相关论文: The internal law of a material can be discovered f…
Real-time simulation of elastic structures is essential in many applications, from computer-guided surgical interventions to interactive design in mechanical engineering. The Finite Element Method is often used as the numerical method of…
The finite element method (FEM) is among the most commonly used numerical methods for solving engineering problems. Due to its computational cost, various ideas have been introduced to reduce computation times, such as domain decomposition,…
Neural networks have emerged as a powerful tool for modeling physical systems, offering the ability to learn complex representations from limited data while integrating foundational scientific knowledge. In particular, neuro-symbolic…
Deep learning (DL) inverse techniques have increased the speed of artificial electromagnetic material (AEM) design and improved the quality of resulting devices. Many DL inverse techniques have succeeded on a number of AEM design tasks, but…
We propose a new framework for identifying mechanical properties of heterogeneous materials without a closed-form constitutive equation. Given a full-field measurement of the displacement field, for instance as obtained from digital image…
Accurately modeling the mechanical behavior of materials is crucial for numerous engineering applications. The quality of these models depends directly on the accuracy of the constitutive law that defines the stress-strain relation.…
Modeling complex spatiotemporal dynamics, particularly in far-from-equilibrium systems, remains a grand challenge in science. The governing partial differential equations (PDEs) for these systems are often intractable to derive from first…
The potential energy formulation and deep learning are merged to solve partial differential equations governing the deformation in hyperelastic and viscoelastic materials. The presented deep energy method (DEM) is self-contained and…
Unveiling the underlying governing equations of nonlinear dynamic systems remains a significant challenge. Insufficient prior knowledge hinders the determination of an accurate candidate library, while noisy observations lead to imprecise…
Constitutive models play a crucial role in materials science as they describe the behavior of the materials in mathematical forms. Over the last few decades, the rapid development of manufacturing technologies have led to the discovery of…
The discovery of constitutive models for hyperelastic materials is essential yet challenging due to their nonlinear behavior and the limited availability of experimental data. Traditional methods typically require extensive stress-strain or…
Harnessing data to discover the underlying governing laws or equations that describe the behavior of complex physical systems can significantly advance our modeling, simulation and understanding of such systems in various science and…
A data driven finite element method (DDFEM) that accounts for more than two material state variables has been presented in this work. DDFEM framework is motivated from (1,2) and can account for multiple state variables, viz. stresses,…
Physics-constrained data-driven computing is an emerging computational paradigm that allows simulation of complex materials directly based on material database and bypass the classical constitutive model construction. However, it remains…
We propose a Pretrained Finite Element Method (PFEM),a physics driven framework that bridges the efficiency of neural operator learning with the accuracy and robustness of classical finite element methods (FEM). PFEM consists of a physics…
We propose a neural network framework to preclude the need to define or observe incompletely or inaccurately defined states of a material in order to describe its response. The neural network design is based on the classical Coleman-Gurtin…
The potential of neural networks (NN) in engineering is rooted in their capacity to understand intricate patterns and complex systems, leveraging their universal nonlinear approximation capabilities and high expressivity. Meanwhile,…
To fully understand, analyze, and determine the behavior of dynamical systems, it is crucial to identify their intrinsic modal coordinates. In nonlinear dynamical systems, this task is challenging as the modal transformation based on the…
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 dimensionless numbers for a…
Finding self-similarity is a key step for understanding the governing law behind complex physical phenomena. Traditional methods for identifying self-similarity often rely on specific models, which can introduce significant bias. In this…