On transformation strains and uniform fields in multiphase elastic media

Dvorak, George J.; Benveniste, Y.

doi:10.1098/rspa.1992.0062

Cited by 274 publications

(108 citation statements)

References 14 publications

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“…In the present study, the triaxial interaction between matrix and aggregate is proposed to be taken into account by means of the recently developed method of transformation field analysis (Dvorak and Benveniste 1992;Dvorak 1992). For determining the effective elastic properties of the composite, which represents the elastic part of the overall composite response, and for carrying out some calculations of the transformation field analysis, we may choose from several methods available in the micromechanics literature.…”

Section: Introductionmentioning

confidence: 99%

Triaxial Composite Model for Basic Creep of Concrete

1998

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This paper shows how the mechanics of elastic composite materials can be adapted to predict the basic creep of concrete with aging due to hydration. The prediction is made on the basis of the given composition of concrete, the elastic constants of the aggregate, and the aging viscoelastic properties of the portland cement mortar. The triaxial action of the composite is approximated by Dvorak's transformation field analysis. To convert the aging creep problem to an elastic problem of a composite material with inelastic strains, Granger and Bafant's approach is used. This approach relies on Bafant's age-adjusted effective modulus method that reduces the integral-type stress-strain relation for linear aging creep with nonconvolution kernel to a quasi-elastic incremental stress-strain relation with inelastic incremental strain. Explicit expressions for the aging creep properties of concrete as a composite are deduced. The model is calibrated and verified by Ward et al.'s and Counto's test data. The predictions obtained are almost as close as those recently obtained by Granger and Bafant's model. While the present model has the advantage of describing the triaxial composite action in a rational manner, it does not yet capture the effect of the deviation of the aggregate configuration from the case of a contiguous aggregate skeleton of maximum possible compactness. Further refinements in this respect are needed. Another refinement might be needed to take into account possible enhancement of creep in the interface layers between the mortar and the aggregate.

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Section: Introductionmentioning

confidence: 99%

Triaxial Composite Model for Basic Creep of Concrete

1998

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“…In further discussion devoted to overall thermoelastic properties of n-phase SMA materials RVE it is developed original approach based on self-equilibrated eigenstrains influence moduli (SEIM). It was motivated by the method developed in Dvorak and Benveniste [5], see also [6]. Similar approach for two-phase RVE of SMA materials was used in Bernardini, Bernardini and Masiani [2,4].…”

Section: Multiphase Rve With Piecewise Uniform Elastic Properties Andmentioning

confidence: 99%

“…6. The results of classical homogenization theory presented in Dvorak and Benveniste, Dvorak [5,6] cf. also [2] are used in a unique modified manner which employs symmetric and skew-symmetric ingredients of self-equilibrated eigenstrains influence moduli (SEIM) to propose a new estimation method.…”

Section: Introductionmentioning

confidence: 99%

“…In completely independent effort the issue of structure of macroscopic free energy of SMA material was addressed by Bernardini [2], who elaborated micromechanics-based method of the combined estimation of all three terms (a)-(c) for two-phase RVE. He took advantage of the fact that in the case of two-phase medium there are unique connections between fourth-order dimensionless mechanical concentration factor tensors, commonly denoted by the symbol B α -cf., e.g., [5,6,8]-and other properly selected tensor measures of stress concentration. It can be shown that at fixed microstructure geometry and microscopic phase strain field, the tensors B α , ε pt -(c) and scalar φ coh -(b) become unique functions of M. Estimate of M entails definite estimations of the terms (b) and (c).…”

Section: Introductionmentioning

confidence: 99%

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On consistent micromechanical estimation of macroscopic elastic energy, coherence energy and phase transformation strains for SMA materials

Ziółkowski

2016

Continuum Mech. Thermodyn.

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An apparatus of micromechanics is used to isolate the key ingredients entering macroscopic Gibbs free energy function of a shape memory alloy (SMA) material. A new self-equilibrated eigenstrains influence moduli (SEIM) method is developed for consistent estimation of effective (macroscopic) thermostatic properties of solid materials, which in microscale can be regarded as amalgams of n-phase linear thermoelastic component materials with eigenstrains. The SEIM satisfy the self-consistency conditions, following from elastic reciprocity (Betti) theorem. The method allowed expressing macroscopic coherency energy and elastic complementary energy terms present in the general form of macroscopic Gibbs free energy of SMA materials in the form of semilinear and semiquadratic functions of the phase composition. Consistent SEIM estimates of elastic complementary energy, coherency energy and phase transformation strains corresponding to classical Reuss and Voigt conjectures are explicitly specified. The Voigt explicit relations served as inspiration for working out an original engineering practice-oriented semiexperimental SEIM estimates. They are especially conveniently applicable for an isotropic aggregate (composite) composed of a mixture of n isotropic phases. Using experimental data for NiTi alloy and adopting conjecture that it can be treated as an isotropic aggregate of two isotropic phases, it is shown that the NiTi coherency energy and macroscopic phase strain are practically not influenced by the difference in values of austenite and martensite elastic constants. It is shown that existence of nonzero fluctuating part of phase microeigenstrains field is responsible for building up of so-called stored energy of coherency, which is accumulated in pure martensitic phase after full completion of phase transition. Experimental data for NiTi alloy show that the stored coherency energy cannot be neglected as it considerably influences the characteristic phase transition temperatures of SMA material.Keywords SMA · NiTi alloys · Adaptive composite · Macroscopic free energy functions · Gibbs energy · Micromechanics · Coherence energy · Stored coherency energy · Ultimate phase transformation eigenstrains · Self-equilibrated eigenstrains influence moduli · SEIM · Effective property estimates · Martensitic phase transformationThe coming into existence of the present paper would not be possible without contributions and long discussions with Professor Bogdan Raniecki who passed away suddenly on August 2014. I dedicate this work to his memory. dx is an average of a local field over a region occupied by volume V α . When volume V α is occupied by phase α then A α denotes α phase average.It is accepted that internal energy and internal entropy of all kinds of martensitic phases at microscopic thermodynamic reference state (m.t.r.s.)-i.e., at zero local stresses ( σ (x) = 0) and reference temperature (T = T 0 ), are the same, e.g., (u 0 α, α =1 = u M α = u A − u 0 , u A ≡ u 0 1 ) and (s 0 α, α =1 = s M α = s A − s 0 , s A ≡...

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“…[5] and [376][377][378], employing a database to directly map the effective behavior from macroscopic information addressed in Refs. [379][380][381][382][383], transformation field analysis [384][385][386][387][388][389][390], or proper orthogonal/generalized decomposition [391-397].…”

Section: Analysis At the Rve Levelmentioning

confidence: 99%

Aspects of Computational Homogenization at Finite Deformations: A Unifying Review From Reuss' to Voigt's Bound

Saeb

Steinmann

Javili

2016

Applied Mechanics Reviews

185

138

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The objective of this contribution is to present a unifying review on strain-driven computational homogenization at finite strains, thereby elaborating on computational aspects of the finite element method. The underlying assumption of computational homogenization is separation of length scales, and hence, computing the material response at the macroscopic scale from averaging the microscopic behavior. In doing so, the energetic equivalence between the two scales, the Hill-Mandel condition, is guaranteed via imposing proper boundary conditions such as linear displacement, periodic displacement and antiperiodic traction, and constant traction boundary conditions. Focus is given on the finite element implementation of these boundary conditions and their influence on the overall response of the material. Computational frameworks for all canonical boundary conditions are briefly formulated in order to demonstrate similarities and differences among the various boundary conditions. Furthermore, we detail on the computational aspects of the classical Reuss' and Voigt's bounds and their extensions to finite strains. A concise and clear formulation for computing the macroscopic tangent necessary for FE 2 calculations is presented. The performances of the proposed schemes are illustrated via a series of two-and three-dimensional numerical examples. The numerical examples provide enough details to serve as benchmarks.

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On transformation strains and uniform fields in multiphase elastic media

Cited by 274 publications

References 14 publications

Triaxial Composite Model for Basic Creep of Concrete

Triaxial Composite Model for Basic Creep of Concrete

On consistent micromechanical estimation of macroscopic elastic energy, coherence energy and phase transformation strains for SMA materials

Aspects of Computational Homogenization at Finite Deformations: A Unifying Review From Reuss' to Voigt's Bound

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