Book Review: Finite deformation of an elastic solid

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On the Energy of Deformation of an Elastic Solid.

In the theory of elasticity as at present accepted' it is assumed that the energy of deformation is a function of the strain components and the various types of crystalline media are distinguished from one another and from an isotropic medium by the form of this function. It is the object of the present note to show that the mere assumption that the energy of deformation is a function of the st...

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Elastic-plastic Deformation at Finite Strains

In some circumstances, elastic-plastic deformation occurs in which both components of strain are finite. Such situations fall outside the scope of classical plasticity theory which assumes either infinitesimal strains or plastic-rigid theory for large strains. The present theory modifies the kinematics to include finite elastic and plastic strain components. For situations requiring this genera...

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Multiscale Evaluation of the Nonlinear Elastic Properties of Carbon Nanotubes Under Finite Deformation

This paper deals with the calculation of the elastic properties for single-walled carbon nanotubes (SWCNTs) under axial deformation and hydrostatic pressure using the atomistic-based continuum approach and the deformation mapping technique. A hyperelastic model based on the higher-order Cauchy-Born (HCB) rule being applicable at finite strains and accounting for the chirality and material nonli...

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Finite element analysis of elastic-plastic solids under Vickers indentation: surface deformation

Finite element modeling has been used to study the development of surface deformation during indentation with a Vickers indenter. A wide range of materials with different elastic modulus and yield stresses are examined. Results show that in a pyramidal indentation process, for a perfectly plastic material, sinking-in during loading can change to pile-up in unloading. This phenomenon depends on ...

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Finite-element Formulations for Problems of Large Elastic-plastic Deformation

Abstract-An Eulerian finite element formulation is presented for problems of large elastic-plastic flow. The method is based on Hill’s variational principle for incremental deformations, and is ideally suited to isotropically hardening Prandtl-Reuss materials. Further, the formulation is given in a manner which allows any conventions finite element program, for “small strain” elastic-plastic an...

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ژورنال

عنوان ژورنال: Bulletin of the American Mathematical Society

سال: 1952

ISSN: 0002-9904

DOI: 10.1090/s0002-9904-1952-09627-0