Related papers: A Unified Variational Framework for Planar Elastic…
We develop a contraction-based framework to establish the existence and exponential stability of periodic solutions in planar nonsmooth dynamical systems governed by Filippov differential inclusions. The method integrates a time- and…
Arranging many modules within a bounded domain without overlap, central to the Electronic Design Automation (EDA) of very large-scale integrated (VLSI) circuits, represents a broad class of discrete geometric optimization problems with…
A quasistatic model for a horizontally loaded thin elastic composite at small strains is studied. The composite consists of two adjacent plates whose interface behaves in a cohesive fashion with respect to the slip of the two layers. We…
Despite of the topical engineering need and all scientific investments, the mathematical formulation of modeling elastic deformations in magnetic systems is not yet fully established. Often, especially in electrical engineering…
A general expression for the strain energy of a homogeneous, isotropic, plane extensible elastica with an arbitrary undeformed configuration is derived. This energy constitutes the correct expression for one-dimensional models of polymers…
Continuum strain energy functions are developed for soft biological tissues that possess long fibrillar components. The treatment is based on the model of an elastica, which is our fine scale model, and is homogenized in a simple fashion to…
The scope of this contribution is to present an overview of the theory of structured deformations of continua, together with some applications. Structured deformations aim at being a unified theory in which elastic and plastic behaviours,…
Physics-integrated generative modeling is a class of hybrid or grey-box modeling in which we augment the the data-driven model with the physics knowledge governing the data distribution. The use of physics knowledge allows the generative…
We present a concise derivation of the Boltzmann form for single-particle energy distributions in classical many-body Hamiltonian systems. The derivation relies on two physical facts: coarse-graining-scale invariance of the empirical…
The derivation of nonlocal strong forms for many physical problems remains cumbersome in traditional methods. In this paper, we apply the variational principle/weighted residual method based on nonlocal operator method for the derivation of…
Physics-informed neural networks provide a mesh-free framework for solving partial differential equation-governed problems in solid mechanics. However, most existing formulations in linear elasticity still learn the displacement field…
The development of accurate constitutive models for materials that undergo path-dependent processes continues to be a complex challenge in computational solid mechanics. Challenges arise both in considering the appropriate model assumptions…
Energies and equilibrium equations for thin elastic plates are discussed, with emphasis on several issues pertinent to recent approaches in soft condensed matter. Consequences of choice of basis, choice of invariant strain measures, and of…
We study pattern formation in planar fluid systems driven by intermolecular cohesion (which manifests as a line tension) and dipole-dipole repulsion which are observed in physical systems including ferrofluids in Hele-Shaw cells and…
We describe a new variational lower-bound on the minimum energy configuration of a planar binary Markov Random Field (MRF). Our method is based on adding auxiliary nodes to every face of a planar embedding of the graph in order to capture…
The major challenge in determining a hyperelastic model for a given material is the choice of invariants and the selection how the strain energy function depends functionally on these invariants. Here we introduce a new data-driven…
The mechanical behaviour of solid biological tissues has long been described using models based on classical continuum mechanics. However, the classical continuum theories of elasticity and viscoelasticity cannot easily capture the…
This study presents a physically consistent displacement-driven reformulation of the concept of action-at-a-distance, which is at the foundation of nonlocal elasticity. In contrast to existing approaches that adopts an integral…
We consider a discrete model of planar elasticity where the particles, in the reference configuration, sit on a regular triangular lattice and interact through nearest neighbor pairwise potentials, with bonds modeled as linearized elastic…
A geometrically exact dimensionally reduced order model for the nonlinear deformation of thin magnetoelastic shells is presented. The Kirchhoff-Love assumptions for the mechanical fields are generalised to the magnetic variables to derive a…