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[Solved] Softening exhibits during hysteresis simulation with BB model

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Hello folks,

I use BB model in Abaqus to simulate hysteresis property of a rubber elastomer. The top side is fixed and i input a sinusoidal time-displacement compression superimposed with a mean pre-displacement from the bottom side (Fig.1a), then get the time-response force from the fixed point (Fig.1b). Eventually obtain the displacement-response force relationship, i.e. hysteresis loop (Fig.2 Stress scaling factor of BB model S=0.6 and Fig.3 S=1.2 ).


the right line describes the local amplification part,

the blue arrow indicates the trend of response force.

My question is:

1. Please check out the Figs. 2,3 and the blue arrows in Fig.1. Anyone knows why there is softening of response force when S=0.6 while it nearly doesnt show when S=1.2? Is it Mullins effect? That means BB model can automatically predict Mullins effect as well? And S influences the Mullins effect prediction?

2. Any one knows exactly why Prony series cannot predict the well-known Payne effect? I know its a linear viscoelastic model while BB model is a nonlinear one. But why linear model cannot define payne effect? Get confused anyone knows clearly?

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