Variational Quantum Algorithms for Hyperelasticity: Incorporating Nonlinear Constitutive Behavior

Abstract

This paper extends a recently proposed Variational Quantum Algorithm framework for nonlinear elasticity to a broader class of constitutive nonlinearities involving rational powers of the stretch. One-dimensional incompressible Ogden and Mooney-Rivlin models are employed as representative examples to demonstrate the proposed methodology. Nonlinear constitutive terms are transformed into forms compatible with the available quantum algorithmic primitives through the introduction of auxiliary variables and penalty constraints, yielding approximate solutions via a Variational Quantum Algorithm. An iterative correction strategy based on a sequence of Variational Quantum Algorithms is then introduced to improve solution accuracy. A Numerical example demonstrates the proposed approach.