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The mesoscopic concept is a way to deal with complex materials with an internal structure within continuum mechanics. It consists of extending the domain of the balance equations by mesoscopic variables and of introducing a local…
The paper is devoted to a constitutive solution, limit load analysis and Newton-like methods in elastoplastic problems containing the Mohr-Coulomb yield criterion. Within the constitutive problem, we introduce a self-contained derivation of…
Parameter estimation is a fundamental problem in science and engineering. In many safety-critical applications, one is not only interested in a {\it point} estimator, but also the uncertainty bound that can self-assess the accuracy of the…
The derivation of a Moving Boundary Approximation or of the response of a coherent structure like a front, vortex or pulse to external forces and noise, is generally valid under two conditions: the existence of a separation of time scales…
A typical phase field approach for describing phase separation and coarsening phenomena in alloys is the Cahn-Hilliard model. This model has been generalized to the so-called Cahn-Larch\'e system by combining it with elasticity to capture…
Magnetic field is believed to play an important role in the collapse of a molecular cloud. In particular, due to the properties of magnetic forces, collapse should be easier along magnetic field lines, as supported by the large-scale…
The static as well as the dynamic behaviour of granular material are determined by dynamic {\it and} static friction. There are well known methods to include static friction in molecular dynamics simulations using scarcely understood…
The rate-equation approach is used to describe sequential tunneling through a molecular junction in the Coulomb blockade regime. Such device is composed of molecular quantum dot (with discrete energy levels) coupled with two metallic…
A probabilistic approach to phase-field brittle and ductile fracture with random material and geometric properties is proposed within this work. In the macroscopic failure mechanics, materials properties and exactness of spatial quantities…
As a model of composite material, the fiber bundle model has been chosen -where a bundle of fibers is subjected to external load and fibers have distributed thresholds. For different loading conditions, such a system shows few precursors…
In order to better understand the interaction between pore-fluid overpressure and failure patterns in rocks we consider a porous elasto-plastic medium in which a laterally localized overpressure line source is imposed at depth below the…
It is known that the famous theoretical formula by Koiter for the critical buckling load of circular cylindrical shells under axial compression does not coincide with the experimental data. Namely, while Koiter's formula predicts linear…
We study the sample size dependence of the strength of disordered materials with a flaw, by numerical simulations of lattice models for fracture. We find a crossover between a regime controlled by the fluctuations due to disorder and…
We consider a model for elastic dislocations in geophysics. We model a portion of the Earth's crust as a bounded, inhomogeneous elastic body with a buried fault surface, along which slip occurs. We prove well-posedness of the resulting…
Soft polymers are ubiquitous materials in nature and as engineering materials with properties varying from rate-independent to rate-dependent. Current fracture toughness measures are non-unique for rate-dependent soft materials for varying…
Fluid injection can induce seismicity by altering stresses on pre-existing faults. Here, we investigate minimizing induced seismic hazard by optimizing injection operations in a physics-based forecasting framework. We built a 3D finite…
Anyone who has built a sandcastle recognizes that the addition of liquid to granular materials increases their stability. However, measurements of this increased stability often conflict with theory and with each other [1-7]. A…
We consider the unilateral contact problem between an elastic body and a rigid foundation in a description that includes both Tresca and Coulomb friction conditions. For this problem, we present an a posteriori error analysis based on an…
A Monte Carlo method for the collisional guiding-center Fokker-Planck kinetic equation is derived to include the effects of background magnetic-field nonuniformity. It is shown that, in the limit of a homogeneous magnetic field, the…
The purpose of this study is to propose a modified micromorphic continuum model for granular materials based on a micromechanics approach. In this model, Cauchy stress and the couple stress are symmetric conjugated with the symmetric strain…