Modeling of pitting damage-induced ultrasonic nonlinearity in AL-Whipple shields of spacecraft: Theory, simulation, and experimental validation

Wuxiong Cao, Lei Xu, Zhongqing Su, Baojun Pang, Runqiang Chi, Lei Wang, Xiaoyu Wang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

7 Citations (Scopus)


Pitting damage in the Whipple shield of spacecraft, engendered by a hypervelocity impact (HVI, exceeding 3.0 km/s), is a specific damage modality in large-scale spacecraft (e.g., Space Station). Typically, it features multitudinous craters and cracks disorderedly scattered over a wide region, accompanied with a diversity of microstructural damages (e.g., dislocation plasticity, micro-voids and cracks). This damage modality induces highly complex, mutually-interfering wave scattering in the received ultrasonic waves, making signal interpretation a daunting task, let alone the quantitative characterization of a pitted region. With this motivation, a dedicated modeling technique is proposed to scrutinize the modulation mechanism of various modalities of pitting damage on the probing ultrasonic waves, based on retrofitted nonlinear constitutive equations by comprehensively considering all nonlinearities originated from different damage sources (e.g., inherent material imperfections, as well as the above HVI-induced intensified plasticity and micro-cracks, etc.). On this basis, a quantitative correlation between the nonlinear features (i.e., second harmonics) of ultrasonic waves and the pitting damage severity is established. The modeling technique is experimentally corroborated, and the results demonstrate good consistency in between, revealing that: (1) the proposed modeling approach is feasible to faithfully simulate and precisely evaluate pitting damage-incurred nonlinearities manifested in ultrasonic waves; (2) the ultrasonic nonlinearity intensifies with the increase of pitting damage severity; and (3) the detection sensibility and cumulative effect of second harmonics are related to the “internal resonance” conditions, representing by the excitation frequency. This study yields a structural health monitoring strategy for accurately characterizing pitting-type damage at an embryo stage and surveilling material deterioration progress continuously.

Original languageEnglish
Article number106659
JournalInternational Journal of Mechanical Sciences
Publication statusPublished - 1 Oct 2021


  • Finite element modeling
  • Hypervelocity impact
  • Pitting damage
  • Quantitative characterization
  • Ultrasonic nonlinearity

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • General Materials Science
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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