The Burgers material, also known as the Burgers model or Burgers body, is a phenomenological model used in rheology to describe the viscoelastic behavior of materials. It is a four-element model that combines the Maxwell model and the Kelvin-Voigt model connected in series. This arrangement allows the Burgers model to capture a wide range of viscoelastic phenomena, including instantaneous elastic response, delayed elastic response (creep recovery), viscous flow, and stress relaxation.
Components
The Burgers model is constructed from four ideal mechanical elements:- Elastic Spring ($E_M$): Represents the instantaneous elastic response and is part of the Maxwell model.
- Viscous Dashpot ($\eta_M$): Represents the irreversible viscous flow and is also part of the Maxwell model.
- Elastic Spring ($E_K$): Represents the delayed or retarded elastic response and is part of the Kelvin-Voigt model.
- Viscous Dashpot ($\eta_K$): Represents the delayed viscous response (retardation) and is also part of the Kelvin-Voigt model.
In the Burgers model, the Maxwell model (spring $E_M$ and dashpot $\eta_M$ in series) is connected in series with the Kelvin-Voigt model (spring $E_K$ and dashpot $\eta_K$ in parallel).
Material Behavior
The Burgers model is particularly adept at simulating complex time-dependent material behaviors:- Creep: When a constant stress is applied, the material exhibits an immediate elastic strain, followed by a time-dependent increase in strain. This creep process involves both a recoverable (delayed elastic) and an irrecoverable (viscous flow) component, eventually leading to a steady-state viscous flow if the stress is maintained.
- Creep Recovery: Upon removal of the constant stress, the instantaneous elastic strain is recovered immediately. The delayed elastic strain is then gradually recovered over time. However, the irreversible viscous deformation accumulated during the creep phase remains as permanent deformation.
- Stress Relaxation: Under a constant applied strain, the stress within the material decreases over time as the material reconfigures internally to relieve the strain.
- Constant Strain Rate: When subjected to a constant rate of strain, the model can predict the evolving stress, often showing an initial rapid increase followed by a more gradual rise towards a steady state, or a constant stress in the long term, depending on the relative magnitudes of the components.
Mathematical Description
The behavior of a Burgers material is governed by a linear ordinary differential equation that relates stress ($\sigma$), strain ($\varepsilon$), and their respective time derivatives. The constitutive equation typically involves two characteristic time constants: a relaxation time (associated with the Maxwell component) and a retardation time (associated with the Kelvin-Voigt component).Applications
The Burgers model finds extensive use across various scientific and engineering disciplines to characterize and predict the time-dependent mechanical properties of a diverse range of materials, including:- Polymers: Modeling the viscoelasticity of plastics, elastomers, and other polymeric systems.
- Biological Tissues: Describing the time-dependent mechanical response of soft tissues such as skin, muscles, tendons, and cartilage.
- Geological Materials: Analyzing creep and relaxation phenomena in rocks, soil, ice, and other geological formations, crucial for understanding long-term deformation and stability.
- Food Science: Understanding the texture, flow, and deformation characteristics of various food products.
- Bituminous Materials: Characterizing the viscoelastic properties of asphalts and other binders used in pavement engineering, which are highly temperature- and time-dependent.