2026/03/18 by Shawn Samuel Carl McAdam, Samuel Opoku Agyemang, Alexei F. Cheviakov +1 · 1 voice
Engineering · Mathematics · Physics and Astronomy · #Compressibility #Dispersion (optics) #Elasticity and Material Modeling #Elasticity and Wave Propagation #Hyperelastic material #Longitudinal wave #Love wave #Mechanical wave #Nonlinear system #Surface wave #Thermoelastic and Magnetoelastic Phenomena #Viscoelasticity #Wave propagation #math-ph #math.AP #math.NA #nlin.SI
paper · pdf · open access · doi:10.48550/arxiv.2603.18296
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2026/03/18 · arxiv published 2026/03/18 · arxiv updated 2026/03/18 · openalex created_date 2026/03/21 · openalex updated_date 2026/07/28
General equations describing shear displacements in incompressible hyperelastic materials, holding for an arbitrary form of strain energy density function, are presented and applied to the description of nonlinear Love-type waves propagating on an interface between materials with different mechanical properties. The model is valid for a broad class of hyper-viscoelastic materials. For a cubic Yeoh model, shear wave equations contain cubic and quintic differential polynomial terms, including viscoelasticity contributions in terms of dispersion terms that include mixed derivatives uxxt of the material displacement. Full (2+1)-dimensional numerical simulations of waves propagating in the bulk of a two-layered solid are undertaken and analyzed with respect to the source position and mechanical properties of the layers. Interfacial nonlinear Love waves and free upper surface shear waves are tracked; it is demonstrated that in the fully nonlinear case, the variable wave speed of interface and surface waves generally satisfies the linear Love wave existence condition c1 < \absv < c2, while tending to the larger material wave speed c1 or c2 for large times.