Related papers: Defect screening and load transfer in minimal hard…
Stress analysis of heterogeneous media, like composite materials, using Finite Element Analysis (FEA) has become commonplace in design and analysis. However, determining stress distributions in heterogeneous media using FEA can be…
We present simulations of static model sandpiles in two dimensions (2D) and focus on the stress distribution in such arrays made of discrete particles. We use the simplest possible model, i.e. spherical particles with a linear spring and a…
Nonlinearity is crucial to the performance of a deep (neural) network (DN). To date there has been little progress understanding the menagerie of available nonlinearities, but recently progress has been made on understanding the r\^ole…
We present a minimalistic approach to simulations of force transmission through granular systems. We start from a configuration containing cohesive (tensile) contact forces and use an adaptive procedure to find the stable configuration with…
The problem of reliability of a large distributed system is analyzed via a new mathematical model. A typical framework is a system where a set of files are duplicated on several data servers. When one of these servers breaks down, all…
We describe a phase transition that gives rise to structurally non-trivial states in a two-dimensional ordered network of particles connected by harmonic bonds. Monte Carlo simulations reveal that the network supports, apart from the…
Naturally occurring materials are often disordered, with their bulk properties being challenging to predict from the structure, due to the lack of underlying crystalline axes. In this paper, we develop a digital pipeline from…
In solid mechanics, Data-driven approaches are widely considered as the new paradigm that can overcome the classic problems of constitutive models such as limiting hypothesis, complexity, and high dependence on training data. However,…
Stress transmission in planar open-cell cellular solids is analysed using a recent theory developed for marginally rigid granular assemblies. This is made possible by constructing a one-to-one mapping between the two systems. General…
Entangled networks are ubiquitous in tissues, polymers, and fabrics. However, their mechanics remain insufficiently understood due to the complexity of the topological constraints at the network level. Here, we develop a mathematical…
We develop a continuum theory for equilibrium elasticity of a network of crosslinked semiflexible filaments, spanning the full range between flexible entropy-driven chains to stiff athermal rods. We choose the 3-chain constitutive model…
We first report a detailed transmission electron microscopy study of dislocation networks (DNs) formed at shallowly buried interfaces obtained by bonding two GaAs crystals between which we establish in a controlled manner a twist and a tilt…
Neural scaling laws and double-descent phenomena suggest that deep-network training obeys a simple macroscopic structure despite highly nonlinear optimization dynamics. We derive such structure directly from gradient descent in function…
There has been a significant recent surge in deep neural network (DNN) techniques. Most of the existing DNN techniques have restricted model formats/assumptions. To overcome their limitations, we propose the nonparametric transformation…
The mechanics of complex soft matter often cannot be understood in the classical physical frame of flexible polymers or rigid rods. The underlying constituents are semiflexible polymers, whose finite bending stiffness ($\kappa$) leads to…
Porous materials -- natural or engineered -- often exhibit dual pore-network structures that govern processes such as mineral exploration and hydrocarbon recovery from tight shales. Double porosity/permeability (DPP) mathematical models…
We characterize the force state of shear-loaded granular matter by relating the macroscopic stress to statistical properties of the force network. The purely repulsive nature of the interaction between grains naturally provides an upper…
This work presents a multi-level modeling and design framework for weft knitted fabrics, beginning with a volumetric finite element analysis capturing their mechanical behavior from fundamental principles. Incorporating yarn-level data, it…
Many natural materials exhibit highly complex, nonlinear, anisotropic, and heterogeneous mechanical properties. Recently, it has been demonstrated that data-driven strain energy functions possess the flexibility to capture the behavior of…
Despite the increasing importance of strain localization modeling (e.g., failure analysis) in computer-aided engineering, there is a lack of effective approaches to capturing relevant material behaviors consistently across multiple length…