Recent results in nonlinear viscoelastic wave propagation

In this article we present a review of some recent theoretical and experimental developments in the field of nonlinear viscoelastic wave propagation. Confining our attention to the case of one-dimensional strain, we review the theories of shock and acceleration wave propagation in general materials with memory and discuss the correlation of these theoretical predictions with some recent experimental results obtained for a particular polymeric solid. Fundamental to this work is the existence of steady shock waves and the fact that they can be generated in a one-dimensional experimental configuration. Using such experimental steady wave observations, a procedure is outlined for determining the material response functions necessary for predicting the growth or decay of shock and acceleration waves in viscoelastic materials. It is further shown that by using a particular constitutive assumption (either purely mechanical or thermomechanical) the complete one dimensional constitutive equation governing the material response can be evaluated from steady shock wave measurements. B paбoтe дaeтcя oбзop Heкoгopыч пocлeдHыч, тeopeтичecкич и экcпepимeитaльHыч paзpaбoтoк B oблacти pacпpocтpaHeHия HeлииeйHыч, Bязкoyпpyгич BoлH. OгpaHичиBaя BHимaHиe к cлyчaю oдHopaзмepHoй дeфopмaции, пepecмaтpиBaютcя тeopии pacпpocтpaHeHия yдapиыч и ycкopeHHыч BoлH B oбщич мaтepиaлaч c пaмятью. oбcyждaeтcя, тaкжe, кoppeляция мeждy зтими тeopeтичecкими пpeдcкaзaHиями и Heкoтopыми пocлeдHыми зкcпepимeHтaльHыми peзyльтaтaми, пoлyчeHHыми для oпpeдeлeHHыч тBepдыч тeл из пoлимepoB, ocHoBHым для зтoй paбoты яBляeтcя cyщecтBoBaHиe cтaциoHapHыч yдapHыч BoлH и фaкт, чтo мoжHo зти BoлHы oбpaзoBыBaть зкcпepимeHтaльHo для oдиopaзмepHoгo oчepтaHия. Ha ocHoBe экcпepимeHтaльHыч HaблюдeHий тaкичжe cтaциoHapHыч BoлH, дaeтcя oчepк мeтoдики oпpeдeлeHия фyHкций пoBeдeHия мaтepиaлoB, Heoбчoдимыч для пpeдcкaзaиия pocтa и зaтyчaHия yдapHыч и ycкopeHHыч BoлH B Bязкoyпpyгич мaтepиaлaч. Кpoмe тoгo yкaзaHo, чтo Ha ocHoBe пpимeHeHия ocoбoгo, кoHcтитyтиBHoгo пpeдпoлoжeHия (либo BпoлHe мeчaHичecкoгo либo тepмoдиHaмичecкoгo) мoжHo oпpeдeHить пoлHoe oдHo paзмepHoe кoHcтитyтиBиoe ypaBHeHиe пoBeдeHия мaтepиaлa, кaк pяз из измepeHий cтaпиoHapяoй yдapHoй BoлHы.