# Cell division in deep material networks applied to multiscale strain localization modeling

arXiv: https://arxiv.org/abs/2101.07226 · HTML: https://mlsanity.com/paper/2101.07226/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 74 references that are in the map.
- First posted on arXiv 18 Jan 2021.

## Builds on (most cited first, 9 of 9)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [On the Properties of Neural Machine Translation: Encoder-Decoder Approaches](https://mlsanity.com/paper/1409.1259/) (2014)
- [A deep material network for multiscale topology learning and accelerated nonlinear modeling of heterogeneous materials](https://mlsanity.com/paper/1807.09829/) (2018)
- [Model-Free Data-Driven Inelasticity](https://mlsanity.com/paper/1808.10859/) (2018)
- [A Physics-Constrained Data-Driven Approach Based on Locally Convex Reconstruction for Noisy Database](https://mlsanity.com/paper/1907.12651/) (2019)
- [A numerical method for computing the overall response of nonlinear composites with complex microstructure](https://mlsanity.com/paper/2012.08962/) (2020)
- [Exploring the 3D architectures of deep material network in data-driven multiscale mechanics](https://mlsanity.com/paper/1901.04832/) (2019)
- [Deep material network with cohesive layers: Multi-stage training and interfacial failure analysis](https://mlsanity.com/paper/1908.04858/) (2019)
- [Intelligent multiscale simulation based on process-guided composite database](https://mlsanity.com/paper/2003.09491/) (2020)

## Built on by (most cited first, 2 of 2)

- [LS-DYNA Machine Learning-based Multiscale Method for Nonlinear Modeling of Short Fiber-Reinforced Composites](https://mlsanity.com/paper/2301.02738/) (2023)
- [Systematic Performance Assessment of Deep Material Networks for Multiscale Material Modeling](https://mlsanity.com/paper/2602.07192/) (2026)

## Abstract (arXiv)

Despite the increasing importance of strain localization modeling (e.g., failure analysis) in computer-aided engineering, there is a lack of effective approaches to capturing relevant material behaviors consistently across multiple length scales. We aim to address this gap within the framework of deep material networks (DMN) -- a machine learning model with embedded mechanics in the building blocks. A new cell-division scheme is proposed to track the scale transition through the network, and its consistency is ensured by the physics of fitting parameters. Essentially, each microscale node in the bottom layer is described by an ellipsoidal cell with its dimensions back-propagated from the macroscale material point. New crack surfaces in the cell are modeled by enriching cohesive layers, and failure algorithms are developed for crack initiation and evolution in the implicit DMN analysis. Besides studies on a single material point, we apply the multiscale model to concurrent multiscale simulations for the dynamic crush of a particle-reinforced composite tube and various tests on carbon fiber reinforced polymer composites. For the latter, experimental validations on an off-axis tensile test specimen are also provided.