Time-dependent response of incompressible membranes based on quasi-linear viscoelasticity theory

Author(s):  
Farzam Dadgar-Rad ◽  
Nasser Firouzi

Modern concrete structures, realized through complex sequential construction techniques and/or characterized by significant non-homogeneities, are in general very sensitive to the effects of time-dependent behaviour of concrete (creep and shrinkage). Guidelines for the evaluation of these effects were developed in the last decades by international pre-standard and standard institutions on the basis of a common, although progressively evolving, scientific background, and of a substantially worldwide harmonized format. The author discusses the development, with his large personal involvement, of this favourable scenario, evidencing areas of well established consensus and open problems. One pending problem is still represented by the uncertainties of prediction models, with particular regards to the multi-decade long-term prediction of creep. In what concerns the evaluation of the structural effects of creep, it is commonly accepted that a reliable analysis of the structural response in service conditions may be performed on the basis of the theory of ageing linear viscoelasticity, first established by Italian mathematician V. Volterra at the dawn of 20th century. The paper discusses the computational implications of this approach with reference on the one hand to the adoption of realistic advanced models for the prediction of the creep behaviour of concrete, and, on the other hand, to the complexity and sequential character of the constructions, and illustrates current updated guidelines developed at the international level for the evaluation of the effects of creep, both in the conceptual and preliminary design stages and in the subsequent detailed construction-stage and long-term reliability analyses of complex and sequential structures. These guidelines are intended to deal also with other phenomena, which are responsible of causing deviations from aging linear viscoelasticity, like tensile cracking, cyclic creep, and stress relaxation in prestressing tendons at variable strain, as well as the effects of humidity and temperature variations. The paper must be intended as a homage to the memory of CEB (Comité Euro-International du Béton, Euro-International Committee for Concrete) Honorary Member and member of the Academy of Construction and Architecture of the USSR Alexei A. Gvozdev, for long-time head of the laboratory of reinforced concrete of NIIZHB, the Institute for Concrete and Reinforced Concrete now named after him, for his crucial role in encouraging and assisting the author in the initial steps of transporting into CEB and FIP (Fédération Internationale de la Précontrainte, International Federation for Prestressing) ambient the fundaments of this new advanced format for creep analysis, to which the school of Soviet scientists and Gvozdev himself had given a fundamental contribution. The present edition of the paper incorporates some significant updates related to the advancement in the international debate, with respect to the previous edition published in the Journal “Industrial and Civil Engineering” (Promyshlennoe i grazhdanskoe stroitel’stvo) of December 2014.


2015 ◽  
Vol 22 (4) ◽  
pp. 636-648 ◽  
Author(s):  
Alan S Wineman

This work considers the inflation and extension of an elastomeric tubular membrane when its material exhibits a time-dependent response. Three different models for time-dependent response are considered: finite linear viscoelasticity, Pipkin–Rogers non-linear viscoelasticity, and thermally induced chemorheological degradation. The first two are based on different assumptions about stress relaxation effects while the third accounts for time-dependent microstructural changes due to simultaneous scission and re-cross-linking of macromolecular network junctions. Each of these models describes a material response that softens with time. It is shown that the constitutive equations for all three models are included in a general non-linear single-integral constitutive equation. In previous work, for elastic membranes, the material is fixed and a localized bulge may form as the load increases. In this work, the load is specified, and a localized bulge may form as the membrane material undergoes a time-dependent response. It is assumed that the extension and inflation histories are initially uniform, but there may be a time when a localized bulge-like deformation starts to form. This is treated as branching from the uniform extension and inflation history. For times beyond this ‘branching time’, the governing equations are satisfied by both the continuation of the initial uniform deformation history and the branched deformation history for the bulge. A unified condition for determining this branching time, applicable to all three models, is derived in terms of the general non-linear single-integral constitutive equation. Post-branching response is not considered here.


Meccanica ◽  
2021 ◽  
Author(s):  
Raffaele Barretta ◽  
Francesco Marotti de Sciarra ◽  
Francesco P. Pinnola ◽  
Marzia S. Vaccaro

AbstractNonlocal hereditariness in Bernoulli–Euler beam is investigated in this paper. An approach to solve that problem is proposed and some analytical solutions are provided. To this aim, time-dependent hereditary behavior is modeled by means of non-integer order operators of the fractional linear viscoelasticity. While, space-dependent nonlocal phenomena are simulated through the integral stress-driven formulation. These two approaches are combined providing a new model able to simulate nonlocal viscoelastic bending problem. Several application samples of the proposed formulation and a thorough parametric study are presented showing the influences of hereditariness and nonlocal effects on the mechanical bending response. Proposed formulation can be useful for design and optimization of structures used in advanced applications when local elastic theory cannot be adopted.


Author(s):  
G. A. C. Graham

SynopsisThe traditional method of solution to problems in linear viscoelasticity theory involves the direct application of the Laplace transform to the relevant field equations and boundary conditions. If the shape of the body under consideration or the type of boundary condition specified at a point or both vary with time then this method no longer works. In this paper we investigate the applicability of stress function solutions to this situation. It is shown that for time-dependent ablating regions a generalization of the Papkovich Neuber stress function solution of elasticity holds. As an example the stress and displacement fields are calculated for the problem of an infinite viscoelastic body with a spherical ablating stress free cavity and prescribed time-dependent stresses at infinity.


Sign in / Sign up

Export Citation Format

Share Document