Uniaxial Tensile instabilities of a Class of Compressible Solids with Plastic Non-Normality.
Nisha Mohan (Caltech), Julia Greer (Caltech), Alan Needleman (University of North Texas), Justine Cheng (Polytechnic School)
Instability in Solids and Structures
Mon 2:40 - 4:00
Barus-Holley 190
A fundamental question that motivates exploring deformation of materials with complex microstructures is how to extract the intrinsic material response from simple mechanical tests. Motivated by a model that qualitatively captured the response of vertically aligned carbon nanotube (VACNT) pillars in uniaxial compression, we describe the uniaxial tensile response of a class of compressible elastic-viscoplastic solids. In[1, 2],an elastic viscoplastic constitutive relation with plastic compressibility, plastic non-normality and a hardening-softening-hardening hardness function was used to model experimentally obtained uniaxial compression data of cylindrical VACNT micro-pillars. Complex deformation modes were found in uniaxial compression, which include a sequential buckling-like collapse of the type seen in experiments. These complex deformation modes led to the overall stress-strain signature of the pillar not being of the same form as the input material hardness function. We explore the relation between the input material response and the overall stress strain behavior in uniaxial tension using the constitutive framework of [1, 2]. A simple one dimensional analysis reveals the types of instability modes to be expected. Dynamic, finite deformation finite element calculations are carried out to explore the dependence of diffuse necking, localized necking and propagating band deformation modes on characteristics of the hardness function. Attention is devoted to uncovering implications for obtaining intrinsic material properties of complex hierarchical structures, for example vertically aligned carbon nanotubes (VACNTs), from uniaxial tension experiments. [1&2] S. B. Hutchens, A. Needleman, and J. R. Greer, "Erratum to “Analysis of uniaxial compression of vertically aligned carbon nanotubes” [Journal of the Mechanics and Physics of Solids 59 (2011) 2227–2237]," Journal of the Mechanics and Physics of Solids, vol. 60, pp. 1753-1756, 10// 2012.