用于超弹性的变分量子算法：纳入非线性本构行为
Variational Quantum Algorithms for Hyperelasticity: Incorporating Nonlinear Constitutive Behavior
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中文总结 AI 辅助
该研究扩展变分量子算法框架至含应变率有理幂的本构非线性类，结合辅助变量与惩罚约束处理非线性项，通过迭代校正策略提升解精度，并用一维不可压缩模型验证方法有效性。
中文摘要 AI 辅助
本文将近期提出的用于非线性弹性的变分量子算法（VQA）框架扩展至更广泛的含应变率有理幂的本构非线性类，以一维不可压缩Ogden模型和Mooney-Rivlin模型为代表性示例验证所提方法。通过引入辅助变量与惩罚约束，将非线性本构项转换为适配现有量子算法基元的形式，经变分量子算法得到近似解；随后提出基于一系列变分量子算法的迭代校正策略以提升解的精度，数值算例验证了该方法的有效性。
英文摘要
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.
