Homogeneous Deformations of Brauer Tree Algebras

Abstract

Based on tilting theory, we demonstrate the existence of homogeneous deformations for the Brauer tree algebras, which are derived naturally from a tilting complex.     

Second-order estimates for the large-deformation response of particle-reinforced rubbersEstimations homogénéisées pour le comportement mécanique des caoutchoucs renforcés en grandes déformations

This paper presents the application of a recently proposed ‘second-order’ homogenization method (J. Mech. Phys. Solids 50 (2002) 737–757) to the estimation of the effective behavior of hyperelastic composites subjected to finite deformations. The main feature of the method is the use of ‘generalized’ secant moduli that depend not only on the phases averages of the fields, but also on the phase covariance tensors. The use of the method is illustrated in the context of particle-, or fiber-reinforced elastomers and estimates analogous to the well-known Hashin–Shtrikman estimates for linear-elastic composites are generated. The new estimates improve on earlier estimates (J. Mech. Phys. Solids 48 (2000) 1389–1411) neglecting the use of fluctuations. In particular, the new estimates, unlike the earlier ones, are capable of recovering the exact incompressibility constraint when the matrix is also taken to be incompressible. To cite this article: O. Lopez-Pamies, P. Ponte Castañeda, C. R. Mecanique 331 (2003).     

Reissner矩形板的弯曲问题

本文根据Rcissncr平板理论,提出了矩形中厚板弯曲问题的解答,应用本文中的(5)、(9)式,可求解通常边界条件下,承受横向均布力q_0以及承受横向均布力和板边法向弯矩等组合荷载共同作用下的矩形中厚板的弯曲问题,而且使这类问题的解答规律化。     

On Generating Isochoric Finite Deformations

New isochoric finite deformations may be generated from any such deformation described in rectangular Cartesian coordinates by changing coordinate systems.      

The spectral curve theory for (k,l)-symmetric CMC surfaces

Constant mean curvature surfaces in $S^3$ can be studied via their associated family of flat connections. In the case of tori this approach has led to a deep understanding of the moduli space of all CMC tori. For compact CMC surfaces of higher genus the theory is far more involved due to the non abelian nature of their fundamental group. In this paper we extend the spectral curve theory for tori developed in Hitchin (1990), Pinkall and Sterling (1989) and for genus 2 surfaces (Heller, 2014) to CMC surfaces in $S^3$ of genus $g=k\cdot l$ with commuting ${\mathbb{Z}}_{k+1}$ and ${\mathbb{Z}}_{l+1}$ symmetries. We determine their associated family of flat connections via certain flat line bundle connections parametrized by the spectral curve. We generalize the flow on spectral data introduced in Heller (2015) and prove the short time existence of this flow for certain families of initial surfaces. In this way we obtain countably many $1-$parameter families of new CMC surfaces of higher genus with prescribed branch points and prescribed umbilics.     

Non-linearity in rheology —an essay of classification

Different non-linear phenomena (such as non-Newtonian flow, large elastic deformations, instabilities of different types and many others) are the heart of rheology. Therefore many attempts were carried out to find quantitative, or at least qualitative, models of non-linear behavior. The general or perhaps most attractive way of developing rheological constitutive equations consists in the search for the most general method to describe everything in the framework of a single approach. Naturally, this leads to very complicated and ambiguous equations. Meanwhile, it is reasonable to try another way based on separating observed phenomena into different types depending on observed phenomena into different types depending on their physical origin. An attempt to propose such their physical origin. An attempt to propose such classification of nonlinear rheological effects is made.According to the assumed scheme three levels of non-linearity are distinguished. There is a group of phenomena which originate as a consequence of finite elastic deformations. This is weak non-linearity related to equilibrium properties of a matter. The second level can be characterized as strong non-linearity. It is related to reversible structure changes, developing in time and connected with changes in relaxation properties of a matter. This group of effects can be treated as kinetic phenomena. Lastly, the third level of non-linearity is connected with breaking or phase transitions induced by deformations. This leads to the most severe consequences and can be treated as effects of thermodynamic nature. It is shown that some well known rheological effects can be explained if we consider them as a superposition of non-linearity of different types.Presented as keynote lecture at the European Rheology Meeting, September 4–9, 1994, Sevilla, Spain     

A comparative study of kinematic hardening rules at finite deformations

Kinematic hardening models describe a specific kind of plastic anisotropy which evolves with the deformation process. It is well known that the extension of constitutive relations from small to finite deformations is not unique. This applies also to well-established kinematic hardening rules like that of Armstrong-Frederick or Chaboche. However, the second law of thermodynamics offers some possibilities for generalizing constitutive equations so that this ambiguity may, in some extent, be moderated. The present paper is concerned with three possible extensions, from small to finite deformations, of the Armstrong-Frederick rule, which are derived as sufficient conditions for the validity of the second law. All three models rely upon the multiplicative decomposition of the deformation gradient tensor into elastic and plastic parts and make use of a yield function expressed in terms of the so-called Mandel stress tensor. In conformity with this approach, the back-stress tensor is defined to be of Mandel stress type as well. In order to compare the properties of the three models, predicted responses for processes with homogeneous and inhomogeneous deformations are discussed. To this end, the models are implemented in a finite element code (ABAQUS).     

Large deformations of nonlinear viscoelastic and multi-responsive beams

This study presents analyses of deformations in nonlinear viscoelastic beams that experience large displacements and rotations due to mechanical, thermal, and electrical stimuli. The studied beams are relatively thin so that the effect of the transverse shear deformation is neglected, and the stretch along the transverse axis of the beams is also ignored. It is assumed that the plane that is perpendicular to the longitudinal axis of the undeformed beam remains plane during the deformations. The nonlinear kinematics of the finite strain beam theory presented by Reissner [27] is adopted, and a nonlinear viscoelastic constitutive relation based on a quasi-linear viscoelastic (QLV) model is considered for the beams. Deformation in beams due to mechanical, thermal, and electric field inputs are incorporated through the use of time integral functions, by separating the time-dependent function and nonlinear measures of field variables. The nonlinear measures are formulated by including higher order terms of the field variables, i.e. strain, temperature, and electric field. Responses of beams under mechanical, thermal, and electrical stimuli are illustrated and the effects of nonlinear constitutive relations on the overall deformations of the beams are highlighted.     

On the large strain deformation behavior of silicone-based elastomers for biomedical applications

The results of a comprehensive mechanical analysis of five silicone-based elastomers are presented. Large strain monotonic tests were performed under uniaxial, strip biaxial and equi-biaxial stress states. Based on the multiaxial experimental data, hyperelastic constitutive models were determined for each material. The small strain elastic modulus ranges from 49 kPa to 1.5 MPa, and the materials show different degrees of non-linearity of their stress-strain response. Data on the time and history dependence allow determining the deviation from the behavior predicted using a non-dissipative hyperelastic constitutive model. Next to representing a guideline for a comprehensive characterization of highly deformable materials, the present results provide data which can be used for the selection of an appropriate material, depending on the specific application. The corresponding models can be used to simulate the performance of each elastomer in applications involving large strains and multiaxial loading states.