Wojciech Sumelka

The Numerical Analysis of the Intrinsic Anisotropic Microdamage Evolution in Elasto-Viscoplastic Solids

The objective of the present article is to show the formulation for elastic-viscoplastic material model accounting for intrinsic anisotropic microdamage. The strain-induced anisotropy is described by the evolution of the intrinsic microdamage process — defined by the second-order microdamage tensor. The first step of the possibility of identification procedure (calibration of parameters) are also accounted and illustrated by numerical examples.

THERMOELASTICITY IN THE FRAMEWORK OF THE FRACTIONAL CONTINUUM MECHANICS

Fractional continuum mechanics is the generalization of classical mechanics utilizing fractional calculus. Contrary to classical theory, the obtained description is non-local, which is inherently the consequence of the fractional derivative definition based on the interval. So, all fields obtained in the framework of this new formulation, such as temperature, thermal stresses, total stresses, displacements, etc., at the specific point of interest, depend on the information from its surroundings. The dimensions of these surroundings and the ways of influencing the results are governed by the fractional differential operator applied. In this article, the application of the fractional continuum mechanics to thermoelasticity is presented. A classical solution is obtained as a special case.

Application of fractional continuum mechanics to rate independent plasticity

In the paper the generalisation of classical rate independent plasticity using fractional calculus is presented. This new formulation is non-local due to properties of applied fractional differential operator during definition of kinematics. In the description small fractional strains assumption is hold together with additive decomposition of total fractional strains into elastic and plastic parts. Classical local rate independent plasticity is recovered as a special case.

Fractional Euler–Bernoulli beams: Theory, numerical study and experimental validation

Abstract In this paper the classical Euler – Bernoulli beam (CEBB) theory is reformulated utilising fractional calculus. Such generalisation is called fractional Euler–Bernoulli beams (FEBB) and results in non-local spatial description. The parameters of the model are identified based on AFM experiments concerning bending rigidities of micro-beams made of the polymer SU-8. In experiments both force as well as deflection data were recorded revealing significant size effect with respect to outer dimensions of the specimens. Special attention is also focused on the proper numerical solution of obtained fractional differential equation.

Thermal Stresses in Metallic Materials Due to Extreme Loading Conditions

The role of thermal stresses, understood as stresses introduced by a uniform or nonuniform temperature change in a body which is somehow constrained against expansion or contraction, in metallic materials due to extreme loading conditions is under consideration. The thermomechanical couplings (thermal expansion and thermal plastic softening phenomena) have a fundamental impact on damage and localization phenomena due to their influence on the propagation and interaction of the deformation waves. Such processes include strain rates over 107s-1 and temperatures reaching the melting point. It should be emphasized, that apart from thermal effects, the anisotropy of damage (both initial and induced by deformation) plays a central role in the overall process. The aforementioned dynamic events are described in this paper in terms of the Perzynas type viscoplasticity model recently developed by the authors, including the anisotropic damage. The discussed constitutive structure has a deep physical interpretation derived from the analysis of a single crystal and polycrystal behaviors.

Linear and non-linear free vibration of nano beams based on a new fractional non-local theory

Purpose Recently, a new formulation has been introduced for non-local mechanics in terms of fractional calculus. Fractional calculus is a branch of mathematical analysis that studies the differential operators of an arbitrary (real or complex) order and is used successfully in various fields such as mathematics, science and engineering. The purpose of this paper is to introduce a new fractional non-local theory which may be applicable in various simple or complex mechanical problems. Design/methodology/approach In this paper (by using fractional calculus), a fractional non-local theory based on the conformable fractional derivative (CFD) definition is presented, which is a generalized form of the Eringen non-local theory (ENT). The theory contains two free parameters: the fractional parameter which controls the stress gradient order in the constitutive relation and could be an integer and a non-integer and the non-local parameter to consider the small-scale effect in the micron and the sub-micron scales. The non-linear governing equation is solved by the Galerkin and the parameter expansion methods. The non-linearity of the governing equation is due to the presence of von-Karman non-linearity and CFD definition. Findings The theory has been used to study linear and non-linear free vibration of the simply-supported (S-S) and the clamped-free (C-F) nano beams and then the influence of the fractional and the non-local parameters has been shown on the linear and non-linear frequency ratio. Originality/value A new parameter of the theory (the fractional parameter) makes the modeling more fixable – this model can conclude all of integer and non-integer operators and is not limited to special operators such as ENT. In other words, it allows us to use more sophisticated mathematics to model physical phenomena. On the other hand, in the comparison of classic fractional non-local theory, the theory applicable in various simple or complex mechanical problems may be used because of simpler forms of the governing equation owing to the use of CFD definition.

Designing of Multilayered Protective Panels Against Improvised Debris

This paper presents the design process of multilayered protective panels used to protect people and property from debris resulting from the explosion. A series of numerical analysis were conducted, which allowed to find the number of aluminium sheets to fill the barrier and to determine their shape in order to stop penetration. In this work not only the design process, that employs the most current engineering tools, is presented, but also behaviour of metallic materials under extreme dynamic loading.

Computer estimation of plastic strain localization and failure for large strain rates using viscoplasticity

The problem of modelling extreme dynamic events for metallic materials including strain rates over 107 s-1 and temperatures reaching melting point is still vivid in theoretical, applied and computational mechanics. Such thermomechanical processes are highly influenced by elasto-viscoplastic wave effects (their propagation and interaction) and varying initial anisotropy caused by existing defects in metals structure like microcracks, microvoids, mobile and immobile dislocations densities being together a cause of overall induced anisotropy during deformation (from the point of view of meso-macro continuum mechanics approach). It should be emphasised, that the most reliable way for estimation of such processes needs nowadays a complex phenomenological models due to limitations of current experimental techniques (it is still not possible to measure the evolution of crucial quantities e.g. temperature for extreme dynamic processes) and computational capabilities.

Brain modelling in the framework of anisotropic hyperelasticity with time fractional damage evolution governed by the Caputo-Almeida fractional derivative

In this paper the human brain tissue constitutive model for monotonic loading is developed. The model in this work is based on the anisotropic hyperelasticity assumption (the transversely isotropic case) together with modelling of the evolving load-carrying capacity (scalar damage) whose change is governed by the Caputo-Almeida fractional derivative. This allows the brain constitutive law to include the memory during progressive damage, due to the characteristic time length scale which is an inherent attribute of the fractional operator. Furthermore, the rate dependence of the overall brain tissue model is included as well. The theoretical model is finally calibrated and validated with a set of experimental data.