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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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Residual stresses reside in a structure even after removing the original stress inducer. This phenomenon often arises from varied plastic deformations across different parts of a structure. Consider a rod stretched beyond its yield point. It will not regain its original length due to permanent deformation. Even after load removal, the rod does not entirely lose stress because of uneven plastic deformations, resulting in residual stresses. The computation of these stresses in structures is...
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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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Studying stress transformation is essential in understanding how stress components within a material, like a cube under plane stress, change with rotation. This change is analyzed by considering a prismatic element within the cube. As the element rotates, the stress components acting on it—both normal and shearing stresses—change in magnitude and orientation. This change is quantified using trigonometric functions of the rotation angle, relating the forces acting on the rotated element's...
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In materials that exhibit elastic and plastic behavior, known as elastoplastic materials, residual stresses can accumulate when these materials experience plastic deformation. This deformation arises from either high levels of shearing stress or significant strains. Residual stresses are internal stresses that persist within a material after removing the external force causing deformation. This phenomenon is demonstrated when observing the behavior of a shaft under torque; notably, the...
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Modelling Volumetric Growth in Soft Solids via Residual Stress.

Ruoyu Huang1, Raymond W Ogden2, Raimondo Penta2

  • 1Lightweight Manufacturing Centre, University of Strathclyde, Renfrew, PA3 2EF UK.

Journal of Elasticity
|September 22, 2025
PubMed
Summary

This study advances nonlinear elasticity theory for volumetric growth in soft solids by using residual stress in unloaded configurations to model developing structures and stresses. Computational examples demonstrate insights into residual stress and morphology development.

Keywords:
Nonlinear elasticityResidual stressVolumetric growth

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Area of Science:

  • Continuum Mechanics
  • Solid Mechanics
  • Biomechanics

Background:

  • Nonlinear elasticity theory for volumetric growth was previously introduced.
  • Residual stress in intact unloaded configurations is key to understanding growth.
  • Modeling growth requires assessing developing unloaded configurations and residual stresses.

Purpose of the Study:

  • To further develop and apply nonlinear elasticity theory for volumetric growth.
  • To utilize residual stress in unloaded configurations for growth assessment.
  • To computationally illustrate growth in soft solids.

Main Methods:

  • The theory is formulated using free energy per unit mass and associated energy functions.
  • A thick-walled spherical shell model is used for illustration.
  • Computational programs are outlined for analyzing developing configurations.

Main Results:

  • The study examines growth of a thick-walled spherical shell using prototype energy functions.
  • Several growth laws for spherical shells under internal pressure are discussed.
  • Numerical results illustrate the evolution of growth and associated residual stress.

Conclusions:

  • Growth modeling based on unloaded configurations offers insights into residual stress and morphology.
  • These developments are accessible to experimental observation.
  • The presented theory and computational examples provide a framework for analyzing volumetric growth in soft solids.