to an arbitrary (non-equilibrated) voxelized stress field obtained, for example, by means of synchrotron X-ray diffraction techniques. The method consists in finding the equilibrated stress field closest (in $L^2$-norm sense) to the measured non-equilibrated stress field, via the solution of an optimization problem. The extraction of the divergence-free (equilibrated) part of a general (non-equilibrated) field is performed using the Hodge decomposition of a symmetric matrix field, which is the generalization of the Helmholtz decomposition of a vector field into the sum of an irrotational field and a solenoidal field. The combination of: a) the Euler-Lagrange equations that solve the optimization problem, and b) the Hodge decomposition, gives a differential expression that contains the bi-harmonic operator and two times the curl operator acting on the measured stress field. These high-order derivatives can be efficiently performed in Fourier space. The method is applied to filter the non-equilibrated parts of a synthetic piecewise constant stress fields with a known ground truth, and stress fields in Gum Metal, a beta-Ti-based alloy measured in-situ using Diffraction Contrast Tomography (DCT). In both cases, the largest corrections were obtained near grain boundaries.

cond-mat.mtrl-sci↗

arXiv2020

Dislocation interactions in olivine control postseismic creep of the upper mantle

Changes in stress applied to mantle rocks, such as those imposed by earthquakes, induce a period of evolution in viscosity and microstructure. This transient creep is often modelled based on stress transfer among slip systems due to grain interactions. However, recent experiments have demonstrated that the intragranular accumulation of stresses among dislocations is the dominant cause of strain hardening in olivine at low temperatures, raising the question of whether the same process contributes to transient creep at higher temperatures. Here, we demonstrate that olivine samples deformed at 25°C or 1150 to 1250°C both contain stress heterogeneities of ~1 GPa that are imparted by dislocations and have correlation lengths of ~1 micrometre. The similar stress distributions formed in both temperature regimes indicate that accumulation of stresses among dislocations also provides a contribution to transient creep at high temperatures. The results motivate a new generation of models that capture these intragranular processes and may refine predictions of evolving mantle viscosity over the earthquake cycle.

cond-mat.mtrl-sci↗

arXiv2014

Combined effects of anisotropy and tension-compression asymmetry on the torsional response of AZ31 Mg

In this paper it is demonstrated that only by accounting for the combined effects of anisotropy and tension-compression asymmetry both at single crystal and polycrystal levels, it is possible to explain and accurately predict the peculiarities of the room-temperature torsional response of a strongly textured AZ31 Mg material. This is shown by using two modeling frameworks, namely: the viscoplastic self-consistent (VPSC) polycrystal model that accounts for tension-compression asymmetry of the mechanical response of a polycrystalline aggregate due to the occurrence of twinning at single crystal level, and an anisotropic plasticity model based on an orthotropic yield criterion that accounts for tension-compression asymmetry in plastic flow at macroscopic level, developed by Cazacu et al. (2006). It is shown that unlike Hill's (1948), the latter macroscopic criterion quantitatively predicts the experimental results, namely: that the sample with axial direction along the rolling direction contracts, while the sample with axial direction along the normal direction elongates. Moreover, it is demonstrated that these experimentally observed axial effects in torsion can be also quantitatively predicted with the VPSC polycrystal model only if both slip and twinning are considered active at single crystal level. On the other hand, if it is assumed that the plastic deformation is fully accommodated by crystallographic slip, the predicted axial strains are very close with that obtained with Hill (1948) criterion, which largely underestimate the measured axial strains.

cond-mat.mtrl-sci↗