Discontinuities and plasticity.

*(English)*Zbl 0667.73025
Nonsmooth mechanics and applications, CISM Courses Lect. 302, 279-340 (1988).

[For the entire collection see Zbl 0652.00016.]

According to the author plasticity and spatial discontinuities are two companion phenomena. The first part of the paper is devoted to the mathematical formulation of limit analysis (statical and kinematical formulations, homogeneous material, duality result, vector fields with bounded deformation, relaxed problems), and the second one to the elasto- plasticity theories (the Hencky model, and the Prandtl-Reuss model, the variational formulation for these models, and examples of discontinuous solutions). The problem of a thin layer of small width and compressed between two elastic bodies, when the width goes to zero is studied in part four (the case of elastic sheet compressed between two plastic bodies would, however, be more interesting from the physical point of view!).

The definition of epi-convergence, and a model of rigid blocks slipping one over the other, when the block size tends to zero (homogenized problem where the theory of epi-convergence is used), and the limits of variational problems are given in the last part of the paper. Open problems and bibliographical comments are given after each part.

According to the author plasticity and spatial discontinuities are two companion phenomena. The first part of the paper is devoted to the mathematical formulation of limit analysis (statical and kinematical formulations, homogeneous material, duality result, vector fields with bounded deformation, relaxed problems), and the second one to the elasto- plasticity theories (the Hencky model, and the Prandtl-Reuss model, the variational formulation for these models, and examples of discontinuous solutions). The problem of a thin layer of small width and compressed between two elastic bodies, when the width goes to zero is studied in part four (the case of elastic sheet compressed between two plastic bodies would, however, be more interesting from the physical point of view!).

The definition of epi-convergence, and a model of rigid blocks slipping one over the other, when the block size tends to zero (homogenized problem where the theory of epi-convergence is used), and the limits of variational problems are given in the last part of the paper. Open problems and bibliographical comments are given after each part.

Reviewer: N.Cristescu

##### MSC:

74C99 | Plastic materials, materials of stress-rate and internal-variable type |

74R20 | Anelastic fracture and damage |

74S30 | Other numerical methods in solid mechanics (MSC2010) |