Journal
APPLIED MATHEMATICAL MODELLING
Volume 40, Issue 5-6, Pages 3938-3950Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.apm.2015.10.045
Keywords
Logarithmic strains; Work-conjugacy; Mapping tensors; Hyperelasticity; Plasticity; Viscoelasticity
Funding
- Direccion General de Proyectos de Investigation of the Ministerio de Economia y Competitividad of Spain [DPI2011-26635]
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In this paper we show that mapping tensors may be constructed to transform any arbitrary strain measure in any other strain measure. We present the mapping tensors for many usual strain measures in the Seth-Hill family and also for general, user-defined ones. These mapping tensors may also be used to transform their work-conjugate stress measures. These transformations are merely geometric transformations obtained from the deformation gradient and, hence, are valid regardless of any constitutive equation employed for the solid. Then, advantage of this fact may be taken in order to simplify the form of constitutive equations and their numerical implementation and thereafter, perform the proper geometric mappings to convert the results-stresses, strains and constitutive tangents- to usually employed measures and to user-selectable ones for input and output We herein provide the necessary transformations. Examples are the transformation of small strains formulations and algorithms to large deformations using logarithmic strains. (C) 2015 Elsevier Inc. All rights reserved.
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