Zeliang Liu

Data-driven self-consistent clustering analysis of heterogeneous materials with crystal plasticity

To analyze complex, heterogeneous materials, a fast and accurate method is needed. This means going beyond the classical finite element method, in a search for the ability to compute, with modest computational resources, solutions previously infeasible even with large cluster computers. In particular, this advance is motivated by composites design. Here, we apply similar principle to another complex, heterogeneous system: additively manufactured metals.

A deep material network for multiscale topology learning and accelerated nonlinear modeling of heterogeneous materials

Abstract In this paper, a new data-driven multiscale material modeling method, which we refer to as deep material network, is developed based on mechanistic homogenization theory of representative volume element (RVE) and advanced machine learning techniques. We propose to use a collection of connected mechanistic building blocks with analytical homogenization solutions to describe complex overall material responses which avoids the loss of essential physics in generic neural network. This concept is demonstrated for 2-dimensional RVE problems and network depth up to 7. Based on linear elastic RVE data from offline direct numerical simulations, the material network can be effectively trained using stochastic gradient descent with backpropagation algorithm, further enhanced by model compression methods. Importantly, the trained network is valid for any local material laws without the need for additional calibration or micromechanics assumption. Its extrapolations to unknown material and loading spaces for a wide range of problems are validated through numerical experiments, including linear elasticity with high contrast of phase properties, nonlinear history-dependent plasticity and finite-strain hyperelasticity under large deformations. By discovering a proper topological representation of RVE with fewer degrees of freedom, this intelligent material model is believed to open new possibilities of high-fidelity efficient concurrent simulations for a large-scale heterogeneous structure. It also provides a mechanistic understanding of structure–property relations across material length scales and enables the development of parameterized microstructural database for material design and manufacturing.

Subharmonic Resonance of Geometrical Nonlinear Structure in 2-D Periodic Elastic System for Mechanical Wave Filtering

A dynamical analysis is conducted on a representative volume element of a periodic continuous structure. It is proven that the internal part attached to the frame is not constrained to periodic propagation conditions according to a finite element formulation. Hence a periodic structure in 2-D plane with a dynamic absorber in each element can be well designed to block the propagation of elastic waves in specific frequency domains, known as band gap around prescribed frequencies. To overcome the limit of linear vibrating internal structures we introduce an inclusion with geometrical nonlinearities which exhibits a nonlinear localized oscillation since the excitation frequency falls in the neighborhood of one-third of the main resonance frequency, known as subharmonic resonance. A combined configuration is taken as an example including clamp-clamp beams in rectangular periodic frame. According to the band structures and derivation, the designed structure can filter out waves at frequencies lower than fundamental resonance frequency of internal structure, which means the mechanism based on subharmonic resonance may enhance the functions for mechanical wave filtering and further energy harvesting. doi: 10.12783/SHM2015/133