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Artificial Neural Networks (ANNs) have demonstrated remarkable utility in various challenging machine learning applications. While formally verified properties of their behaviors are highly desired, they have proven notoriously difficult to…
Task-driven design of soft robots requires models that are physically accurate and computationally efficient, while remaining transferable across actuator designs and task scenarios. However, existing modeling approaches typically face a…
This work presents a finite element method for simulating dynamic processes that involve the coupled evolution of dislocation motion and crack propagation. The method numerically solves the Concurrent Atomistic-Continuum (CAC) formulation…
The mechanical behavior of inelastic materials with microstructure is very complex and hard to grasp with heuristic, empirical constitutive models. For this purpose, multiscale, homogenization approaches are often used for performing…
This manuscript presents the Quantum Finite Element Method (Q-FEM) developed for use in noisy intermediate-scale quantum (NISQ) computers and employs the variational quantum linear solver (VQLS) algorithm. The proposed method leverages the…
In the present work, a machine learning based constitutive model for electro-mechanically coupled material behavior at finite deformations is proposed. Using different sets of invariants as inputs, an internal energy density is formulated…
An accurate, physically-based, and differentiable model of soft robots can unlock downstream applications in optimal control. The Finite Element Method (FEM) is an expressive approach for modeling highly deformable structures such as…
Spatial numerical integration is essential for finite element analysis. Currently, numerical integration schemes, mostly based on Gauss quadrature, are widely used. Herein, we present an alternative semi-analytical approach for mass matrix…
In this paper, we provide a theoretical analysis of a type of operator learning method without data reliance based on the classical finite element approximation, which is called the finite element operator network (FEONet). We first…
This work presents a practical finite element modeling strategy, the Crack Element Method (CEM), for simulating the dynamic crack propagation in two-dimensional structures. The method employs an element-splitting algorithm based on the…
An emerging trend in deep learning research focuses on the applications of graph neural networks (GNNs) for mesh-based continuum mechanics simulations. Most of these learning frameworks operate on graphs wherein each edge connects two…
The local geometrical randomness of metal foams brings complexities to the performance prediction of porous structures. Although the relative density is commonly deemed as the key factor, the stochasticity of internal cell sizes and shapes…
Accurate and efficient modeling of soft-tissue interactions is fundamental for advancing surgical simulation, surgical robotics, and model-based surgical automation. To achieve real-time latency, classical Finite Element Method (FEM)…
The cost and accuracy of simulating complex physical systems using the Finite Element Method (FEM) scales with the resolution of the underlying mesh. Adaptive meshes improve computational efficiency by refining resolution in critical…
The finite element methods (FEM) are important techniques in engineering for solving partial differential equations, but they depend heavily on element shape quality for stability and good performance. In this paper, we introduce the…
We present a framework for generating universal semantic embeddings of chemical elements to advance materials inference and discovery. This framework leverages ElementBERT, a domain-specific BERT-based natural language processing model…
Uncertainty quantification (UQ) plays a critical role in verifying and validating forward integrated computational materials engineering (ICME) models. Among numerous ICME models, the crystal plasticity finite element method (CPFEM) is a…
We present a multiscale simulation framework that couples the Finite Element Method with molecular dynamics. Bypassing traditional equations of state (EOS) by using in-line atomistic simulations, the method offers the advantage of…
We present a coupling of the Finite Element and the Boundary Element Method in an isogeometric framework to approximate either two-dimensional Laplace interface problems or boundary value problems consisting in two disjoint domains. We…
We introduce a novel architecture and computational framework for formal, automated analysis of systems with a broad set of nonlinearities in the feedback loop, such as neural networks, vision controllers, switched systems, and even simple…