Browsing by Author "Borokinni, Adebowale Samuel"

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    An investigation of a theory of strain-gradient plasticity accounting for energetic dependence on the divergence of the plastic strain
    (Mathematics,Obafemi Awolowo University, 2015) Borokinni, Adebowale Samuel
    This work considered strain-gradient plasticity theory. The effects of internal microforces in plastically deformed bodies were investigated through additional explicit dependence of energy function on the divergence of plastic strain. The principle of virtual power was employed to model the macroscopic and microscopic force balances; first and second law of thermodynamics were used to construct the local dissipation inequality; and von Mises yield criterion, local dissipation inequality together with tensor derivatives of free-energy function were used to establish the constitutive relations. These constitutive relations and microscopic force balance were employed in deriving the governing flow rule for the problem under consideration. For the purpose of numerical solution, a Ritz finite element method was used. The results obtained showed that internal microforces counterbalance the polar microforces in plastically deformed bodies. Furthermore, the obtained flow rule generalizes the Gurtin-Anand flow rule. In the case of plane strain problem, it was revealed that pure shear can be achieved even if the deformation process is not purely dissipative whereas, pure shear is only achieved for purely dissipative deformation in literature. For a fixed dissipative length scale l, and varying energetic length scales Q and L, the plastic strain in the plastically deformed bodies at any time t decreases. Finite element solutions for one dimensional visco-plastic problems showed that whenever the rate-sensitivity parameter m = 1, the plastic strain for each time attains a threshold, while the plastic strain increases with time. The finite element solution of a purely energetic process in which m = 0, revealed that the plastic strain is approximately zero at some region of the one dimensional visco-plastic solid. This study concluded that the internal microforces counterbalance the polar microstresses in plastically deformed bodies.