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The first constitutive equation (constitutive law) was developed by Robert Hooke and is known as Hooke's law.It deals with the case of linear elastic materials.Following this discovery, this type of equation, often called a "stress-strain relation" in this example, but also called a "constitutive assumption" or an "equation of state" was commonly used.
The microplane model, conceived in 1984, [1] is a material constitutive model for progressive softening damage. Its advantage over the classical tensorial constitutive models is that it can capture the oriented nature of damage such as tensile cracking, slip, friction, and compression splitting, as well as the orientation of fiber reinforcement.
Modeling them as linear functions can significantly simplify the differential constitutive equations that are used to describe the property. Equations describing relevant materials properties are often used to predict the attributes of a system. The properties are measured by standardized test methods.
A Burgers material is a viscoelastic material having the properties both of elasticity and viscosity. It is named after the Dutch physicist Johannes Martinus Burgers . Overview
The constitutive relation is expressed as a linear first-order differential equation: = + ˙ This model represents a solid undergoing reversible, viscoelastic strain. Upon application of a constant stress, the material deforms at a decreasing rate, asymptotically approaching the steady-state strain.
where is the volume fraction of the fibers in the composite (and is the volume fraction of the matrix).. If it is assumed that the composite material behaves as a linear-elastic material, i.e., abiding Hooke's law = for some elastic modulus of the composite and some strain of the composite , then equations 1 and 2 can be combined to give
Johannes Ferdinand "Hans" Besseling (10 March 1928 – 9 May 2015) [1] was professor emeritus of Engineering Mechanics at the Delft University of Technology, worked in the field of the application of solid mechanics to the analysis of structures; constitutive equations for the mathematical description of material behaviour. His specialities are ...
Constitutive equations for the type of mechanism have been developed for each deformation mechanism and are used in the construction of the maps. The theoretical shear strength of the material is independent of temperature and located along the top of the map, with the regimes of plastic deformation mechanisms below it.