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State of the Art and Future Trends in Material Modeling pp 443–484Cite as

Hencky Strain and Logarithmic Rate for Unified Approach to Constitutive Modeling of Continua

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Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 100))

Abstract

A survey is presented for new approaches and main results in developing finite deformation elastic and inelastic constitutive models of continua based on Hencky’s logarithmic strain and the co-rotational logarithmic rate. Emphasis is placed on four aspects, including (i) a new set of Hencky invariants by means of which new and explicit approaches are established to obtain multi-axial elastic potentials for rubber-like solids; (ii) log-rate-based self-consistent elastoplastic constitutive models for finite deformation behaviors of usual metals, shape memory alloys and soft solids; (iii) innovative elastoplastic J2–flow models automatically incorporating cyclic and non-cyclic failure effects as inherent constitutive features; as well as (iv) the latest discovery of the deformable micro-continua that display all known quantum effects exactly as do quantum entities at atomic scale, such as electrons, etc. These suggest that both Hencky strain and the co-rotational logarithmic rate play a unified role in modeling large elastic and inelastic deformation behaviors of a wide variety of continua covering usual metals and alloys, shape memory alloys, polymeric solids and, perhaps unexpectedly, quantum entities at atomic scale. In particular, complete responses over the entire strain range up to failure are also covered in a broad, unified sense. In passing, most recent issues raised concerning the appropriateness of the logarithmic rate with reference to the elastoplastic J2–flow model are clarified by examining the applicability ranges of both the Hencky elastic potential and the von Mises yield function, etc.

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Authors and Affiliations

  1. School of Mechanics and Construction Engineering and MOE Key Lab of Disaster Forecast and Control in Engineering, Jinan University, 510632, Guangzhou, China

    Si-Yu Wang, Lin Zhan, Hui-Feng Xi & Heng Xiao

  2. Institute of Mechanics, Ruhr-University Bochum, D-44780, Bochum, Germany

    Otto T. Bruhns

  3. Shanghai Institute of Applied Mathematics and Mechanics & School of Mechanics and Engineering Science, Shanghai University, 200072, Shanghai, China

    Heng Xiao

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  1. Si-Yu Wang
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  2. Lin Zhan
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  3. Hui-Feng Xi
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  4. Otto T. Bruhns
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  5. Heng Xiao
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Correspondence to Heng Xiao .

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Editors and Affiliations

  1. Faculty of Mechanical Engineering, Otto von Guericke University Magdeburg, Magdeburg, Sachsen-Anhalt, Germany

    Holm Altenbach

  2. Faculty of Mechanical Engineering, Esslingen University of Applied Sciences, Esslingen, Germany

    Andreas Öchsner

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Wang, SY., Zhan, L., Xi, HF., Bruhns, O.T., Xiao, H. (2019). Hencky Strain and Logarithmic Rate for Unified Approach to Constitutive Modeling of Continua. In: Altenbach, H., Öchsner, A. (eds) State of the Art and Future Trends in Material Modeling . Advanced Structured Materials, vol 100. Springer, Cham. https://doi.org/10.1007/978-3-030-30355-6_19

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