Cycle-finite module categories

We describe the structure of module categories of finite dimensional algebras over an algebraically closed field for which the cycles of nonzero nonisomorphisms between indecomposable finite dimensional modules are finite (do not belong to the infinite Jacobson radical of the module category). Moreover, geometric and homological properties of these module categories are exhibited

Discrete derived categories I: homomorphisms, autoequivalences and t-structures

Discrete derived categories were studied initially by Vossieck (J Algebra 243:168–176, 2001) and later by Bobiński et al. (Cent Eur J Math 2:19–49, 2004). In this article, we describe the homomorphism hammocks and autoequivalences on these categories. We classify silting objects and bounded t-structures

Fe analysis of strain localization in concrete in elasto-plasticity and damage mechanics with non-local softening

Results of Finite Element Method (FEM) simulations of a strain localization in concrete specimens are presented. Two different continuum approaches have been used to model to behaviour of concrete: (i) an elasto-plastic constitutive law with the Drucker-Prager criterion in the compression regime and the Rankine criterion in the tensile regime, with isotropic hardening and softening and (ii) an isotropic continuum damage model with the equivalent strain corresponding to the Rankine failure criterion and modified Huber-Mises criterion in terms of strains, with exponential softening. Both constitutive models were enriched by non-local terms to describe strain localization properly, ensure mesh-independence in the softening regime and capture the deterministic size effect. The constitutive models were used to simulate strain localization in concrete in two boundary value problems under plane strain conditions, viz. uniaxial tension and three-point bending. The effect of the characteristic length on load-displacement curves and widths of strain localization is discussed

Application of Extended Finite Element Method to Cracked Concrete Elements – Numerical Aspects

The paper deals with the application of the eXtended Finite Element Method (XFEM) to simulations of discrete macro-cracks in plain concrete specimens under tension, bending and shear. Fundamental relationships and basic discrete constitutive laws were described. The most important aspects of the numerical implementation were discussed. Advantages and disadvantages of the method were outline

Symulacje zarysowania w elementach betonowych z zastosowaniem podejścia ciągłego i nieciągłego

The paper presents results of numerical simulations of fracture in concrete using two different approaches. First, fracture was modelled in a smeared way by an elasto-plastic and a damage continuum model. In elasto-plasticity, a Rankine criterion was used. The degradation of the stiffness in the damage model was described as a scalar variable of an equivalent strain measure. To ensure mesh-independent results, a non-local theory was used. Second, fracture was simulated as discontinuities with the aid of cohesive elements and Extended Finite Element Method (XFEM). The experimental benchmark test for concrete by Nooru-Mohamed under mixed mode conditions was modelled. The obtained numerical results were compared with the corresponding experimental ones.W pracy przedstawiono wyniki symulacji numerycznych MES pękania w betonie z wykorzystaniem dwóch różnych podejść. Po pierwsze, zastosowano ciągły (przesmarowany) opis rys w teorii plastyczności oraz model degradacji modułu sprężystości z różnymi opisami odkształcenia zastępczego w ramach kontynualnej mechaniki uszkodzeń. Oba prawa rozszerzono o długość charakterystyczną mikrostruktury w ramach teorii nielokalnej w celu uzyskania wyników niezależnych od siatki MES. Po drugie, jako alternatywę do symulacji propagacji rys zastosowano nieciągły opis pola przemieszczeń, wykorzystując elementy kohezyjne oraz rozszerzoną metodę elementów skończonych XFEM. Przeprowadzono symulacje numeryczne testu Nooru-Mohamada z jednoczesnym rozciąganiem i ścinaniem betonu. Uzyskane wyniki numeryczne porównano z wynikami doświadczalnymi

Modelling of concrete behaviour with a non-local continuum damage approach

The paper presents FE-results on the behaviour of concrete under plane strain conditions. The material was modelled using a simple isotropic damage continuum model. The model was enriched by non-local terms to avoid a pathological mesh-sensitivity and to obtain a well-posed rate boundary value problem. The constitutive model was used to simulate localization of deformation in 3 benchmark problems: a double-edge notched specimen under uniaxial tension and a notched beam under three- and four-point bending. Attention was laid on the effect of a characteristic length on the load-displacement curves and strain localization. The FE-results were compared with experiments and other numerical studies

A Non-local elasto-plastic model to describe localisations of deformation in concrete

The paper presents numerical simulations of behaviour of concrete elements subjected to uniaxial compression for plane strain. FE-calculations are performed with two different elasto-plastic constitutive laws for concrete. Numerical results obtained suffer from mesh sensivity due to the presence of material softening. To obtain a well-posed boundary problem and a mesh independent solution, conventional constitutive laws with softening require an extension (called regularisation) to describe properly the localisations of deformations. In this paper elasto-plastic constitutive laws are extended by non-local strain terms. Owing to them, localisations of deformations are realistically captured

Modelowanie lokalizacji odkształceń w materiałach quasi-kruchych z zastosowaniem modelu sprężysto-plastycznego

The paper presents results of numerical simulations of strain localization in quasi-brittle materials (like concrete) under plane strain conditions. To model the material behaviour, an isotropic elasto-plastic-damage model combining elasto-plasticity and scalar damage was used. An elasto-plastic constitutive law using a Drucker-Prager yield surface (in compression) and Rankine yield surface (in tension) was defined. A modified failure criterion by Rankine for the equivalent strain using an exponential evolution law was assumed within damage mechanics. To obtain mesh-independent results of strain localization, the model was enhanced by non-local terms in the softening regime. A four-point bending test of a concrete beam with a single notch was numerically simulated using the finite element method. FE-results were compared with laboratory experiments.W artykule przedstawiono wyniki symulacji numerycznych lokalizacji odkształceń w materiałach quasi-kruchych (jak beton) w płaskim stanie odkształcenia. Do opisu materiału przyjęto izotropowy model sprężysto-plastyczno-zniszczeniowy uwzględniający prawo sprężysto-plastyczne ze skalarną degradacją sztywności. W przypadku prawa sprężysto-plastycznego przyjęto kryterium plastyczności Druckera-Pragera w ściskaniu i kryterium plastyczności Rankine'a w rozciąganiu. Degradację sprężystą opisano z wykorzystaniem definicji odkształcenia zastępczego wegług warunku Rankine'a i wykładniczym prawem ewolucji. W celu otrzymania wyników niezależnych od siatki elementów skończonych, w obszarze osłabienia przyjęto teorię nielokalną. Przedstawiono wyniki symulacji numerycznych dla belki betonowej z nacięciem obciążonej dwoma siłami skupionymi. Wyniki numeryczne porównane z wynikami doświadczalnymi