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RESEARCH PAPERS

# Multiscale Thermodynamic Significance of the Scale Invariance Approach in Continuum Inelasticity

[+] Author and Article Information
Q. Yang

Department of Hydraulic Engineering, Tsinghua University, Beijing 100084, P. R. Chinayangq@tsinghua.edu.cn

X. Chen

School of Mechanics & Civil Engineering, China University of Mining & Technology (Beijing), Beijing 100083, P. R. China

W. Y. Zhou

Department of Hydraulic Engineering, Tsinghua University, Beijing 100084, P. R. China

In this paper, Einstein’s summation convention is adopted for repeated indexes. However, if an index range is listed like $α$ in Eq. 22, the index is considered as a free index without the summation convention.

Even so, no actual inelastic behavior is likely to be so simply characterized, as remarked by Rice (3).

J. Eng. Mater. Technol 128(2), 125-132 (Aug 05, 2005) (8 pages) doi:10.1115/1.2172271 History: Received January 02, 2005; Revised August 05, 2005

## Abstract

In this paper, the scale invariance approach from micro- to macro-plasticity by Aifantis (1995, “From Micro- to Macro-plasticity: The Scale Invariance Approach,” ASME J. Eng. Mater., 117, pp. 352–355) and Ning and Aifantis (1996, “Anisotropic Yield and Plastic Flow of Polycristalline Solids,” Int. J. Plasticity, 12, pp. 1221–1240) is investigated within Rice’s normality structure (1971, “Inelastic Constitutive Relations for Solids: An Integral Variable Theory and its Application to Metal Plasticity,” J. Mech. Phys. Solids, 19, pp. 433–455; 1975, “Continuum Mechanics and Thermodynamics of Plasticity in Relation to Microscale Deformation Mechanisms,” Constitutive Equations in Plasticity, A. S. Argon, ed., MIT Press, Cambridge, MA, pp. 23–79). The normality structure provides a minimal framework of multiscale thermodynamics, and the dissipation equivalence between the microscale and macroscale is ensured by a variational equation which can be further formulated into principle of maximum equivalent dissipation. It is revealed in this paper that within the framework of normality structure, the so-called hypothesis of generalized scale invariance holds for the kinetic rate laws, flow rules, and orthogonality conditions in the sense of Aifantis (1995, “From Micro- to Macro-plasticity: The Scale Invariance Approach”). Stemming from Rice’s kinetic rate laws, the generalized scale invariance reflects the inherent self-consistent character of the normality structure. If the plastic work rate is assumed to be equal to the intrinsic dissipation rate, the kinematic hardening plasticity as a demonstration of the scale invariance approach by Aifantis (1995, “From Micro- to Macro-plasticity: The Scale Invariance Approach”), can be well accommodated within the framework of normality structure. Therefore, the scale invariance approach is justified from a multiscale thermodynamic viewpoint. It is further shown that the maximization procedure in this approach just corresponds to the principle of maximum equivalent dissipation.

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