A Concept for the Development of Mathematical and Mechanical Models for the Deformations of Composites under Uniaxial Load


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Title: A Concept for the Development of Mathematical and Mechanical Models for the Deformations of Composites under Uniaxial Load

Author(s): S. Popovics

Publication: Special Publication

Volume: 266


Appears on pages(s): 37-56

Keywords: composite average; creep; creep recovery; modulus of elasticity; optimization; spring-dashboard model.

Date: 10/1/2009

The primary purpose of this paper is to introduce and demonstrate the applicability of a statistical concept, the average, for the modeling of the deformations of two-phase composites under load. Concrete is modeled as a well-compacted two-phase composite, the hardened paste as the matrix, and the aggregate as the dispersed phase. Only the paste has creep. The demonstration is done by the development of novel viscoelastic models and their mathematical equivalents for the instantaneous as well as time-dependent deformations of concrete, as a two-phase composite, under load. The underlying principle of the work is based on an extension of earlier publications by the writer in which averages of the averages of the related the phases, the composite averages are offered for the estimation of the modulus of elasticity of composites. Since experimental results supported the composite average method, CAM, quite well for this, it seemed worthwhile to investigate whether the method can be extended for the calculation of time-dependent deformations. The extension consists of the addition of dashboard elements to the existing composite average spring models for the modulus of elasticity of concrete, for the estimation of creep. This is the combinations of two existing spring-dash models for the calculation of the creep: the Poyinting-Thomson model with the Maxwell model the results of which are two CAMs that are determined by the type of combination between these two: one for normal-weight concretes when the two models are connected in a series, and the other, when they are in parallel for lightweight-aggregate concretes. Experimental data on creep with uniaxial loading taken from the literature support these composite models well. Among others, the data and the models show that during the period when the creep development is gradually decelerating: 1. creep values as a function of loading time, give straight lines, let us call them creep lines (compliance functions) in semi-log system as well as in log-log system of coordinates. Consequently, they can be approximated both by logarithmic as well as power functions. Such formulas are suitable for the estimation of creep at a later time from an earlier measurement; and 2. various creep lines of comparable concretes may be parallel, regardless at what age t' the loading started. It is shown that the new models are: well supported by experimental results within reasonable time limits; they are conceptually simple and logical; they are novel; they can consider the composition of the concrete; they represent both E and creep; and they are valid both normal-weight and lightweight-aggregate concretes.