No abstract

No abstract

In this article biaxial constrained recovery in a thick-walled shape memory alloy (SMA) ring with a rectangular cross-section is modeled using the theory of generalized plasticity, which is developed by Jacob Lubliner and Ferdinando Auricchio. As a mechanical obstacle that delays free recovery in a SMA ring, a steel ring is used. The result of constrained recovery is the generation of high stresses in both the rings. All equations are written in a closed form in terms of infinite series. Theoretical results are compared with experimental findings and good agreement is found when SMA rings are in the domain of recoverable strains.

This contribution investigated repeated elastoplastic pure plane bending/unbending process of beams made of material with an elastic-linear hardening rheological model. The attention is focused on beams with cross sections which have at least one axis of symmetry and are initially straight or have constant radius of curvature. Elastoplastic deflection states of beams after repeated bending/unbending process are determined using the large displacement theory. Experiments were conducted to verify the theory for beams made of aluminium alloy AA 5050-H38 with rectangular cross sections. It is shown that maximal relative difference between experimental and theoretical results in the case of a largely curved beams after repeated bending/unbending process is 1.27%.

This paper analyzes large deflection profiles of slender, inextensible cantilever beams of prismatic and non-prismatic longitudinal shapes with rectangular cross-sections subjected to a concentrated moment at the free end. The stress-strain relationship of the material is represented by the Ludwick constitutive law. Different non-linear stress-strain relations in tensile and compressive domain are considered. The main purpose of this paper is to investigate the influence of geometrical and material non-linearities on the shape of the deflection curve. The solution of a strongly non-linear set of equations is obtained numerically. In the case when non-linear stress-strain relationship in tensile and compressive domain is identical, an analytical solution is given in terms of infinite series. Several examples for a variety of different shapes of beams are presented considering both linearly and non-linearly elastic materials in the elastic domain.KEY WORDS: large deflections, non-prismatic cantilever beam, end moment, Ludwick formula, material non-linearity.