Elastic-Plastic Constitutive Theory With Finite Deformation

Elastic-plastic constitutive theory is currently attracting much attention in academic circles of solid mechanics . There still exist some, even fundamental , problems which are yet unsolved. This thesis aims at investigating and attempting to clarify these problems. Some of the most influential constitutive elastic-plastic theories are analyzed and compared . And in the course of critical review of the existing theories , Some attempts are made for their refinement .The thesis is divided into three parts :The first part is devoted to the study of constitutive elastic theory with finite deformation . The Noll's Theorem (or Green-Naghdi- Rivlin's Theorem) is extended to the case of arbitrary deformable frame transformation , and hence the constitutive elastic relations can be founded on the basis of the principle of invariance of energy balance.In the second part the constitutive elastic-plastic theory is Studied The consistency of the multiplication decomposition of deformation gradient and the addition decomposition of strain tensor is demonstrated . Two conditions are explicitly elucidated for correct definition of elastic and plastic strain rate tensors , namely , the condition of objectivity with respect to the frame transformation ( called the condition of Q-objectivity) and the condition of invariance. with respect +o -the rotation of iV mediate configuration ( called the condition of Q-invariance. ) ? A "new general definition of elastic and plastic strain rate -tensors is suggested . The theory of Stmo and Ortiz is extended to the thermal case , and the condition of validity of the theory is demonstrated . Constitutive relations in rate "form in current configuration are derived for the theories of Hill and Rice , and of Mandel as well , with the internal variables being any scajars > vectors or tensors .The -third part is engaged \n the s+udy of spins used for co-rata-tional objective derivatives of tensors . The expression for the spin of Strain-rate frame is derived , and the spin is used in solving the simple shear problem by -the constitutive model of Prager and Ziegler . The results show that this spin is a suitable canditate for the use \n constitutive, relations.