Nonlinear Maxwell-Type Elastoviscoplastic Model: General Properties of Stress Relaxation Curves and Restrictions on the Material Functions
Authors: Khokhlov A.V. | Published: 22.11.2017 |
Published in issue: #6(75)/2017 | |
DOI: 10.18698/1812-3368-2017-6-31-55 | |
Category: Mathematics and Mechanics | Chapter: Solid Mechanics | |
Keywords: viscoelasticity, viscoplasticity, restrictions on the material functions, tension compression asymmetry, stress relaxation curves, equilibrium stress value, rate sensitivity, superplasticity, polymers |
The study analytically examines a nonlinear Maxwell-type constitutive relation with two arbitrary material functions in order to find out qualitative properties of the basic quasistatic curves generated by the model and to reveal its capabilities and applicability scope. The constitutive relation is targeted at adequate modeling of the main rheological phenomena set which is typical for non-ageing rheonomic materials exhibiting non-linear hereditary properties, strong positive strain rate sensitivity, secondary creep, yielding at constant stress and tension compression asymmetry. It is applicable for simulation of mechanical behavior of various polymers, their solutions and melts, solid propellants, sandasphalt concretes, composite materials, ices, titanium and aluminum alloys, ceramics at high temperature, etc. General qualitative properties of the stress relaxation curves generated by the model in uniaxial isothermal case are studied analytically under minimal primary restrictions on both material functions. We examined the relaxation rate evolution, conditions for monotonicity and convexity of relaxation curves, their asymptotics and stress limit value at infinity, their dependences on the material functions, a given strain level and initial loading stage characteristics. As a result, we reveаled the additional necessary restrictions which should be imposed on the material functions to provide an adequate description of basic rheological phenomena related to stress relaxation and typical test curves properties of a wide class of elastoviscoplastic materials. Finally, we discovered two different cases in the model behavior depending on qualitative properties of the material functions, namely, in the first case the equilibrium (limit) stress value is nonzero and the model simulates solid behavior, and in the second case the equilibrium value of stress is zero and the model simulates liquid behavior
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