Related papers: Formal justification of a continuum relaxation mod…
The Adaptive Stabilized Finite Element method (AS-FEM) developed in Calo et. al. combines the idea of the residual minimization method with the inf-sup stability offered by the discontinuous Galerkin (dG) frameworks. As a result, the…
This work focuses on the thermodynamics of pseudo-elastic models which represent the Mullins effect. Two established models are analyzed theoretically, their thermomechanical properties are derived, and certain critical points are…
We address the question whether observables of an exactly solvable model of electrons coupled to (optical) phonons relax into large time stationary state values and investigate if the asymptotic expectation values can be computed using a…
The compliance matrix for a general anisotropic material is usually expressed in an arbitrarily chosen coordinate system, which brings some confusion or inconvenience in identifying independent elastic material constants and comparing…
A two dimensional amorphous material is modeled as an assembly of mesoscopic elemental pieces coupled together to form an elastically coherent structure. Plasticity is introduced as the existence of different minima in the energy landscape…
We study the free energy and dynamics of a closed elastic filament (a one-dimensional curve in two dimensions) whose local internal state is specified by curvature, stretch, and a scalar density field representing, for example, the…
The advancement of generalized deepfake disruption is constrained by the interruption imbalance, a fundamental bottleneck inherent to the generation of universal perturbations. We reveal that conventional static gradient normalization…
We have formulated a relaxation mechanism for ferrites and ferromagnetic metals whereby the coupling between the magnetic motion and lattice is based purely on continuum arguments concerning magnetostriction. This theoretical approach…
An accurate description of elastic effects of coherent microstructures is necessary for the predictive modeling of microstructural evolution in many structural materials. To date, there has not been a demonstration on how continuum…
We construct a finite element approximation of a strain-limiting elastic model on a bounded open domain in $\mathbb{R}^d$, $d \in \{2,3\}$. The sequence of finite element approximations is shown to exhibit strong convergence to the unique…
We investigate by means of molecular dynamics simulation a coarse-grained polymer glass model focusing on (quasi-static and dynamical) shear-stress fluctuations as a function of temperature T and sampling time $\Delta t$. The linear…
A recently introduced model describing -on a 1d lattice- the velocity field of a granular fluid is discussed in detail. The dynamics of the velocity field occurs through next-neighbours inelastic collisions which conserve momentum but…
For solving unsteady hyperbolic conservation laws on cut cell meshes, the so called small cell problem is a big issue: one would like to use a time step that is chosen with respect to the background mesh and use the same time step on the…
We propose a generic model to describe the mechanical response and failure of systems which undergo a series of stick-slip events when subjected to an external load. We model the system as a bundle of fibers, where single fibers can…
Many systems, when initially placed far from equilibrium, exhibit surprising behavior in their attempt to equilibrate. Striking examples are the Mpemba effect and the cooling-heating asymmetry. These anomalous behaviors can be exploited to…
This work presents an extended formulation of maximal stiffness design, within the framework of the topology optimization. The mathematical formulation of the optimization problem is based on the postulated principle of equal dissipation…
The enforcement of global energy conservation in phase-field fracture simulations has been an open problem for the last 25 years. Specifically, the occurrence of unstable fracture is accompanied by a loss in total potential energy, which…
We consider the simplest one-constant model, put forward by J. Ericksen, for nematic liquid crystals with variable degree of orientation. The equilibrium state is described by a director field $\mathbf{n}$ and its degree of orientation $s$,…
This paper presents an algorithm for Monte Carlo fixed-lag smoothing in state-space models defined by a diffusion process observed through noisy discrete-time measurements. Based on a particles approximation of the filtering and smoothing…
The stress-strain constitutive law for viscoelastic materials such as soft tissues, metals at high temperature, and polymers, can be written as a Volterra integral equation of the second kind with a \emph{fading memory} kernel. This…