Setting Material Function Design Targets for Linear Viscoelastic Materials and Structures

Abstract

Rheologically complex materials are described by function-valued properties with dependence on a timescale (linear viscoelasticity), input amplitude (nonlinear material behavior), or more generally both (nonlinear viscoelasticity). This complexity presents a difficulty when trying to utilize these material systems in engineering designs. Here, we focus on linear viscoelasticity and a methodology to identify the desired viscoelastic behavior. This is an early-stage design step to optimize target (function-valued) properties before choosing or synthesizing a real material. In linear viscoelasticity, it is not obvious which properties can be treated as independent design variables. Thus, it is nontrivial to select the most design-appropriate constitutive model, to be as general as possible, but not violate fundamental restrictions. We use the Kramers–Kronig constraint to show that frequency-dependent moduli (e.g., shear moduli G′(ω) and G″(ω)) cannot be treated as two independent design variables. Rather, a single function such as the relaxation modulus (e.g., K(t) for force-relaxation or G(t) for stress relaxation) is an appropriate function-valued design variable. A simple case study is used to demonstrate the framework in which we identify target properties for a vibration isolation system. Viscoelasticity improves performance. Different parameterizations of the kernel function are optimized and compared for performance. While parameterization may limit the generality of the kernel function, we do include a nonobvious representation (power law) that is found in real viscoelastic material systems and in the spring-dashpot paradigm would require an infinite number of components. Our methodology provides a means to answer the question, “What viscoelastic properties are desirable?” This ability to identify targeted behavior will be useful for subsequent stages of the design process including the selection or synthesis of real materials.

Developing and Comparing Alternative Design Optimization Formulations for a Vibration Absorber Example

“…If the input frequency changes, however, vibration amplitude can increase significantly (i.e., the system is not robust to changes in frequency). One possible strategy to improve robustness to frequency changes is to utilize a damper with a frequencydependent VEM [16]. This is important because the drive motor will pass through a range of frequencies upon startup, even if it normally operates at a fixed speed.…”

A Multiobjective Adaptive Surrogate Modeling-Based Optimization (MO-ASMO) Framework Using Efficient Sampling Strategies

“…Sprung mass m 1 represents the vehicle body mass, while unsprung mass m 2 represents the mass of the suspension components and wheel set. A previous study demonstrated that viscoelasticity can improve vibration isolation performance throughout a wide range of frequencies [44,45]. We replaced the linear damper c 1 between sprung and unsprung mass in Fig.…”

“…In the sliding contact problem, this would support inclusion of additional physical phenomena in the model, while still enabling solution in a practical time period. Another possible implication of this algorithm is to simultaneous design problems of rheologically complex material and the corresponding system [51,44,45]. The algorithm presented here would be especially beneficial in this case as material functions design, e.g., viscoelasticity, need to be constrained to align them more closely with physically realizable materials.…”

Complex Fluids in Energy Dissipating Systems

“…Oscillatory characterization of complex fluids in general, and viscoelastic fluids in particular, provides information about the performance of the fluid at different frequencies and amplitudes, which are also parameters relevant in vibrations. Even though in all oscillatory shear tests (SAOS, MAOS and LAOS) the viscoelastic properties are traditionally characterized by means of the frequency-dependent shear viscoelastic moduli (G and G ), Corman et al [159] demonstrated in their pioneering work that these are not appropriate design parameters in general, as they cannot be treated as two independent design variables. According to this, the key to optimizing the design of passive energy dissipating systems based on viscoelastic fluids is to choose design variables encompassing the most general and measurable material behavior without violating fundamental restrictions (e.g., Kramers-Kronig), such as the relaxation modulus G(t), which is a single viscoelastic function meeting all these criteria.…”