Chapter 4
Unified Mechanics Theory
The term unified is used to describe the unification of universal laws of motion of
Newton and laws of thermodynamics at ab-initio level. As we discussed in earlier
chapters, Newton’s laws do not account for energy loss. They only govern what
happens to a system in initial moment a load is applied. However, the laws of
thermodynamics control what happens after the initial moment over time. Historically, continuum mechanics is based on the laws of Newton only and phenomenological test data fit empirical models that are supposed to satisfy thermodynamics’
laws introduce energy loss... In the next section, we will discuss the earlier work on
using thermodynamics in continuum mechanics.
4.1 Literature Review of Use of Thermodynamics
in Continuum Mechanics
Efforts to unify Newtonian mechanics and thermodynamics have been attempted
since the first formulation of laws of thermodynamics. Because Newton’s laws do
not account for dissipation of energy, researchers used different methods to incorporate energy dissipation into mechanics formulations to be able to formulate
degradation, fracture, and fatigue and life span predictions. Most of these efforts
have been based on phenomenological curve fitting methods, where a polynomial
potential is used to curve fit the fracture, or degradation test data. There are no
unifying theme among these models other than fitting a polynomial to a test data and
using it in conjunction with Newton’s laws. For the sake of completeness, we will
summarize some of them. While we do not claim to include every effort, we will
summarize the most well-known work in the field.
Lagrangian mechanics (1781) [long before Thermodynamics laws were written]
can be considered the first attempt to include nonconservative forces into Newton’s
laws. Quoting from Haddad’s (2017) seminal work on literature review of
© Springer Nature Switzerland AG 2021
C. Basaran, Introduction to Unified Mechanics Theory with Applications,
https://doi.org/10.1007/978-3-030-57772-8_4
115
Unified Mechanics Theory
The term unified is used to describe the unification of universal laws of motion of
Newton and laws of thermodynamics at ab-initio level. As we discussed in earlier
chapters, Newton’s laws do not account for energy loss. They only govern what
happens to a system in initial moment a load is applied. However, the laws of
thermodynamics control what happens after the initial moment over time. Historically, continuum mechanics is based on the laws of Newton only and phenomenological test data fit empirical models that are supposed to satisfy thermodynamics’
laws introduce energy loss... In the next section, we will discuss the earlier work on
using thermodynamics in continuum mechanics.
4.1 Literature Review of Use of Thermodynamics
in Continuum Mechanics
Efforts to unify Newtonian mechanics and thermodynamics have been attempted
since the first formulation of laws of thermodynamics. Because Newton’s laws do
not account for dissipation of energy, researchers used different methods to incorporate energy dissipation into mechanics formulations to be able to formulate
degradation, fracture, and fatigue and life span predictions. Most of these efforts
have been based on phenomenological curve fitting methods, where a polynomial
potential is used to curve fit the fracture, or degradation test data. There are no
unifying theme among these models other than fitting a polynomial to a test data and
using it in conjunction with Newton’s laws. For the sake of completeness, we will
summarize some of them. While we do not claim to include every effort, we will
summarize the most well-known work in the field.
Lagrangian mechanics (1781) [long before Thermodynamics laws were written]
can be considered the first attempt to include nonconservative forces into Newton’s
laws. Quoting from Haddad’s (2017) seminal work on literature review of
© Springer Nature Switzerland AG 2021
C. Basaran, Introduction to Unified Mechanics Theory with Applications,
https://doi.org/10.1007/978-3-030-57772-8_4
115