Research

Research Interests

Computational modeling and advanced numerical methods for engineering and applied sciences. Our work is carried out within the MoCCAI group (Modelado Computacional en Ciencias Aplicadas e Ingeniería), ICAI (CONICET-UNCUYO) and FCAI-UNCUYO, San Rafael, Argentina, on modular in-house C++/OpenMP software built over open-source environments.

• High-order phase-field modeling of fracture mechanics in thin shells
  Nucleation and propagation of cracks in brittle thin shells undergoing large deformations. The line evolved from second-order phase-field models for thin shells, to fourth-order formulations discretized with maximum-entropy approximants, and to variational models coupling fracture and buckling in brittle sheets. Current work extends these models to slightly anisotropic, prestressed biological materials such as the arterial wall. 

• Fluid-structure interaction and phase-field fracture in thin shells: rupture of cerebral aneurysms
  Hemodynamic loads are computed by CFD on patient-specific geometries (AneuriskWeb) in OpenFOAM and coupled through preCICE to an in-house Kirchhoff-Love thin-shell solver with variable thickness and nearly incompressible hyperelasticity, whose integrity is described by a fourth-order phase field. Initial studies addressed mesh convergence with boundary-layer refinement on real aneurysm segments, and Newtonian versus non-Newtonian blood models.
  Ongoing work: physiological prestress estimation (MULF), bidirectional FSI under natural conditions and localized microcatheter loading, and critical WSS regions as precursors of wall degradation.
  Next step: physics-informed surrogate models (PINN) to predict hemodynamics in new patients without full CFD.

• Cerebral aneurysm morphometry, biomechanical descriptors and data-driven rupture risk assessment
  Shape descriptors of intracranial aneurysms based on 3-D geometric and Zernike moment invariants, computed on closed triangle meshes through the divergence theorem. Probabilistic rupture-risk indicators built by statistical and machine learning on morphological, hemodynamic and biomechanical descriptors. Automatic isolation of the region of interest in arterial-tree models for population studies, implemented in AneuSI, an open-source C++ library (VTK, ITK, CGAL). Biomechanical analysis of variable-thickness aneurysm walls under microcatheter contact, with sensitive regions identified by dimensionality reduction and unsupervised clustering.
  Code: https://github.com/grupomoccai/AneuSI

• Micromechanical modeling of elastic wave propagation for cryo-ultrasonic inspection of additively manufactured parts
  Elastic wave propagation in heterogeneous media, aimed at non-destructive cryo-ultrasonic testing of parts built by additive manufacturing. Temperature-dependent micromechanical homogenization of ice with nanoparticles, including the interfacial premelting layer. In collaboration with Pennsylvania State University. 

• Advanced discretization: maximum-entropy approximants and subdivision surfaces
  Smooth discretizations for fourth-order PDEs and interface problems: local maximum-entropy approximants and Loop subdivision surfaces, used throughout the thin-shell, phase-field and FSI solvers of the group.

Previous topics

• Nonlinear dimensionality reduction for manifold processing
  Calculations on smooth manifolds of small dimension d sampled by scattered points in a high-dimensional space. The point set is partitioned into subregions of trivial topology; the local geometric structure is revealed by nonlinear dimensionality reduction; each region is parametrized with smooth meshfree (local maximum-entropy) approximants; and the local descriptions are patched together by a partition of unity. No global parametrization is needed, so the approach applies to manifolds of any genus.

• Maximum entropy approximants [Marino Arroyo, LME beta-Matlab code, CME-Matlab code]
  Local maximum-entropy (LME) approximants with spatially varying locality parameter, and cell-based maximum-entropy (CME) approximants, with Matlab implementations. 

• Meshfree thin-shell analysis
  Kirchhoff-Love thin-shell analysis directly from scattered points, using maximum-entropy approximants and, for complex geometries, local parametrizations obtained by manifold learning.

• Quantitative analysis of the Euglenoid movement [Movie 1 Movie 2]
  Kinematic reconstruction and mechanical interpretation of the shape changes of euglenids from video microscopy.

• Automatic identification of collective variables in biomolecules
  Smooth, nonlinear and data-driven collective variables for the modeling and enhanced sampling of molecular conformations.

• Nonlinear model reduction for finite solid dynamics
  Reduced-order models for finite-deformation elastodynamics built on the nonlinear low-dimensional manifold, identified by manifold learning, on which the dynamics evolves.

• Computational modeling of flexoelectricity in dielectric solids
  Flexoelectricity couples electric polarization to strain gradients, so it becomes significant at small scales and in non-uniform deformation fields. Its continuum model leads to fourth-order PDEs, solved here with smooth meshfree (local maximum-entropy) approximants. The work quantified the flexoelectric response of dielectric solids and its size effects, revisited the pyramid-compression experiments used to measure flexoelectric coefficients through three-dimensional simulations, and showed that flexoelectricity induces fracture toughening and a toughness asymmetry. In collaboration with LaCàN, UPC-BarcelonaTech.

Point-set manifold processing for computational mechanics

In many applications, one would like to perform calculations on smooth manifolds of small dimension d embedded in a high-dimensional space of dimension D. Often, a continuous description of such manifold is not known, and instead it is sampled by a set of scattered points in high dimensions. This poses a serious challenge. We approximate the point-set manifold as an overlapping set of smooth parametric descriptions, whose geometric structure is revealed by statistical learning methods, and then parametrized by meshfree methods. This approach avoids any global parameterization, and hence is applicable to manifolds of any genus and complex geometry. It combines four ingredients:

1. partitioning of the point set into subregions of trivial topology,

2. the automatic detection of the local geometric structure of the manifold by nonlinear dimensionality reduction techniques,

3. the local parameterization of the manifold using smooth meshfree (here local maximum-entropy) approximants, and

4. patching together the local representations by means of a partition of unity.

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