Abstract
A simple and rigorous formulation of elastic component of elastoplastic model for geomaterials is presented. Although linear relation between elastic volumetric strain and mean principal stress in log scale is assumed in most of the usual models, linear relation between each principal stress and the corresponding principal elastic strain in log scale is assumed. Incorporating Poisson's ratio, three principal stresses vs. three elastic principal strain relation is obtained. Also, assuming coaxially between stresses and elastic strains, this relation can be transformed to stress- elastic strain relation in general coordinate. The material parameters of the proposed model of the elastic component are the same as those of the usual models, i.e., swelling index κ and Poisson's ratio ν. This proposed model can describe typical unloading behaviour of various shear tests and constant stress ratio unloading tests reported before.
Highlights
In 3D elastoplastic modelling, though there have been many discussions on the modelling of plastic component, few attentions are paid to elastic component
Elastic component of most elastoplastic models is expressed by incremental non-linear Hooke’s law using the swelling index and the Poisson’s ratio. According to this modelling, the elastic volumetric stain is independent of the stress path, but other strains depend on the stress path
From Eq (4), three principal stresses are expressed as the functions of three principal elastic strains
Summary
In 3D elastoplastic modelling, though there have been many discussions on the modelling of plastic component, few attentions are paid to elastic component. Elastic component of most elastoplastic models is expressed by incremental non-linear Hooke’s law using the swelling index and the Poisson’s ratio. According to this modelling, the elastic volumetric stain is independent of the stress path, but other strains (e.g., deviatoric strain) depend on the stress path. Implicit formulation such as return mapping in elastoplastic analysis requires unique relation not between stress increments and elastic strain increments but between stresses and elastic strains. Tangential Young’s modulus E is proportional to mean principal stress p and expressed as follows using the swelling index on e-lnp relation in isotropic or Ko unloading compression tests, and Poisson’s ratio : d=(2/3)( a- r) (%)
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