Mathematical modelling of rate-independent pseudoelastic SMA material

The paper presents a procedure for the formulation of constitutive equations for rate-independent pseudoelastic SMA material models. The procedure applies a rheological scheme representing mechanical properties of the material. An additive decomposition of strains into two parts is proposed. The first part describes strains of a perfectly elastic body while the second part may be represented by a combination of a rigid perfectly elastic body and a rigid perfectly plastic body. It is demonstrated that the key problem of formulation of constitutive relationships is to derive the 1st order differential equation with respect to the tensor describing the second part of the strain field. This equation may be obtained in explicit form starting from the variational inequalities defining non-elastic parts of rheological model. The uniqueness of the obtained differential equation has been proved. A numerical implementation of the constitutive relationships of SMA material was done through the user subroutine module VUMAT within the FE commercial code ABAQUS/Explicit. As an example we analyzed the problem of vibration of a simple 3D structure made of SMA.     

An instrumented vehicle for offroad dynamics testing

The paper presents an instrumented vehicle that was equipped with measuring systems to perform complete dynamics tests, especially in off-road conditions. The equipment consists of four wheel dynamometers, a steering robot, and a differential GPS system together with an inertial platform, a non-contact vehicle speed sensor, and an on-board computer with software to control the devices and collect experimental data. The four wheel dynamometers measure six elements; based on strain gage force transducers, it measures three orthogonal forces and three moments. The steering robot can control the steering wheel of the vehicle at a variety of excitation modes; it can carry out typical vehicle dynamics tests (ISO 7401, ISO 4138, ISO/TR3888, etc.) as well as custom engineered tests at a wide range of setting parameters (steer angle rate up to 1600 deg/s). The differential GPS system gives true time vehicle kinematics data (velocities, accelerations, angles, etc.) at 10-ns sample rate and 20-mm accuracy. The base vehicle, a Suzuki Vitara 4 × 4, required no special modifications or changes to install the measuring equipment. The paper also describes typical tests performed with the use of the instrumented vehicle together with sample results.     

On typically real functions which are generated by a fixed typically real function

Let T be the family of all typically real functions, i.e. functions that are analytic in the unit disk Δ:= {z ∈ ℂ: |z| < 1}, normalized by f(0) = f′(0) − 1 = 0 and such that Imz Im f(z) ⩾ 0 for z ∈ Δ.     

History-dependent subdifferential inclusions and hemivariational inequalities in contact mechanics

We consider a class of subdifferential inclusions involving a history-dependent term for which we provide an existence and uniqueness result. The proof is based on arguments on pseudomonotone operators and fixed point. Then we specialize this result in the study of a class of history-dependent hemivariational inequalities. Such kind of problems arises in a large number of mathematical models which describe quasistatic processes of contact between a deformable body and an obstacle, the so-called foundation. To provide an example we consider a viscoelastic problem in which the frictional contact is modeled with subdifferential boundary conditions. We prove that this problem leads to a history-dependent hemivariational inequality in which the unknown is the velocity field. Then we apply our abstract result in order to prove the unique weak solvability of the corresponding contact problem.     

Strong immersion is a well-quasi-ordering for semicomplete digraphs

We prove that the strong immersion order is a well-quasi-ordering on the class of semicomplete digraphs, thereby strengthening a result of Chudnovsky and Seymour (2011, J. Comb. Theory, Series B, 101, 47–53) that this holds for the class of tournaments.     

Differential Tests for Plurisubharmonic Functions and Koch Curves

Potential Analysis - We study minimum sets of singular plurisubharmonic functions and their relation to upper contact sets. In particular we develop an algorithm checking when a naturally...     

Geometric properties of F-normed Orlicz spaces

Aequationes mathematicae - The paper deals with F-normed functions and sequence spaces. First, some general results on such spaces are presented. But most of the results in this paper concern...     

Phase transformation in shape memory alloys: a numerical approach for thermomechanical modeling via peridynamics

Meccanica - The work is devoted to the numerical aspects of the modeling tool elaborated to simulate the phenomenon of solid phase transformation in shape memory alloys. Particularly, a nonlocal...     

Quasi-arithmetic-type invariant means on probability space

Aequationes mathematicae - For a family $$(\mathscr {A}_x)_{x \in (0,1)}$$ of integral quasi-arithmetic means satisfying certain measurability-type assumptions we search for an integral mean K such...