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Article
Clustering-enhanced Lattice discrete particle modeling for quasi-brittle fracture and fragmentation analysis
This study focuses on predicting and quantifying fragmentation phenomena under high impulsive dynamic loading, such as blast, impact, and penetration events, which induce plastic deformation, fracture, and fra...
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Article
Benchmark study of melt pool and keyhole dynamics, laser absorptance, and porosity in additive manufacturing of Ti-6Al-4V
Metal three-dimensional (3D) printing involves a multitude of operational and material parameters that exhibit intricate interdependencies, which pose challenges to real-time process optimization, monitoring, ...
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Article
Open AccessPhysics guided heat source for quantitative prediction of IN718 laser additive manufacturing processes
Challenge 3 of the 2022 NIST additive manufacturing benchmark (AM Bench) experiments asked modelers to submit predictions for solid cooling rate, liquid cooling rate, time above melt, and melt pool geometry fo...
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Article
Solving diffusive equations by proper generalized decomposition with preconditioner
Proper Generalized Decomposition (PGD) approximates a function by a series of modes, each of them taking a variable-separated form. This allows drastic reduction in numerical complexity, particularly suits hig...
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Article
Machine learning meta-models for fast parameter identification of the lattice discrete particle model
When simulating the mechanical behavior of complex materials, the failure behavior is strongly influenced by the internal structure. To account for such dependence, models at the length scale of material heter...
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Article
Convolution Hierarchical Deep-Learning Neural Network Tensor Decomposition (C-HiDeNN-TD) for high-resolution topology optimization
High-resolution structural topology optimization is extremely challenging due to a large number of degrees of freedom (DoFs). In this work, a Convolution-Hierarchical Deep Learning Neural Network-Tensor Decomp...
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Article
Convolution hierarchical deep-learning neural network (C-HiDeNN) with graphics processing unit (GPU) acceleration
We propose the Convolution Hierarchical Deep-learning Neural Network (C-HiDeNN) that can be tuned to have superior accuracy, higher smoothness, and faster convergence rates like higher order finite element met...
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Article
Convolution Hierarchical Deep-learning Neural Networks (C-HiDeNN): finite elements, isogeometric analysis, tensor decomposition, and beyond
This paper presents a general Convolution Hierarchical Deep-learning Neural Networks (C-HiDeNN) computational framework for solving partial differential equations. This is the first paper of a series of papers...
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Article
Deep Learning Discrete Calculus (DLDC): a family of discrete numerical methods by universal approximation for STEM education to frontier research
The article proposes formulating and codifying a set of applied numerical methods, coined as Deep Learning Discrete Calculus (DLDC), that uses the knowledge from discrete numerical methods to interpret the deep l...
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Article
Special issue of computational mechanics on machine learning theories, modeling, and applications to computational materials science, additive manufacturing, mechanics of materials, design and optimization
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Article
HiDeNN-FEM: a seamless machine learning approach to nonlinear finite element analysis
The hierarchical deep-learning neural network (HiDeNN) (Zhang et al. Computational Mechanics, 67:207–230) provides a systematic approach to constructing numerical approximations that can be incorporated into a...
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Article
An introduction to kernel and operator learning methods for homogenization by self-consistent clustering analysis
Recent advances in operator learning theory have improved our knowledge about learning maps between infinite dimensional spaces. However, for large-scale engineering problems such as concurrent multiscale simu...
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Article
Open AccessCorrection to: Eighty Years of the Finite Element Method: Birth, Evolution, and Future
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Article
A State-of-the-Art Review on Machine Learning-Based Multiscale Modeling, Simulation, Homogenization and Design of Materials
Multiscale simulation and homogenization of materials have become the major computational technology as well as engineering tools in material modeling and material design. However, the concurrent multiscale si...
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Article
Open AccessData-driven discovery of dimensionless numbers and governing laws from scarce measurements
Dimensionless numbers and scaling laws provide elegant insights into the characteristic properties of physical systems. Classical dimensional analysis and similitude theory fail to identify a set of unique dim...
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Article
Next-generation prognosis framework for pediatric spinal deformities using bio-informed deep learning networks
Predicting pediatric spinal deformity (PSD) from X-ray images collected on the patient’s initial visit is a challenging task. This work builds on our previous method and provides a novel bio-informed framework...
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Article
Concurrent n-scale modeling for non-orthogonal woven composite
Concurrent analysis of composite materials can provide the interaction among scales for better composite design, analysis, and performance prediction. A data-driven concurrent n-scale modeling approach ( ...
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Article
Open AccessEighty Years of the Finite Element Method: Birth, Evolution, and Future
This document presents comprehensive historical accounts on the developments of finite element methods (FEM) since 1941, with a specific emphasis on developments related to solid mechanics. We present a histor...
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Article
Macroscale Property Prediction for Additively Manufactured IN625 from Microstructure Through Advanced Homogenization
Design of additively manufactured metallic parts requires computational models that can predict the mechanical response of the parts considering the microstructural, manufacturing, and operating conditions. Th...
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Article
Open AccessMechanistic data-driven prediction of as-built mechanical properties in metal additive manufacturing
Metal additive manufacturing provides remarkable flexibility in geometry and component design, but localized heating/cooling heterogeneity leads to spatial variations of as-built mechanical properties, signifi...
