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Related Concept Videos

Members Made of Elastoplastic Material01:19

Members Made of Elastoplastic Material

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The behavior of elastoplastic materials under bending stresses, particularly in structural members with rectangular cross-sections, is crucial for predicting material responses and understanding failure modes. Initially, when a bending moment is applied, the stress distribution across the section follows Hooke's Law and is linear and elastic. This distribution means the stress increases from the neutral axis to the maximum at the outer fibers, up to the elastic limit.
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Deformation occurs in axial and transverse directions when an axial load is applied to a slender bar. This deformation impacts the cubic element within the bar, transforming it into either a rectangular parallelepiped or a rhombus, contingent on its orientation. This transformation process induces shearing strain. Axial loading elicits both shearing and normal strains. Applying an axial load instigates equal normal and shearing stresses on elements oriented at a 45° angle to the load axis.
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The generalized Hooke's Law is a broadened version of Hooke's Law, which extends to all types of stress and in every direction. Consider an isotropic material shaped into a cube subjected to multiaxial loading. In this scenario, normal stresses are exerted along the three coordinate axes. As a result of these stresses, the cubic shape deforms into a rectangular parallelepiped. Despite this deformation, the new shape maintains equal sides, and there is a normal strain in the direction of the...
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The living membranes are flexible due to their fluid mosaic nature; however, their bending into different shapes is an active process regulated by specific lipids and proteins. The membrane bending can be transient as seen in vesicles or stable for a long time as in microvilli. Cells regulate the size, location, and duration of the membrane curvature.
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In the study of elastoplastic members subjected to bending moments, understanding the loading and unloading phases is crucial for assessing material behavior and structural integrity. During the loading phase, as the bending moment increases, the material initially responds elastically, adhering to Hooke's Law, where stress is directly proportional to strain. When the load exceeds the yield strength, plastic deformation occurs, resulting in permanent strain and deformation that remains even...
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Updated: Jul 23, 2025

Quantification of Strain in a Porcine Model of Skin Expansion Using Multi-View Stereo and Isogeometric Kinematics
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Interpretable data-driven modeling of hyperelastic membranes.

Victoria Salamatova1,2, Alexey Liogky2,3

  • 1Institute for Computer Science and Mathematical Modeling, I. M. Sechenov First Moscow State Medical University (Sechenov University), Moscow, Russia.

International Journal for Numerical Methods in Biomedical Engineering
|July 13, 2023
PubMed
Summary

We developed a new method for interpretable data-driven modeling of hyperelastic membrane deformation using Laplace stretch and finite element analysis. This approach enables automatic construction of constitutive relations directly from experimental data.

Keywords:
Laplace stretchconstitutive equationsdata-drivenhyperelastic materialmembrane

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Area of Science:

  • Computational mechanics
  • Materials science
  • Solid mechanics

Background:

  • Hyperelastic membrane deformation requires accurate constitutive models.
  • Existing data-driven approaches can lack interpretability.
  • Deriving constitutive relations from experimental data is challenging.

Purpose of the Study:

  • To propose an interpretable data-driven modeling approach for hyperelastic membrane deformation.
  • To utilize response functions based on Laplace stretch for direct data recovery.
  • To automatically construct data-driven constitutive relations.

Main Methods:

  • Employing response functions derived from hyperelastic potential and Laplace stretch.
  • Utilizing the finite element method for deformation analysis.
  • Recovering response functions directly from experimental data.

Main Results:

  • Explicit formulas for response functions were derived.
  • The approach successfully constructed data-driven constitutive relations.
  • Demonstrated efficacy in modeling membrane inflation using perforated membrane extension test data.

Conclusions:

  • The proposed approach offers an interpretable method for data-driven constitutive modeling.
  • Laplace stretch facilitates direct recovery of response functions from experimental data.
  • This facilitates automated construction of accurate constitutive models for hyperelastic materials.