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Shape-Programming in Hyperelasticity Through Differential Growth.

Rogelio Ortigosa-Martínez1, Jesús Martínez-Frutos2, Carlos Mora-Corral3,4

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Summary
This summary is machine-generated.

This study introduces a novel optimal control approach for shape programming in hyperelastic materials, enabling precise control over material deformation to achieve target shapes using growth tensors.

Keywords:
Differential growthHyperelasticityNumerical simulation methodsOptimal controlShape-programmingSoft robotics

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Area of Science:

  • Solid Mechanics
  • Materials Science
  • Computational Mechanics

Background:

  • The growth-driven shape-programming problem seeks to determine material growth to achieve desired deformations.
  • Existing methods often rely on simplifying assumptions like stress-free conditions.

Purpose of the Study:

  • To develop and analyze an optimal control framework for shape programming in hyperelastic bodies.
  • To investigate both compatible and incompatible growth scenarios.
  • To extend shape programming to include boundary conditions and external loads.

Main Methods:

  • Formulation within optimal control theory in hyperelasticity.
  • Utilizing Hausdorff distance for shape comparison and incorporating actuation complexity in cost functionals.
  • Mathematical analysis for well-posedness and gradient-based optimization algorithms for numerical approximation.
  • Application of inverse techniques for broader problem applicability.

Main Results:

  • The study proves the well-posedness of the formulated optimal control problem.
  • Gradient-based optimization algorithms are successfully applied for numerical approximation.
  • Inverse techniques are demonstrated to handle more generic situations than analytical methods.
  • Numerical experiments on beam-like and shell geometries validate the proposed scheme.

Conclusions:

  • The proposed optimal control framework effectively addresses the growth-driven shape-programming problem in hyperelasticity.
  • The inclusion of boundary conditions and external loads enhances the applicability of shape programming.
  • Numerical methods, particularly inverse techniques, provide a powerful tool for approximating solutions in complex scenarios.