The material motion satisfies the formal equationequation(28)ρsd2xdt2=∇·σ,where ρs CCG-63802 the material density, x is the position vector of the material and σ is the Cauchy stress tensor. If we denote F the deformation gradient tensor, then the Cauchy stress tensor is computed byequation(29)σ=1JFSFT,where J is the determinant of F and S is the second Piola-Kirchhoff stress tensor.
In the present study, a viscoelastic or a visco-plastic material layer over a non-deformable substrate is considered. For illustration, a polyurea-like material is used and is modeled as a viscoelastic material with the following time dependent values for the shear modulus, G:equation(30)G(t)=G∞+(Go-G∞)e-βt,G(t)=G∞+(Go-G∞)e-βt,with Go and G∞ being the initial and long term values of the shear modulus and β the relaxation time. The values selected for these parameters are shown in the corresponding section below.
The second material model tectonic plates we used was based on the Johnson–Cook model , which relates the stress, σ, to the effective plastic strain, ?p , normalized strain rate, ε?p∗, and normalized temperature, T∗:equation(31)σ=[A+Bεpn][1+Clnε?p∗][1-T∗m].