Related papers: A unifying perspective: the relaxed linear micromo…
We introduce a simple one-dimensional sandpile model that undergoes relaxation oscillations. A single model can account for self-organized critical behavior and relaxation oscillations, depending on the manner in which it is driven,…
We perform the linear stability analysis for a new model for poromechanical processes with inertia (formulated in mixed form using the solid deformation, fluid pressure, and total pressure) interacting with diffusing and reacting solutes…
The vertex model is widely used to simulate the mechanical properties of confluent epithelia and other multicellular tissues. This inherently discrete framework allows a Cauchy stress to be attributed to each cell, and its symmetric…
We consider mechanics of composite materials in which thin inclusions are modeled by lower-dimensional manifolds. By successively applying the dimensional reduction to junctions and intersections within the material, a geometry of…
A variational model to simultaneously treat Stress-Driven Rearrangement Instabilities, such as boundary discontinuities, internal cracks, external filaments, edge delamination, wetting, and brittle fractures, is introduced. The model is…
A continuum model of crystalline solid equilibrium is presented in which the underlying periodic lattice structure is taken explicitly into account. This model also allows for both point and line defects in the bulk of the lattice and at…
This study explores the role that the microstructure plays in determining the macroscopic static response of porous elastic continua and exposes the occurrence of position-dependent nonlocal effects that are strictly correlated to the…
A recent paper [J. A. Evans, D. Kamensky, Y. Bazilevs, "Variational multiscale modeling with discretely divergence-free subscales", Computers & Mathematics with Applications, 80 (2020) 2517-2537] introduced a novel stabilized finite element…
The transition from quasi-static slip growth to dynamic rupture propagation constitutes one possible scenario to describe earthquake nucleation. If this transition is rather well understood for homogeneous faults, how the friction…
We introduce a class of continuum mechanical models aimed at describing the behaviour of viscoelastic fluids by incorporating concepts originated in the theory of solid plasticity. Within this class, even a simple model with constant…
Earthquake fault zones are more complex, both geometrically and rheologically, than an idealised infinitely thin plane embedded in linear elastic material. To incorporate nonlinear material behaviour, natural complexities, and multi-physics…
Homogenisation empowers the efficient macroscale system level prediction of physical scenarios with intricate microscale structures. Here we develop an innovative powerful, rigorous and flexible framework for asymptotic homogenisation of…
We develop a unified relative entropy framework for macroscopic limits of kinetic equations with Riesz-type interactions and Fokker-Planck relaxation. Our analysis covers three prototypical singular regimes: the diffusive limit leading to a…
Direct numerical simulations of mechanical metamaterials are prohibitively expensive due to the separation of scales between the lattice and the macrostructural size. Hence, multiscale continuum analysis plays a pivotal role in the…
This study presents a generalized multiscale nonlocal elasticity theory that leverages distributed order fractional calculus to accurately capture coexisting multiscale and nonlocal effects within a macroscopic continuum. The nonlocal…
The complexity of the frictional dynamics at the microscopic scale makes difficult to identify all of its controlling parameters. Indeed, experiments on sheared elastic bodies have shown that the static friction coefficient depends on…
We study thermal relaxation in ordered arrays of coupled nonlinear elements with external driving. We find, that our model exhibits dynamic self-organization manifested in a universal stretched-exponential form of relaxation. We identify…
A method for homogenization of a heterogeneous (finite or periodic) elastic composite is presented. It allows direct, consistent, and accurate evaluation of the averaged overall frequency-dependent dynamic material constitutive relations.…
We consider a linearly elastic composite medium, which consists of a homogeneous matrix containing statistically inhomogeneous random set of heterogeneities and loaded by inhomogeneous remote loading. The new general integral equation is…
We study the relaxation dynamics of systems of straight, parallel crystal dislocations, starting from initially random and uncorrelated positions of the individual dislocations. A scaling model of the relaxation process is constructed by…