Maxwell Viscoelastic Stress Relaxation Calculator

Viscoelastic Mechanics: Calculate time-dependent relaxation modulus ($G(t)$), instantaneous stress decay ($\tau(t)$), and Deborah number ($De$).

Prony Series Maxwell Modes

Mode 1 Modulus $g_1$ (kPa):

Mode 1 Relaxation $\lambda_1$ (s):

Mode 2 Modulus $g_2$ (kPa):

Mode 2 Relaxation $\lambda_2$ (s):

Equilibrium Modulus $G_e$ (kPa):

Step Strain & Observation Time

Step Strain $\gamma_0$ (fraction):

Observation Time $t$ (s):

Stress Relaxation Output

Relaxation Modulus ($G(t)$)

-- kPa

Initial G(0): -- kPa

Decayed Stress ($\tau(t)$)

-- kPa

Initial τ(0): -- kPa

Stress Remaining

-- %

Relaxed: -- %

Deborah Number ($De$)

Behavior regime

Generalized Maxwell Principles:

• $G(t) = G_e + \sum g_i \exp(-t / \lambda_i)$. Uncrosslinked melts decay to zero ($G_e = 0$); crosslinked rubbers retain elastic plateau ($G_e > 0$).

• Zero-shear viscosity is the integral of relaxation modulus: $\eta_0 = \int_0^\infty G(t) dt = \sum g_i \lambda_i$.

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Maxwell Viscoelastic Stress Relaxation Calculator

Prony Series Maxwell Modes

Step Strain & Observation Time

Stress Relaxation Output

Frequently Asked Questions