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ver wonder why the stress in Maxwell materials disappears over time? What’s the secret behind this “relaxation time”
In the field of materials science, Maxwell materials represent the simplest viscoelastic model, showing the characteristics of typical liquids. This material exhibits viscous flow over long periods of time but has an additional elastic hindrance during rapid deformation. The name comes from the model proposed by James Clerk Maxwell in 1867, which brought the concept to prominence.
The biggest feature of Maxwell material is its stress attenuation after sudden deformation. This phenomenon is called stress relaxation, and one of the core behind it is the so-called "relaxation time".
The basic structure of the Maxwell model consists of a pure viscous damper and a pure elastic spring in series. Such a structure allows the material to express its stress and strain relationship in a certain way when it is acted upon by external forces. The length of the response time directly affects how the stress decays over time when the material encounters external stress or strain. The most obvious manifestation of this is the relaxation time.
What is relaxation time?
When a Maxwell material is suddenly deformed and maintained at a certain strain, the stress of the material will decay on a characteristic time scale. This characteristic time is the relaxation time, and its value is \({\frac {\eta }{E}}\), where E is the elastic modulus and eta is the viscosity coefficient. During this time, the material will exhibit continued stress reduction with strain, resulting in a final stress trend toward zero.
The relationship between the decay of stress and time over time has also aroused great interest in the behavior of materials. The change from fluid to solid gives a clearer interpretation in the context of restricted shapes. .
Under numerous strain conditions, the characteristics of Maxwell materials make it possible that the final deformation will show significant irreversibility when small stress is applied for a long time.
The relationship between stress and strain
In the Maxwell model, the changes in stress σ and strain ε are described by corresponding equations. These equations are based on time derivatives, which indicates the dynamic interaction between stress and strain. For a variety of different change situations, such as sudden stress, fixed strain rate or constant strain rate, the Maxwell model has its own suitable understanding mode.
When the material is suddenly subjected to stress σ0, the elastic component deforms immediately, while the deformation of the viscous component maintains a constant rate. This kind of performance shows the difference in the recovery ability and flow characteristics of the material over time, especially when the stress is relieved, the elastic part recovers and the viscous part no longer changes, bringing new thinking.
When a material is released, elastic and irreversible deformation creates a structure that cannot be ignored, showing how a material can be reshaped under pressure to achieve its long-lasting properties.
The meaning of dynamic modulus
The dynamic modulus of a Maxwell material is more than just a number, it reflects how the material behaves at different frequencies. Under different operating conditions, the material's response varies with the intensity and duration of applied stress, further highlighting its rheological properties. This allows scientists and engineers to consider these properties when designing new materials to address a variety of practical functional needs.
Maxwell materials research provides the foundation for many industries, including polymers, metals, and biomaterials. Whether it is used to design excellent engineering systems or explore new applications in medicine, there is no doubt that understanding of their essential properties is the key to success.
However, the interactive relationship between the irreversibility of strain and time forces us to think, does this mean that the limits of the material itself and the eternal change are intertwined with each other?
