Viscous approximation of quasistatic evolutions for a coupled elastoplastic-damage model

Employing the technique of vanishing viscosity and time rescaling, we show the existence of quasistatic evolutions for elastoplastic materials with incomplete damage affecting both the elastic tensor and the plastic yield surface, in a softening framework and in small strain assumptions

Quasistatic crack growth based on viscous approximation: a model with branching and kinking

Employing the technique of vanishing viscosity and time rescaling, we show the existence of quasistatic evolutions of cracks in brittle materials in the setting of antiplane shear. The crack path is not prescribed a priori and is chosen in an admissible class of piecewise regular sets that allows for branching and kinking

Cohesive fracture with irreversibility: Quasistatic evolution for a model subject to fatigue

In this paper we prove the existence of quasistatic evolutions for a cohesive fracture on a prescribed crack surface, in small-strain antiplane elasticity. The main feature of the model is that the density of the energy dissipated in the fracture process depends on the total variation of the amplitude of the jump. Thus, any change in the crack opening entails a loss of energy, until the crack is complete. In particular this implies a fatigue phenomenon, i.e. a complete fracture may be produced by oscillation of small jumps. The first step of the existence proof is the construction of approximate evolutions obtained by solving discrete-Time incremental minimum problems. The main difficulty in the passage to the continuous-Time limit is that we lack of controls on the variations of the jump of the approximate evolutions. Therefore we resort to a weak formulation where the variation of the jump is replaced by a Young measure. Eventually, after proving the existence in this weak formulation, we improve the result by showing that the Young measure is concentrated on a function and coincides with the variation of the jump of the displacement

Singular limits of a coupled elasto-plastic damage system as viscosity and hardening vanish

The paper studies the asymptotic analysis of a model coupling elastoplasticity and damage depending on three parameters—governing viscosity, plastic hardening, and convergence rate of plastic strain and displacement to equilibrium—as they vanish in different orders. The notion of limit evolution obtained is proven to coincide in any case with a notion intro- duced by Crismale and Rossi (SIAM J Math Anal 53(3):3420–3492, 2021), moreover, such solutions are closely related to those obtained in the vanishing-viscosity limit by Crismale and Lazzaroni (Calc Var Part Differ Equ 55(1):17, 2016), for the analogous model where only the viscosity parameter was present

Derivation of linear elasticity for a general class of atomistic energies

The purpose of this paper is the derivation, in the framework of Gamma-convergence, of linear elastic continuum theories from a general class of atomistic models, in the regime of small deformations. Existing results are available only in the special case of one-well potentials accounting for very short interactions. We consider here the general case of multi-well potentials accounting for interactions of finite but arbitrarily long range. The extension to this setting requires a novel idea for the proof of the Gamma-convergence which is interesting in its own right and potentially relevant in other applications

Rate-Independent Damage in Thermo-Viscoelastic Materials with Inertia

We present a model for rate-independent, unidirectional, partial damage in visco-elastic materials with inertia and thermal effects. The damage process is modeled by means of an internal variable, governed by a rate-independent flow rule. The heat equation and the momentum balance for the displacements are coupled in a highly nonlinear way. Our assumptions on the corresponding energy functional also comprise the case of the Ambrosio\u2013 Tortorelli phase-field model (without passage to the brittle limit). We discuss a suitable weak formulation and prove an existence theorem obtained with the aid of a (partially) decoupled time-discrete scheme and variational convergence methods. We also carry out the asymptotic analysis for vanishing viscosity and inertia and obtain a fully rate-independent limit model for displacements and damage, which is independent of temperature

Some remarks on a model for rate-independent damage in thermo-visco-elastodynamics

This note deals with the analysis of a model for partial damage, where the rate- independent, unidirectional flow rule for the damage variable is coupled with the rate-dependent heat equation, and with the momentum balance featuring inertia and viscosity according to Kelvin-Voigt rheology. The results presented here combine the approach from Roubicek [1, 2] with the methods from Lazzaroni/Rossi/Thomas/Toader [3]. The present analysis encompasses, differently from [2], the monotonicity in time of damage and the dependence of the viscous tensor on damage and temperature, and, unlike [3], a nonconstant heat capacity and a time-dependent Dirichlet loading

Historical social contracts and their legacy: a disaggregated analysis of the medieval republics

We study the comparative political economy within the territories ruled by the medieval republics in Northern Italy. Building on the historical evidence, we conceptualize the emergence of more inclusive vs. extractive institutions in these sovereign polities as driven by the interests of local rulers and their need to build state capacity. We provide novel insights on the role of geography and historical contingencies in the development of public governance, individual attitudes, and social-inclusion, which mutually supported each other and persisted over time. We measure the origin, territorial evolution, and disappearance of all the sovereign polities that ruled over the Italian peninsula during the period of 1000-1800 AD. The empirical analysis connects contemporary socio-economic outcomes across spatially disaggregated northern Italian localities, at the municipality level, to local political history. We distinguish between so-called “communal” and “maritime republics” and show that the intensity and stability of exposure to the different types of republican rule in pre-industrial times continues to shape local public good provision and individual fiscal compliance, and has left a tangible imprint on today’s population diversity

Radiation and magnetic field effects on new semiconductor power devices for HL-LHC experiments

The radiation hardness of commercial Silicon Carbide and Gallium Nitride power MOSFETs is presented in this paper, for Total Ionizing Dose effects and Single Event Effects, under gamma, neutrons, protons and heavy ions. Similar tests are discussed for commercial DC-DC converters, also tested in operation under magnetic field