Formulation of continuous/discontinuous Galerkin methods for strain gradient-dependent damage

Continuum damage models are widely used to represent the development of microscopic defects that coalesce into a macroscopic crack. The microscopic defects cause a progressive weakening or softening of the material (damage). Strain gradient-dependent terms have been included in some damage theories to regularize them, and thereby avoid a pathological mesh-dependence in the solution. A strain gradient-dependent damage model is considered here for the simulation of this feature in quasi-brittle materials. In the model considered, the damage parameter depends upon a regularized equivalent strain. The regularization is introduced through a dependency on the Laplacian of an equivalent strain measure. The introduction of the Laplacian of the strain leads to numerical difficulties as the governing differential equations are fourth-order, and additional boundary conditions must be specified. The application of such a model in a standard finite element framework requires $C^1$ continuity of the shape functions. Here, a continuous/discontinuous mixed Galerkin method is presented which avoids the need for high-order continuity. The formulation allows the use of $C^0$ or $C^{-1}$ interpolations for the regularized strain field and a $C^0$ interpolation of the displacement field. Numerical examples are presented to validate the formulation in one and two dimensions. Several interpolations are tested extensively in one dimension in order to provide guidance for the most appropriate formulations in two dimensions. The formulation is applied to crack propagation in a three-point bending test, with the computed result being independent of the discretization

A continuous/discontinuous Galerkin formulation for a strain gradient-dependent damage model: 2D results

The numerical solution of strain gradient-dependent continuum problems has been hindered by continuity demands on the basis functions. The presence of terms in constitutive models which involve gradients of the strain eld means that the $C^0$ continuity of standard nite element shape functions is insu cient. In this work, a continuous/discontinuous Galerkin formulation is developed to solve a strain gradient-dependent damage problem in a rigorous manner. Potential discontinuities in the strain field across element boundaries are incorporated in the weak form of the governing equations. The performance of the formulation is tested in one dimension for various interpolations, which provides guidance for two-dimensional simulations

Automated modelling of viscoelastic flow using FEniCS

Using high-level abstractions, it is possible to efficiently automate the development of finite element models. This has advantages in terms of rapid development, a dramatic reduction in programming errors and offers the possibility of performing special optimisations to produced highly efficient code. The power of this concept is illustrated using tools from the FEniCS project for the simulation of a viscoelastic fluid in an Eulerian framework, and the benchmark problem of a sphere falling in a cylinder pipe is simulated

Salt weathering of sandstone during drying : effect of primary and secondary crystallisation

ACTInternational audienc

Simulazione di transizioni di fase diffusive e deformative

Il calcolo degli organi di macchina richiede una descrizione molto accurata delle caratteristiche del materiale;ciò non può prescindere dalla descrizione dei trattamenti termici ai quali il pezzo è stato sottoposto.La simulazione dei trattamenti termici degli acciai viene normalmente affrontata mediante modelli di naturafenomenologica che fanno largo uso di leggi empiriche per descrivere l’evoluzione della microstrutturaall’interno del pezzo. Tuttavia, l’impiego di leggi empiriche richiede un’apposita taratura dei parametri delmodello; inoltre tali leggi, per loro natura, non chiariscono fino in fondo le ragioni fisiche per le quali ifenomeni in gioco avvengono. Ne consegue che tale metodo è fortemente limitato nella sua generalità.Il problema può essere affrontato nella sua globalità, ossia prendendo in considerazione gli effetti termici,meccanici e di transizione di fase, partendo da una descrizione della struttura interna del materiale a scalamicroscopica ed inserita in un contesto termodinamicamente consistente.In particolare, in questo lavoro viene proposto un modello a parametri di fase alla scala microscopica capacedi descrivere trasformazioni di fase sia diffusive sia deformative e dunque di modellare, rispettivamente, latrasformazione da austenite a perlite e quella da austenite a martensite. Il modello, per la formulazione e lasua natura, risulta consistente con i principi della termodinamica e permette una descrizione delletrasformazioni diffusiva e deformativa e dei fenomeni termici in un contesto unificato.Le equazioni sulle quali si basa sono: l’equazione del moto, il bilancio della massa di carbonio (che porta allaequazione di Cahn-Hilliard) e l’equazione del calore completa, che deriva dal bilancio di energia interna. Acausa della natura non-locale del modello e della presenza di equazioni differenziali alle derivate parziali finoal quarto ordine, la soluzione del problema così formulato risulta complessa da un punto di vistacomputazionale; per questo motivo è stato messo a punto uno strumento numerico sofisticato ma robusto.Sono stati inoltre condotti alcuni test numerici che mostrano le potenzialità dell’approccio. Il modello risultacapace di cogliere le principali caratteristiche esibite alla scala microscopica dalle transizioni di fase perliticae martensitica, le interazioni fra queste e l’influenza dei fenomeni meccanici e termici

A macroscale, phase-field model for shape memory alloys with non-isothermal effects: influence of strain-rate and environmental conditions on the mechanical response

A Ginzburg-Landau model for the macroscopic behaviour of a shape memory alloy is proposed. The model is one-dimensional in essence, in that we consider the effect of the martensitic phase transition in terms of a uniaxial deformation along a fixed direction and we use a scalar order parameter whose equilibrium values describe the austenitic phase and the two martensitic variants. The model relies on a Ginzburg-Landau free energy defined as a function of macroscopically measurable quantities, and accounts for thermal effects; couplings between the various relevant physical aspects are established according to thermodynamic consistency. The theoretical model has been implemented within a finite-element framework and a number of numerical tests are presented which investigate the mechanical behaviour of the model under different conditions; the results obtained are analysed in relation to experimental evidences available in literature. In particular, the influence of the strain-rate and of the ambient conditions on the response of the model is highlighted.Comment: 23 pages research article, 13 figure

Geopolymers reinforced with natural fibers: A comparison among different sources

The performance of different natural fibers (hemp, kenaf and bamboo) used to formulate composites with an alkali-activated matrix based on metakaolin is evaluated. Short fibers were randomly dispersed up to about 3% of the binder weight, and the fresh and cured properties of the derived composites were determined. Up to the investigated fraction, it is still possible to obtain adequate workability without the supply of additional water or additives. Upon modification with fibers, the mechanical behavior changes from completely brittle to pseudoplastic with increased toughness. The flexural strength increases by up to 80% at the highest bamboo amount and up to 20% for kenaf. Hemp fibers have a negligible effect on flexural strength but strongly improve the materials’ toughness. Moreover, the addition of fibers does not change the manner in which the material interacts with moisture. Indeed, the water uptake of the modified samples was comparable to that of the unmodified samples, and the composites showed a decreased rate of water diffusion as the amount of fiber increased

CO₂ leakage can cause loss of benthic biodiversity in submarine sands

One of the options to mitigate atmospheric CO2 increase is CO2 Capture and Storage in sub-seabed geological formations. Since predicting long-term storage security is difficult, different CO2 leakage scenarios and impacts on marine ecosystems require evaluation. Submarine CO2 vents may serve as natural analogues and allow studying the effects of CO2 leakage in a holistic approach. At the study site east of Basiluzzo Islet off Panarea Island (Italy), gas emissions (90–99% CO2) occur at moderate flows (80–120 L m−2 h−1). We investigated the effects of acidified porewater conditions (pHT range: 5.5–7.7) on the diversity of benthic bacteria and invertebrates by sampling natural sediments in three subsequent years and by performing a transplantation experiment with a duration of one year, respectively. Both multiple years and one year of exposure to acidified porewater conditions reduced the number of benthic bacterial operational taxonomic units and invertebrate species diversity by 30–80%. Reduced biodiversity at the vent sites increased the temporal variability in bacterial and nematode community biomass, abundance and composition. While the release from CO2 exposure resulted in a full recovery of nematode species diversity within one year, bacterial diversity remained affected. Overall our findings showed that seawater acidification, induced by seafloor CO2 emissions, was responsible for loss of diversity across different size-classes of benthic organisms, which reduced community stability with potential relapses on ecosystem resilience

A computational multiscale approach to couple hygro-mechanical responses of large-scale masonry walls

We present a computational multiscale approach to the nonlinear problems of humidity diffusion and mechanical damage of large-scale masonry walls, and their coupling in terms of the effects of the humidity diffusion on the mechanical response and the effects of the mechanical degradation on the diffusion process. Such an approach allows us to recover, both efficiently and accurately, the complex nonlinear response of large-scale walls, which are in general hard to be solved by means of standard numerical tools. Two representative tests of two- and three-storey walls are here analyzed, and the corresponding results reported and commented, aiming to show how samples like these can potentially serve as reference solutions for more applicative purposes