Related papers: Material data identification in generalized contin…
This paper offers a conceptually straightforward method for the calculation of stresses in polarisable media based on the notion of a drive form and its property of being closed in spacetimes with symmetry. After an outline of the notation…
We introduce a robust framework for learning various generalized Hamiltonian dynamics from noisy, sparse phase-space data and in an unsupervised manner based on variational Bayesian inference. Although conservative, dissipative, and…
Flowing granular materials often abruptly arrest if not driven by sufficient applied stresses. Such abrupt cessation of motion can be economically expensive in industrial materials handling and processing, and is significantly consequential…
A main goal of data-driven materials research is to find optimal low-dimensional descriptors, allowing us to predict a physical property, and to interpret them in a human-understandable way. In this work, we advance methods to identify…
Many real-world scientific processes are governed by complex nonlinear dynamic systems that can be represented by differential equations. Recently, there has been increased interest in learning, or discovering, the forms of the equations…
Although the notion of mechanical noise is expected to play a key role in the non-linear rheology of athermally sheared amorphous systems, its characterization has so far remained elusive. Here, we show using molecular dynamic simulations…
The understanding of the material properties of the layered transition metal dichalcogenides (TMDs) is critical for their applications in structural composites. The data-driven machine learning (ML) based approaches are being developed in…
Data-driven methods offer efficient and robust solutions for analyzing complex dynamical systems but rely on the assumption of I.I.D. data, driving the development of generalization techniques for handling environmental differences. These…
We study the problem of identifying the dynamics of a linear system when one has access to samples generated by a similar (but not identical) system, in addition to data from the true system. We use a weighted least squares approach and…
We present a complete analytical solution for the stress field inside a homogeneous, inside a homogeneous, linearly elastic solid sphere subjected to a concentrated normal load applied on its surface. Starting from the three-dimensional…
We study consequences of long-range elasticity in thermally assisted dynamics of yield stress materials. Within a two-dimensinal mesoscopic model we calculate the mean-square displacement and the dynamical structure factor for tracer…
Stress affects physical and mental health, and wearable devices have been widely used to detect daily stress through physiological signals. However, these signals vary due to factors such as individual differences and health conditions,…
We extend to finite elasticity the Data-Driven formulation of geometrically linear elasticity presented in Conti, M\"uller, Ortiz, Arch.\ Ration.\ Mech.\ Anal.\ 229, 79-123, 2018. The main focus of this paper concerns the formulation of a…
Pattern-forming systems can exhibit a diverse array of complex behaviors as external parameters are varied, enabling a variety of useful functions in biological and engineered systems. First-principles derivations of the underlying…
A general procedure to investigate the elastic response and calculate the elastic constants of stressed and unstressed materials through continuum field modeling, particularly the phase field crystal (PFC) models, is presented. It is found…
Predicting the strength of materials requires considering various length and time scales, striking a balance between accuracy and efficiency. Peierls stress measures material strength by evaluating dislocation resistance to plastic flow,…
Deformations of conventional solids are described via elasticity, a classical field theory whose form is constrained by translational and rotational symmetries. However, flexible metamaterials often contain an additional approximate…
The existence of generalized steady states (GSSs) in nonlinear mechanical systems under moderate temporally aperiodic forcing has only been shown recently. Here we derive systematic expansions for such GSSs and construct a numerical…
We introduce a data-driven approach to the modelling and analysis of viscous fluid mechanics. Instead of including constitutive laws for the fluid's viscosity in the mathematical model, we suggest to directly use experimental data. Only a…
Throughout the history of science, physics-based modeling has relied on judiciously approximating observed dynamics as a balance between a few dominant processes. However, this traditional approach is mathematically cumbersome and only…