Geodesic
Quasistatic frictional problems for elastic and viscoelastic materials
Applications of Mathematics, Tome 47 (2002) no. 4, pp. 341-360 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We consider two quasistatic problems which describe the frictional contact between a deformable body and an obstacle, the so-called foundation. In the first problem the body is assumed to have a viscoelastic behavior, while in the other it is assumed to be elastic. The frictional contact is modeled by a general velocity dependent dissipation functional. We derive weak formulations for the models and prove existence and uniqueness results. The proofs are based on the theory of evolution variational inequalities and fixed-point arguments. We also prove that the solution of the viscoelastic problem converges to the solution of the corresponding elastic problem, as the viscosity tensor converges to zero. Finally, we describe a number of concrete contact and friction conditions to which our results apply.
We consider two quasistatic problems which describe the frictional contact between a deformable body and an obstacle, the so-called foundation. In the first problem the body is assumed to have a viscoelastic behavior, while in the other it is assumed to be elastic. The frictional contact is modeled by a general velocity dependent dissipation functional. We derive weak formulations for the models and prove existence and uniqueness results. The proofs are based on the theory of evolution variational inequalities and fixed-point arguments. We also prove that the solution of the viscoelastic problem converges to the solution of the corresponding elastic problem, as the viscosity tensor converges to zero. Finally, we describe a number of concrete contact and friction conditions to which our results apply.
DOI : 10.1023/A:1021753722771
Classification : 49J40, 58E35, 74B99, 74D05, 74M10
Keywords: elastic material; viscoelastic material; frictional contact; evolution variational inequality; fixed point; weak solution; approach to elasticity; subdifferential boundary conditions 
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     title = {Quasistatic frictional problems for elastic and viscoelastic materials},
     journal = {Applications of Mathematics},
     pages = {341--360},
     year = {2002},
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Chau, Oanh; Motreanu, Dumitru; Sofonea, Mircea. Quasistatic frictional problems for elastic and viscoelastic materials. Applications of Mathematics, Tome 47 (2002) no. 4, pp. 341-360. doi: 10.1023/A:1021753722771

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