However, these three laws are “incomplete.” The following examples can help us
explain what we mean by “incomplete.” For example, if a soccer ball is given an
initial acceleration by a kick according to Newton’s second law, that acceleration is
constant, and it does not degrade. The ball will travel with that acceleration forever
according to F ¼ ma. However, that is obviously not true. In the same fashion,
Newton’s third law (also Hooke’s law, which was published by Robert Hooke
10 years before Newton’s Principia) assumes that reaction due to an applied load
will be constant, without degradation of the material. Of course, materials degrade
and response displacement does not remain constant. Fortunately, energy loss in the
ball and material degradation can be modeled by laws of thermodynamics. Basaran
and Yan published the first paper in (1998) using entropy generation rate as a metric
to account for degradation in electronic solder joints. They implemented it by
modifying Newton’s laws with Boltzmann’s second law of thermodynamics. Since
then, the theory has gone through significant consolidation by experimental verifications and mathematical derivations by many researchers around the world. These
developments are included in Chap. 4.
Chapter 5 presents formulation for thermo-mechanical analysis using the unified
mechanics theory. The chapter includes nonlocal and local mechanics formulation.
Cosserat continuum is explained in great detail and used for introducing length scale
into the continuum mechanics formulation It is presented with simple steps from a
beginner graduate student’s perspective
Chapter 6 is about particle-filled composite materials’ formulation using the
unified mechanics theory. Particle-filled acrylic composite formulation and implementation is presented in the context of small strain formulation.
Chapter 7 covers finite strain formulation of unified mechanics theory. Again,
particle-filled composite material application is presented in detail.
Chapter 8 presents electro-thermo-mechanical loading application of the unified
mechanics theory.
I tried to provide a list of references at the end of each chapter. While they are not
complete, it can help a researcher in the right direction.
References
Hill, R. (1965). Continuum micro-mechanics of elastoplastic polycrystals. Journal of the Mechanics and Physics of Solids, 13(2), 89–101.
Malvern, L. E. (1969). Introduction to the Mechanics of continuous medium. Englewood Cliffs, NJ:
Prentice-Hall.
References
3
explain what we mean by “incomplete.” For example, if a soccer ball is given an
initial acceleration by a kick according to Newton’s second law, that acceleration is
constant, and it does not degrade. The ball will travel with that acceleration forever
according to F ¼ ma. However, that is obviously not true. In the same fashion,
Newton’s third law (also Hooke’s law, which was published by Robert Hooke
10 years before Newton’s Principia) assumes that reaction due to an applied load
will be constant, without degradation of the material. Of course, materials degrade
and response displacement does not remain constant. Fortunately, energy loss in the
ball and material degradation can be modeled by laws of thermodynamics. Basaran
and Yan published the first paper in (1998) using entropy generation rate as a metric
to account for degradation in electronic solder joints. They implemented it by
modifying Newton’s laws with Boltzmann’s second law of thermodynamics. Since
then, the theory has gone through significant consolidation by experimental verifications and mathematical derivations by many researchers around the world. These
developments are included in Chap. 4.
Chapter 5 presents formulation for thermo-mechanical analysis using the unified
mechanics theory. The chapter includes nonlocal and local mechanics formulation.
Cosserat continuum is explained in great detail and used for introducing length scale
into the continuum mechanics formulation It is presented with simple steps from a
beginner graduate student’s perspective
Chapter 6 is about particle-filled composite materials’ formulation using the
unified mechanics theory. Particle-filled acrylic composite formulation and implementation is presented in the context of small strain formulation.
Chapter 7 covers finite strain formulation of unified mechanics theory. Again,
particle-filled composite material application is presented in detail.
Chapter 8 presents electro-thermo-mechanical loading application of the unified
mechanics theory.
I tried to provide a list of references at the end of each chapter. While they are not
complete, it can help a researcher in the right direction.
References
Hill, R. (1965). Continuum micro-mechanics of elastoplastic polycrystals. Journal of the Mechanics and Physics of Solids, 13(2), 89–101.
Malvern, L. E. (1969). Introduction to the Mechanics of continuous medium. Englewood Cliffs, NJ:
Prentice-Hall.
References
3