arXiv subjects

Davi Colli Tozoni

Publications and source records attributed to Davi Colli Tozoni.

3 recordsLinked to original sources

arXiv2024

Differentiable solver for time-dependent deformation problems with contact

We introduce a general differentiable solver for time-dependent deformation problems with contact and friction. Our approach uses a finite element discretization with a high-order time integrator coupled with the recently proposed incremental potential contact method for handling contact and friction forces to solve ODE- and PDE-constrained optimization problems on scenes with complex geometry. It supports static and dynamic problems and differentiation with respect to all physical parameters involved in the physical problem description, which include shape, material parameters, friction parameters, and initial conditions. Our analytically derived adjoint formulation is efficient, with a small overhead (typically less than 10% for nonlinear problems) over the forward simulation, and shares many similarities with the forward problem, allowing the reuse of large parts of existing forward simulator code. We implement our approach on top of the open-source PolyFEM library and demonstrate the applicability of our solver to shape design, initial condition optimization, and material estimation on both simulated results and physical validations.

cs.GR↗

arXiv2023

Cut-Cell Microstructures for Two-scale Structural Optimization

Two-scale topology optimization, combined with the design of microstructure families with a broad range of effective material parameters, is increasingly widely used in many fabrication applications to achieve a target deformation behavior for a variety of objects. The main idea of this approach is to optimize the distribution of material properties in the object partitioned into relatively coarse cells, and then replace each cell with microstructure geometry that mimics these material properties. In this paper, we focus on adapting this approach to complex shapes in situations when preserving the shape's surface is important. Our approach extends any regular (i.e. defined on a regular lattice grid) microstructure family to complex shapes, by enriching it with individually optimized cut-cell tiles adapted to the geometry of the cut-cell. We propose an automated and robust pipeline based on this approach, and we show that the performance of the regular microstructure family is only minimally affected by our extension while allowing its use on 2D and 3D shapes of high complexity.

cs.GR↗

arXiv2019

A parameteric class of composites with a large achievable range of effective elastic properties

In this paper we investigate numerically an instance of the problem of G-closure for two-dimensional periodic metamaterials. Specifically, we consider composites with isotropic homogenized elasticity tensor, obtained as a mixture of two isotropic materials, focusing on the case of a single material with voids. This problem is important, in particular, in the context of designing small-scale structures for metamaterials in the context of additive fabrication, as this type of metamaterials makes it possible to obtain a range of material properties using a single base material. We demonstrate that two closely related simple parametric families based on the structure proposed by O. Sigmund attain good coverage of the space of isotropic properties satisfying Hashin-Shtrikman bounds. In particular, for positive Poisson ratio, we demonstrate that Hashin-Shtrikman bound can be approximated arbitrarily well, within limits imposed by numerical approximation: a strong evidence that these bounds are achievable in this case. For negative Poisson ratios, we numerically obtain a bound which we hypothesize to be close to optimal, at least for metamaterials with rotational symmetries of a regular triangle tiling.

physics.comp-ph↗