Theory of elasticity of coherent inclusions by means of non-metric geometry

✍ Scribed by F. Falk

• Publisher: Springer Netherlands
• Year: 1981
• Tongue: English
• Weight: 601 KB
• Volume: 11
• Category: Article
• ISSN: 0374-3535
• DOI: 10.1007/bf00058079

✦ Synopsis

The concept of extra or quasiplastic deformation is applied to the non-linear theory of elasticity of coherent inclusions in a matrix of different crystal structure. K.-H. Anthony's treatment of extra-deformation by means of non-metric differential geometry is reviewed. We replace his definition of the elastic connexion by a more obvious but equivalent one. The elastic effect of the inclusion can be represented by extra-dislocations whereas the extra-disclination density vanishes, even in the non-linear theory. It is shown that the elastic stress of an inclusion can be cancelled approximately by an arrangement of lattice dislocations. Extra-deformation and extra-dislocation density are specified for a simple model of an inclusion having suffered a martensitic transformation.

1 The stress in the neighbourhood of lattice disclinations would be much larger than either yield point or fracture stress. With regard to lattice disclinations see K.