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A generalized strain approach to anisotropic elasticity.

ABSTRACT: This work proposes a generalized Lagrangian strain function [Formula: see text] (that depends on modified stretches) and a volumetric strain function [Formula: see text] (that depends on the determinant of the deformation tensor) to characterize isotropic/anisotropic strain energy functions. With the aid of a spectral approach, the single-variable strain functions enable the development of strain energy functions that are consistent with their infinitesimal counterparts, including the development of a strain energy function for the general anisotropic material that contains the general 4th order classical stiffness tensor. The generality of the single-variable strain functions sets a platform for future development of adequate specific forms of the isotropic/anisotropic strain energy function; future modellers only require to construct specific forms of the functions [Formula: see text] and [Formula: see text] to model their strain energy functions. The spectral invariants used in the constitutive equation have a clear physical interpretation, which is attractive, in aiding experiment design and the construction of specific forms of the strain energy. Some previous strain energy functions that appeared in the literature can be considered as special cases of the proposed generalized strain energy function. The resulting constitutive equations can be easily converted, to allow the mechanical influence of compressed fibres to be excluded or partial excluded and to model fibre dispersion in collagenous soft tissues. Implementation of the constitutive equations in Finite Element software is discussed. The suggested crude specific strain function forms are able to fit the theory well with experimental data and managed to predict several sets of experimental data.

SUBMITTER: Shariff MHBM

PROVIDER: S-EPMC8742056 | biostudies-literature |

REPOSITORIES: biostudies-literature

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Project description:The extracellular matrix (ECM) of the lung provides physical support and key mechanical signals to pulmonary cells. Although lung ECM is continuously subjected to different stretch levels, detailed mechanics of the ECM at the scale of the cell is poorly understood. Here, we developed a new polydimethylsiloxane (PDMS) chip to probe nonlinear mechanics of tissue samples with atomic force microscopy (AFM). Using this chip, we performed AFM measurements in decellularized rat lung slices at controlled stretch levels. The AFM revealed highly nonlinear ECM elasticity with the microscale stiffness increasing with tissue strain. To correlate micro- and macroscale ECM mechanics, we also assessed macromechanics of decellularized rat lung strips under uniaxial tensile testing. The lung strips exhibited exponential macromechanical behavior but with stiffness values one order of magnitude lower than at the microscale. To interpret the relationship between micro- and macromechanical properties, we carried out a finite element (FE) analysis which revealed that the stiffness of the alveolar cell microenvironment is regulated by the global strain of the lung scaffold. The FE modeling also indicates that the scale dependence of stiffness is mainly due to the porous architecture of the lung parenchyma. We conclude that changes in tissue strain during breathing result in marked changes in the ECM stiffness sensed by alveolar cells providing tissue-specific mechanical signals to the cells. STATEMENT OF SIGNIFICANCE: The micromechanical properties of the extracellular matrix (ECM) are a major determinant of cell behavior. The ECM is exposed to mechanical stretching in the lung and other organs during physiological function. Therefore, a thorough knowledge of the nonlinear micromechanical properties of the ECM at the length scale that cells probe is required to advance our understanding of cell-matrix interplay. We designed a novel PDMS chip to perform atomic force microscopy measurements of ECM micromechanics on decellularized rat lung slices at different macroscopic strain levels. For the first time, our results reveal that the microscale stiffness of lung ECM markedly increases with macroscopic tissue strain. Therefore, changes in tissue strain during breathing result in variations in ECM stiffness providing tissue-specific mechanical signals to lung cells.

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A generalized strain approach to anisotropic elasticity.

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