Linear elasticity

Linear elasticity

Linear elasticity refers to a theory that explains how an elastic medium responds to external forces by deforming in a manner that is proportional to the applied stress. This theory is based on the assumption that the deformations are small and that the relationship between stress and strain is linear.From: Rock Mechanics and Engineering [2017], Compressive stress relaxation behavior of articular cartilage and its effects on fluid pressure and solid displacement due to non-Newtonian flow [2021]

Modeling Fluid Flow

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Published in Mayer Humi, Introduction to Mathematical Modeling, 2017

Mayer Humi

The basic assumption of linear elasticity is that for small deformations the strain and stress tensors are linearly related. Thus τij=∑m,nαijmnemn $$ \tau _{{ij}} = \mathop \sum \limits_{{m,n}}^{{}} \alpha _{{ijmn}} e_{{mn}} $$

Compressive stress relaxation behavior of articular cartilage and its effects on fluid pressure and solid displacement due to non-Newtonian flow

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Published in Computer Methods in Biomechanics and Biomedical Engineering, 2021

Umair Farooq, J. I. Siddique

Linear elasticity is another approach that can be used to analyze the deformation in articular cartilage. During deformation, solids become internally stressed due to external loading. It is a simplification of the more general nonlinear theory of elasticity (Ogden 1997). The major assumptions of linear elasticity are small deformations (or infinitesimal strains) and that the components of stress and strain are related linearly. In the case of linear elasticity, the stress is assumed such that they do not produce yielding in the material body. These assumptions are reasonable for many engineering materials and engineering design scenarios. Linear elasticity is therefore used extensively in structural analysis such as furniture, bridges, buildings, vehicles, and biological tissue, and engineering design, usually with the help of the finite element method.

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Modeling Fluid Flow

Compressive stress relaxation behavior of articular cartilage and its effects on fluid pressure and solid displacement due to non-Newtonian flow