Related papers: A deep learning energy method for hyperelasticity …
An exact arithmetic, memory efficient direct solution method for finite element method (FEM) computations is outlined. Unlike conventional black-box or low-rank direct solvers that are opaque to the underlying physical problem, the proposed…
A method for solving elasticity problems based on separable physics-informed neural networks (SPINN) in conjunction with the deep energy method (DEM) is presented. Numerical experiments have been carried out for a number of problems showing…
Understanding lattice deformations is crucial in determining the properties of nanomaterials, which can become more prominent in future applications ranging from energy harvesting to electronic devices. However, it remains challenging to…
Derivation of the probability density evolution provides invaluable insight into the behavior of many stochastic systems and their performance. However, for most real-time applica-tions, numerical determination of the probability density…
Physical phenomena in the real world are often described by energy-based modeling theories, such as Hamiltonian mechanics or the Landau theory, which yield various physical laws. Recent developments in neural networks have enabled the…
In this paper, the Combined Finite-Discrete Element Method (FDEM) has been applied to analyze the deformation of anisotropic geomaterials. In the most general case geomaterials are both non-homogeneous and non-isotropic. With the aim of…
(Partial) differential equations (PDEs) are fundamental tools for describing natural phenomena, making their solution crucial in science and engineering. While traditional methods, such as the finite element method, provide reliable…
Dual energy X-ray Computed Tomography (DECT) enables to automatically decompose materials in clinical images without the manual segmentation using the dependency of the X-ray linear attenuation with energy. In this work we propose a deep…
Finite element methods (FEM) are popular approaches for simulation of soft tissues with elastic or viscoelastic behavior. However, their usage in real-time applications, such as in virtual reality surgical training, is limited by…
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…
Discrete element modelling (DEM) is one of the most efficient computational approaches to the fracture processes of heterogeneous materials on mesoscopic scales. From the dynamics of single crack propagation through the statistics of crack…
Practical applications of mechanical metamaterials often involve solving inverse problems where the objective is to find the (multiple) microarchitectures that give rise to a given set of properties. The limited resolution of additive…
Many important problems in science and engineering require solving the so-called parametric partial differential equations (PDEs), i.e., PDEs with different physical parameters, boundary conditions, shapes of computation domains, etc.…
The scientific computation of large deformations in elastic-plastic solids is crucial in various manufacturing applications. Traditional numerical methods exhibit several inherent limitations, prompting Deep Learning (DL) as a promising…
Partial Differential Equations (PDEs) are central to science and engineering. Since solving them is computationally expensive, a lot of effort has been put into approximating their solution operator via both traditional and recently…
Contactless and non-invasive estimation of mechanical properties of physical media from optical observations is of interest for manifold engineering and biomedical applications, where direct physical measurements are not possible.…
High performance sheet metals with a multi-phase microstructure suffer from deformation induced damage formation during forming in the constituent phases but importantly also where these intersect. To capture damage in terms of the physical…
Dynamical energy analysis was recently introduced as a new method for determining the distribution of mechanical and acoustic wave energy in complex built up structures. The technique interpolates between standard statistical energy…
The Deep Material Network (DMN) has emerged as a powerful framework for multiscale materials modeling, enabling efficient and accurate prediction of material behavior across different length scales. Unlike conventional data-driven…
We present two effective methods for solving high-dimensional partial differential equations (PDE) based on randomized neural networks. Motivated by the universal approximation property of this type of networks, both methods extend the…