A Thermodynamically Consistent Model of Quasibrittle Elastic Damaged Materials Based on a Novel Helmholtz Potential and Dissipation Function

In the paper, a thermodynamically consistent model of elastic damaged material in the framework of small strain theory is formulated, describing the process of deterioration in quasibrittle materials, concrete in particular. The main goal is to appropriately depict the distinction between material responses in tension and compression. A novel Helmholtz energy and a dissipation potential including three damage parameters are introduced. The Helmholtz function has a continuous first derivative with respect to strain tensor. Based on the assumed functions, the strain–stress relationship, the damage condition, the evolution laws, and the tangent stiffness tensor are derived. The model’s predictions for uniaxial tension, uniaxial compression, uniaxial cyclic compression–tension, and pure shear tests are calculated using Wolfram Mathematica in order to identify the main features of the model and to grasp the physical meaning of an isotropic damage parameter, a tensile damage parameter, and a compressive damage parameter. Their values can be directly bound to changes of secant stiffness and generalized Poisson’s ratio. An interpretation of damage parameters in association with three mechanisms of damage is given. The considered dissipation potential allows a flexible choice of a damage condition. The influence of material parameters included in dissipation function on damage mode interaction is discussed.

Contact interactions in complex fibrous metamaterials

In this work, an extension of the strain energy for fibrous metamaterials composed of two families of parallel fibers lying on parallel planes and joined by connective elements is proposed. The suggested extension concerns the possibility that the constituent fibers come into contact and eventually scroll one with respect to the other with consequent dissipation due to friction. The fibers interact with each other in at least three different ways: indirectly, through microstructural connections that could allow a relative sliding between the two families of fibers; directly, as the fibers of a family can touch each other and can scroll introducing dissipation. From a mathematical point of view, these effects are modeled first by introducing two placement fields for the two fiber families and adding a coupling term to the strain energy and secondly by adding two other terms that take into account the interdistance between the parallel fibers and the Rayleigh dissipation potential (to account for friction).

Explicit form of yield conditions dual to a class of dissipation potentials dependent on three invariants

In the paper, a pragmatic approach to finding the dual formulation for isotropic perfectly plastic materials given a dissipation potential dependent on three cylindrical invariants and involving the Ottosen shape function is proposed and illustrated by examples. The main goal is to provide instructions on how to perform the Legendre transformation used when passing from a dissipation potential to its conjugate yield condition and offer some suggestions regarding calibration for particular potentials dependent on the trace of the strain rate tensor and the product of the norm of its deviator and the Ottosen shape function, which covers a wide class of engineering materials. The classic framework for constitutive modelling of thermodynamically consistent materials within the small deformation theory is used. First, general formulae connecting a dissipation potential dependent on three invariants of the strain rate tensor to the coupled yield condition are derived. Then, they are narrowed down for the aforementioned case of dissipation functions dependent on the Lode angle in a way proposed by Ottosen. Finally, three examples are given involving classical potentials: Beltrami’s, Drucker–Prager’s and Mises–Schleicher’s generalised potential using the shape function. Detailed calculations exposing the introduced technique are performed. Also, a method of the calibration of such potentials leading to explicit mathematical formulae is demonstrated, based on the typical tests located on the tension and compression meridians.

Thermomechanical Modeling of Microstructure Evolution Caused by Strain-Induced Crystallization

The present contribution deals with the thermomechanical modeling of the strain-induced crystallization in unfilled polymers. This phenomenon significantly influences mechanical and thermal properties of polymers and has to be taken into consideration when planning manufacturing processes as well as applications of the final product. In order to simultaneously capture both kinds of effects, the model proposed starts by introducing a triple decomposition of the deformation gradient and furthermore uses thermodynamic framework for material modeling based on the Coleman–Noll procedure and minimum principle of the dissipation potential, which requires suitable assumptions for the Helmholtz free energy and the dissipation potential. The chosen setup yields evolution equations which are able to simulate the formation and the degradation of crystalline regions accompanied by the temperature change during a cyclic tensile test. The boundary value problem corresponding to the described process includes the balance of linear momentum and balance of energy and serves as a basis for the numerical implementation within an FEM code. The paper closes with the numerical examples showing the microstructure evolution and temperature distribution for different material samples.

On the Kachanov-Rabotnov continuum damage model

In this paper two partially complementary formulations of the simple phenomenological Kachanov-Rabotnov continuum damage constitutive model are presented. The models are based on a consistent thermodynamic formulation using proper expressions for the Helmholtz free energy or its complementary form of the dissipation potential. Basic features of the models are discussed and the behaviour in tensile test and creep problems is demonstrated.

New look at an old principle: an alternative formulation of the theorem of minimum entropy production

We formulate a direct generalization of the Prigogine’s principle of minimum entropy production, according to a new isoperimetric variation principle by classical non-equilibrium thermodynamics. We focus our attention on the possible mathematical forms of constitutive equations. Our results show that the Onsager’s reciprocity relations are consequences of the suggested variation principle. Furthermore, we show by the example of the thermo-diffusion such reciprocity relations for diffusion tensor, which are missing in Onsager’s theory. Our theorem applied to the non-linear constitutive equations indicates the existence of dissipation potential. We study the forms of general reciprocity with the dissipation potential. This consideration results in a weaker condition than Li-Gyarmati-Rysselberhe reciprocity has. Furthermore, in the case of electric conductivity in the magnetic field, our theorem shows the correct dependence of the Onsager’s kinetic coefficient by the axial vector of magnetic induction. We show in general that the evolution criterion of the global entropy production is a Lyapunov-function, and so the final stationer state is independent of the initial, time-independent boundary conditions.

Flexural Behaviour of HYFRC Beam Reinforced with GFRP Rebar

This paper offers the experimental have a take a look at at the flexural behaviour of HYFRC beams bolstered with glass fiber bolstered polymer (GFRP) rebar and in comparison with everyday metal reinforcement beams. Three beams reinforced with GFRP rebar and three beams of traditional concrete metal strengthened with absolutely six beams have been casted and tested under two points loading. The partner specimens were casted along with beam and tested for concrete homes. Steel and glass fibres are used toimprove the concrete assets. From checking out, load carrying capability, loaddeflection traits, crack sample, crack width, concrete traces throughout move phase and failure mode have been mentioned stiffness, ductility and power dissipation potential had been additionally calculated. The average ultimate load wearing potential of GFRP rebar and normal steel reinforcement beam is one hundred twenty five.8KN and ninety seven.5KN respectively. The most deflection cited at their closing load inside the GFRP rebar and regular metal reinforcement beam is 27. Three mm and sixteen. 3 mm respectively. It changed into also found that after load elimination, deflected GFRP beam regain its authentic function and crack width also reduced. In metal beam, metallic rebar were yielded, after load elimination, no deflection regain and crack width reduction have been observed

A gradient system with a wiggly energy and relaxed EDP-convergence

For gradient systems depending on a microstructure, it is desirable to derive a macroscopic gradient structure describing the effective behavior of the microscopic scale on the macroscopic evolution. We introduce a notion of evolutionary Gamma-convergence that relates the microscopic energy and the microscopic dissipation potential with their macroscopic limits via Gamma-convergence. This new notion generalizes the concept of EDP-convergence, which was introduced in [26], and is now called relaxed EDP-convergence. Both notions are based on De Giorgi’s energy-dissipation principle (EDP), however the special structure of the dissipation functional in terms of the primal and dual dissipation potential is, in general, not preserved under Gamma-convergence. By using suitable tiltings we study the kinetic relation directly and, thus, are able to derive a unique macroscopic dissipation potential. The wiggly-energy model of Abeyaratne-Chu-James (1996) serves as a prototypical example where this nontrivial limit passage can be fully analyzed.