Constitutive modeling of isotropic hyperelastic materials using proposed phenomenological models in terms of strain invariants

Rubber‐like materials deform largely and nonlinearly under loading and preserve their initial configuration after removal of the load. These materials are usually modeled as being homogeneous, isotropic, and incompressible elastic solids that are supported by experimental data. In this article, a general form for the strain energy density of these materials is assumed as the sum of two independent functions of the first and second strain invariants. Applying the essential requirements on the form of the strain energy density, the mathematical form of these functions is obtained as polynomial, logarithmic, and exponential. Then a general form is derived for the strain energy density of compressible materials and its effectiveness is evaluated for hydrostatic compression and uniaxial tension tests. The determination of material parameters and the evaluation of effectiveness of models are done based on the correlation between the values of the strain energy density (rather than the stresses) cast from the theory and the test data. Comparison of the theoretical predictions with the experimental data indicates that the represented models can achieve a satisfactory agreement with the behavior of different materials. POLYM. ENG. SCI., 56:299–308, 2016. © 2015 Society of Plastics Engineers     

Constitutive modeling of rubberlike materials based on consistent strain energy density functions

Rubberlike materials are characterized by high deformability and reversibility of deformation. From the continuum viewpoint, a strain energy density function is postulated for modeling the behavior of these materials. In this paper, a general form for the strain energy density of these materials is proposed from a phenomenological point of view. Based on the Valanis‐Landel hypothesis, the strain energy density of incompressible materials is expressed as the sum of independent functions of the principal stretches meeting the essential requirements on the form of the strain energy density. It is cleared that the appropriate mathematical expressions for constitutive modeling of these materials are polynomial, logarithmic, and particularly exponential functions. In addition, the material parameters are calculated using a novel procedure that is based on the correlation between the values of the strain energy density (rather than the stresses) cast from the test data and the theory. In order to evaluate the performance of the proposed strain energy density functions, some test data of rubberlike materials with pure homogeneous deformations are used. It is shown that there is a good agreement between the test data and predictions of the models for incompressible isotropic materials. POLYM. ENG. SCI., 2010. © 2010 Society of Plastics Engineers     

Crisis in Urban Water Systems during the Reconstruction Period: A System Dynamics Analysis of Alternative Policies after the 2003 Earthquake in Bam-Iran

Quick restoration of critical infrastructure systems, such as water, electrical power, natural gas, and transportation systems, are essential for rapid and effective post disaster recovery and reconstruction process. A number of previous studies have assessed vulnerability of infrastructure systems to various hazards such as earthquakes, but seldom have the impacts of post disaster policies been considered. In its assessment of the water system in post disaster situation after Bam earthquake, this paper examines the impacts of various reconstruction as well as water management policies on the system failure in operation in terms of the ability of Bam urban water system to meet increased demand trends. Adopting a system dynamics modeling approach and the concept of viability loops, the paper will show that in order to minimize further crisis in the water system during the reconstruction period stricter water management policies need to be considered.     

Hyperelastic materials behavior modeling using consistent strain energy density functions

Hyperelastic materials have high deformability and nonlinearity in load–deformation behavior. Based on a phenomenological approach, these materials are treated as a continuum, and a strain energy density is considered to describe their hyperelastic behavior. In this paper, the mechanical behavior characterization of these materials is studied from the continuum viewpoint. For this purpose, the strain energy density is expressed as sum of independent functions of the mutual multiple of principal stretches. These functions are determined by applying the governing postulates on the form of the strain energy density. It is observed that a consistent strain energy density is expressible in terms of the mathematical functions of polynomial, power law, logarithmic and particularly exponential. The proposed strain energy density functions cover modeling both of compressible and incompressible materials. Moreover, the material parameters of these models are calculated based on the correlation between the values of the strain energy density (rather than the stresses) cast from the test data and the theory. In order to investigate the appropriateness of the proposed models, several experimental data for incompressible and compressible isotropic materials under homogeneous deformations are examined in which the predictions of the proposed models show a good agreement with experimental data.     

Design of spherical vessels under steady-state thermal loading using thermo-elasto–plastic concept

Governing equilibrium equations of thick-walled spherical vessels made of material following linear strain hardening and subjected to a steady-state radial temperature gradient using elasto–plastic analysis are derived. By considering a maximum plastic radius and using the concept of thermal autofrettage for the strengthening mechanism, the optimum wall thickness of the vessel for a given temperature gradient across the wall thickness is obtained. Finally, in the case of thermal loading on a vessel, the effect of convective heat transfer on the optimum thickness is studied and a general formula for the optimum wall thickness and design graphs for several different cases are presented.     

Inhibition of aluminum corrosion in acid solution by environmentally friendly antibacterial corrosion inhibitors: Experimental and theoretical investigations

Protection of Metals and Physical Chemistry of Surfaces - The inhibition performance of penicillin G(I), methicillin(II) and nafcillin(III) on the corrosion of aluminum in a 1 M HCl solution has...     

Constitutive modeling of visco-hyperelastic behavior of double-network hydrogels using long-term memory theory

Double-network hydrogels with viscoelastic behavior are appropriate materials for biomechanical applications. In this article, the standard linear solid (SLS) rheological model for the linear viscoelastic materials is generalized to the viscoelastic materials with large nonlinear deformations. Based on this viewpoint, the constitutive equation is proposed as sum of two parts including the strain-dependent elastic stress, and the viscous stress, which depends on the strain and strain rate. The elastic part of the stress is modeled via considering a hyperelastic strain energy function, while the main core of the viscous stress part requires a time-dependent weight function to satisfy the long-term memory fading principle. In addition, the weight function is proposed such that it can capture the mechanical behavior trend corresponding to the strain and strain rate for a double-network hydrogel in the relaxation test. Finally, to evaluate the performance of the proposed constitutive equation for the mechanical behavior modeling of double-network hydrogels, the tests on these materials have been used, and the material parameters are determined from fitting the experimental results to the theory. The agreement of test and theory results showed that the proposed model is capable to model the mechanical behavior of double-network hydrogels.     

New polynomial strain energy function; application to rubbery circular cylinders under finite extension and torsion

In this article, a strain energy density function is proposed in terms of the principal invariants of the left Cauchy‐Green strain tensor for Rubber‐like materials. This model due to its mathematical structure lies in the category of polynomial hyperelastic models. To compare the performance of the proposed model with the Rivlin set, some test data of rubber‐like materials with pure homogeneous deformations are used. It is shown that the proposed model has better agreement with the test data compared to the selected model. As an application of the proposed model, it is used to obtain a closed form solution for analysis of rubbery solid circular cylinders with S‐shaped and semi J‐shaped mechanical behavior under the torsion superimposed on the axial extension. Moreover, the results predicted from the proposed model are compared to classic models to investigate the results accuracy for simplification done. © 2014 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2015 , 132, 41718.