Journal ArticleDOI
A theory of failure of material with thermal and memory effects
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In this paper, a generalization of hypo-elasticity to include thermal and memory effects is investigated theoretically, and the set of the constitutive equations are regarded as a linear transformation between seven-dimensional spaces composed of stretching and temperature rate, and of stress rate and entropy density rate.Abstract:
A generalization of hypo-elasticity to include thermal and memory effects is investigated theoretically. The set of the constitutive equations are regarded as a linear transformation between seven-dimensional spaces composed of stretching and temperature rate, and of stress rate and entropy density rate. The failure conditions are defined by the linear operator. The linear approximation of the constitutive equations for strain and temperature histories are presented. A special case of the dependence on the histories of deformation and temperature, called the function type, is proposed.read more
Citations
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Journal ArticleDOI
A unified approach to constitutive equations of inelasticity based on tensor function representations
S. Murakami,A. Sawczuk +1 more
TL;DR: In this paper, the applicability of the tensor function theory to the development of elaborate and rational constitutive equations of inelasticity is discussed to facilitate the description of the complicated in-elastic response of structural components.
References
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Journal ArticleDOI
An Approximation Theorem for Functionals, with Applications in Continuum Mechanics
Bernard D. Coleman,Walter Noll +1 more
TL;DR: In this paper, a brief discussion of the physical motivation behind the mathematical considerations to be presented in Part I of this paper is presented. But this discussion is limited to the case where the authors are concerned with a single point of view.
Book ChapterDOI
Foundations of Linear Viscoelasticity
Bernard D. Coleman,Walter Noll +1 more
TL;DR: The classical linear theory of viscoelasticity was apparently first formulated by Boltzmann1 in 1874, and much work has been done on the following aspects: solution of special boundary value problems, reformulation3,4 of the one-dimensional version of the theory in terms of new material functions (such as “creep functions” and frequency-dependent complex “impedances”) which appear to be directly accessible to measurement, experimental determination2b of the material functions for those materials for which the theory appears useful, prediction of the form of the
Journal ArticleDOI
A Generalized Hypo‐Elasticity and Derived Failure Condition
TL;DR: In this article, a generalized hypo-elasticity with memory is proposed, which is regarded as a linear transformation between the stress rate and the stretching, and a representation form of the constitutive functional is presented and the case of retarded history is discussed.
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