Search

We introduce a novel method called the successive node snapping (SNS) scheme to construct conforming meshes for an evolving curve in 2D and 3D, with a given simplicial background mesh. In the procedure, only a small fraction of nodes of the background mesh are moved and the nodal connectivities remain unaltered. The core of the method is to snap chosen nodes to the evolving curve and to simultaneously relax nodes within the vicinity of the curve. Following the curve, we adjust each portion of the curve's neighborhood successively to obtain a mesh conforming to the entire curve. The curve and the background mesh are under very mild geometric requirements: The curve can be open or closed, and the background mesh can have obtuse-angled triangles or tetrahedra as well as acute-angled ones. With no a priori conformity requirements, the same background mesh can be utilized for a series of snapshots of the evolving curve, permitting tractable variable remapping. Since all the operations on the mesh are local, the method is especially suitable for evolving curve problems where the curve only updates a small portion each time, for example, crack propagation in 2D and dislocation dynamics in 3D.

Cellular mechanical metamaterials are a special class of materials whose mechanical properties are primarily determined by their geometry. However, capturing the nonlinear mechanical behavior of these materials, especially those with complex geometries and under large deformation, can be challenging due to inherent computational complexity. In this work, we propose a data-driven multiscale computational scheme as a possible route to resolve this challenge. We use a neural network to approximate the effective strain energy density as a function of cellular geometry and overall deformation. The network is constructed by "learning" from the data generated by finite element calculation of a set of representative volume elements at cellular scales. This effective strain energy density is then used to predict the mechanical responses of cellular materials at larger scales. Compared with direct finite element simulation, the proposed scheme can reduce the computational time up to two orders of magnitude. Potentially, this scheme can facilitate new optimization algorithms for designing cellular materials of highly specific mechanical properties.

We propose an efficient method to reinitialize a level set function to a signed distance function by solving an elliptic problem using the finite element method. The original zero level set interface is preserved by means of applying modified boundary conditions to a surrogate/approximate interface weakly with a penalty method. Narrow band technique is adopted to reinforce the robustness of the proposed method where a smooth initial guess for the nonlinear equation is given by solving a Laplace's equation. Numerical benchmarks in both two dimensions and three dimensions confirm the optimal convergence rates under several different error measures including an interface error measure, showing that our method is accurate and robust. A three-dimensional genus 2 surface is adopted to demonstrate the capability of the method for the reinitialization of complicated geometries.

Time- and temperature-dependent structural relaxation (physical aging) of poly (styrene-b-methyl methacrylate) (PS-b-PMMA) block copolymers was investigated by calorimetry. Our study reveals the interplay of the relaxation responses of the two components of the copolymer in an intermediate temperature regime. That is, when the testing temperature is closely below the glass transition temperatures of PS and PMMA, structural relaxation in these polymer phases takes place concurrently, the corresponding thermogram displays partially superposed dual endothermic peaks as a feature of physical aging in the diblock copolymers. The aging response for each component is identified from a curve fitting method and analyzed by the relaxation of enthalpy. Comparing with the homopolymer analogs, the PS and PMMA in diblock copolymers show enhanced aging rate.

Mechanical metamaterials are artificial structures that exhibit unusual mechanical properties at the macroscopic level due to architected geometric design at the microscopic level. With rapid advancement of multi-material 3D printing techniques, it is possible to design mechanical metamaterials by varying spatial distributions of different base materials within a representative volume element (RVE), which is then periodically arranged into a lattice structure. The design problem is challenging, however, considering the wide design space of potentially infinitely many configurations of multi-material RVEs. We propose an optimization framework that automates the design flow. We adopt variational autoencoder (VAE), a machine learning generative model to learn a latent, reduced representation of a given RVE configuration. The reduced design space allows to perform Bayesian optimization (BayesOpt), a sequential optimization strategy, for the multi-material design problems. In this work, we select two base materials with distinct elastic moduli and use the proposed optimization scheme to design a composite solid that achieves a prescribed set of macroscopic elastic moduli. We fabricated optimal samples with multi-material 3D printing and performed experimental validation, showing that the optimization framework is reliable.