Generalized Maxwell-Kelvin Model for Viscoelastic Materials (LAW40) This law may only be applied to solid elements. Bulk behavior is assumed to be linear:(1) d p d t = K ε ˙ k k MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaadaWcaaqaai aadsgacaWGWbaabaGaamizaiaadshaaaGaeyypa0Jaam4saiqbew7a LzaacaWaaSbaaSqaaiaadUgacaWGRbaabeaaaaa@3FC0@ Shear behavior is computed using a shear factor as:(2) G ( t ) = G ∞ + ∑ 1 5 G i e − β i t MathType@MTEF@5@5@+= feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbbG8FasPYRqj0=yi0dXdbba9pGe9xq=JbbG8A8frFve9 Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaaciGGhbWaae WaaeaacaWG0baacaGLOaGaayzkaaGaeyypa0Jaci4ramaaBaaaleaa cqGHEisPaeqaaOGaey4kaSYaaabCaeaacaWGhbWaaSbaaSqaaiaadM gaaeqaaOGaamyzamaaCaaaleqabaGaeyOeI0IaeqOSdi2aaSbaaWqa aiaadMgaaeqaaSGaamiDaaaaaeaacaaIXaaabaGaaGynaaqdcqGHri s5aaaa@496E@ Figure 1. Maxwell-Kelvin Model β i are time decays, β i = G i η i = 1 τ i with τ i being relaxation time.
