Plasticity - Revision history

Mitjajancic at 10:23, 8 October 2021

2021-10-08T10:23:13Z

← Older revision		Revision as of 10:23, 8 October 2021
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	\end{equation}		\end{equation}

			TO BE FINISHED.
			As previously stated, all of the theory is thoroughly explained in '''Computational Methods for Plasticity - Theory and Applications''' by EA de Souza Neto, mainly chapters 4-7.
	=References=		=References=
	<references/>		<references/>

	~~TO BE FINISHED.~~
	~~As previously stated, all of the theory is thoroughly explained in '''Computational Methods for Plasticity - Theory and Applications''' by EA de Souza Neto, mainly chapters 4-7.~~

Mitjajancic at 10:22, 8 October 2021

2021-10-08T10:22:33Z

← Older revision		Revision as of 10:22, 8 October 2021
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	On this page we conduct numerical studies of plastic deformation by employing the von Mises plasticity model with isotropic hardening. The majority of the theory is explained in detail in '''Computational Methods for Plasticity - Theory and Applications''' by EA de Souza Neto <ref> de Souza Neto, E.A., Peric, D. and Owen, D.R., 2011. Computational methods for plasticity: theory and applications. John Wiley & Sons</ref>. For a more detailed theory description, we strongly recommend reading the book.		On this page we conduct numerical studies of plastic deformation by employing the von Mises plasticity model with isotropic hardening. The majority of the theory is explained in detail in '''Computational Methods for Plasticity - Theory and Applications''' by EA de Souza Neto <ref> de Souza Neto, E.A., Peric, D. and Owen, D.R., 2011. Computational methods for plasticity: theory and applications. John Wiley & Sons</ref>. For a more detailed theory description, we strongly recommend reading the book.
	~~<div class="mw-collapsible-content">~~

	= Introduction =		= Introduction =
	In physics and materials science, ''plasticity'', also known as ''plastic deformation'', is observed when the solid material undergoes permanent deformation in response to applied forces. There are different small-strain elastoplastic constitutive models of plasticity known. The most popular theories are the von Mises, Tresca, Mohr-Coulomb and Drucker-Prager models. The main difference between them is in the computation of yield condition - threshold value after which the deformation is irreversible.		In physics and materials science, ''plasticity'', also known as ''plastic deformation'', is observed when the solid material undergoes permanent deformation in response to applied forces. There are different small-strain elastoplastic constitutive models of plasticity known. The most popular theories are the von Mises, Tresca, Mohr-Coulomb and Drucker-Prager models. The main difference between them is in the computation of yield condition - threshold value after which the deformation is irreversible.
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	\end{equation}		\end{equation}

			=References=
			<references/>

	TO BE FINISHED.		TO BE FINISHED.
	As previously stated, all of the theory is thoroughly explained in '''Computational Methods for Plasticity - Theory and Applications''' by EA de Souza Neto, mainly chapters 4-7.		As previously stated, all of the theory is thoroughly explained in '''Computational Methods for Plasticity - Theory and Applications''' by EA de Souza Neto, mainly chapters 4-7.

Mitjajancic at 10:20, 8 October 2021

2021-10-08T10:20:56Z

← Older revision		Revision as of 10:20, 8 October 2021
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	On this page we conduct numerical studies of plastic deformation by employing the von Mises plasticity model with isotropic hardening. The majority of the theory is explained in detail in '''Computational Methods for Plasticity - Theory and Applications''' by EA de Souza Neto <ref> de Souza Neto, E.A., Peric, D. and Owen, D.R., 2011. Computational methods for plasticity: theory and applications. John Wiley & Sons</ref>. For a more detailed theory description, we strongly recommend reading the book.		On this page we conduct numerical studies of plastic deformation by employing the von Mises plasticity model with isotropic hardening. The majority of the theory is explained in detail in '''Computational Methods for Plasticity - Theory and Applications''' by EA de Souza Neto <ref> de Souza Neto, E.A., Peric, D. and Owen, D.R., 2011. Computational methods for plasticity: theory and applications. John Wiley & Sons</ref>. For a more detailed theory description, we strongly recommend reading the book.
			<div class="mw-collapsible-content">
	= Introduction =		= Introduction =
	In physics and materials science, ''plasticity'', also known as ''plastic deformation'', is observed when the solid material undergoes permanent deformation in response to applied forces. There are different small-strain elastoplastic constitutive models of plasticity known. The most popular theories are the von Mises, Tresca, Mohr-Coulomb and Drucker-Prager models. The main difference between them is in the computation of yield condition - threshold value after which the deformation is irreversible.		In physics and materials science, ''plasticity'', also known as ''plastic deformation'', is observed when the solid material undergoes permanent deformation in response to applied forces. There are different small-strain elastoplastic constitutive models of plasticity known. The most popular theories are the von Mises, Tresca, Mohr-Coulomb and Drucker-Prager models. The main difference between them is in the computation of yield condition - threshold value after which the deformation is irreversible.

Mitjajancic at 10:20, 8 October 2021

2021-10-08T10:20:07Z

← Older revision		Revision as of 10:20, 8 October 2021
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	Do you want to go back to [[Solid Mechanics]]?		Do you want to go back to [[Solid Mechanics]]?

	On this page we conduct numerical studies of ~~'''~~plastic deformation by employing the von Mises plasticity model with isotropic hardening~~'''~~. The majority of the theory is explained in detail in '''Computational Methods for Plasticity - Theory and Applications''' by EA de Souza Neto <ref> de Souza Neto, E.A., Peric, D. and Owen, D.R., 2011. Computational methods for plasticity: theory and applications. John Wiley & Sons</ref>. For a more detailed theory description, we strongly recommend reading the book.		On this page we conduct numerical studies of plastic deformation by employing the von Mises plasticity model with isotropic hardening. The majority of the theory is explained in detail in '''Computational Methods for Plasticity - Theory and Applications''' by EA de Souza Neto <ref> de Souza Neto, E.A., Peric, D. and Owen, D.R., 2011. Computational methods for plasticity: theory and applications. John Wiley & Sons</ref>. For a more detailed theory description, we strongly recommend reading the book.

	= Introduction =		= Introduction =
	In physics and materials science, ''plasticity'', also known as plastic deformation, is observed when the solid material undergoes permanent deformation in response to applied forces. There are different small-strain elastoplastic constitutive models of plasticity known. The most popular theories are the von Mises, Tresca, Mohr-Coulomb and Drucker-Prager models. The main difference between them is in the computation of yield condition - threshold value after which the deformation ~~transits from elastic to plastic range~~.		In physics and materials science, ''plasticity'', also known as ''plastic deformation'', is observed when the solid material undergoes permanent deformation in response to applied forces. There are different small-strain elastoplastic constitutive models of plasticity known. The most popular theories are the von Mises, Tresca, Mohr-Coulomb and Drucker-Prager models. The main difference between them is in the computation of yield condition - threshold value after which the deformation is irreversible.

	This demonstration uses ''the von Mises model, with nonlinear isotropic hardening'', due to its computational implementation ~~simplicity~~ and appropriateness for real-world ~~examples~~.		This demonstration uses ''the von Mises model, with nonlinear isotropic hardening'', due to the simplicity of its computational implementation and appropriateness for real-world applications.

	= Theory of plasticity =		= Theory of plasticity =
	In continuum mechanics, stress is a physical quantity that expresses the internal forces that neighbouring particles of a continuous material exert on each other. When additional external force is applied to the body, the dynamics ~~are~~ described by a second Newton's law		In continuum mechanics, stress is a physical quantity that expresses the internal forces that neighbouring particles of a continuous material exert on each other. When additional external force $\bf f$ is applied to the body, the dynamics can be described by a second Newton's law
	\begin{equation}		\begin{equation}
	\ \nabla \cdot \boldsymbol{\sigma} + \bf{f} = 0		\ \nabla \cdot \boldsymbol{\sigma} + \bf{f} = 0,
	\end{equation}		\end{equation}
			where $\boldsymbol \sigma $ is the stress tensor. Now contrary to the elastic response, where the relationship between the deformation $\bf u$ and stress $\boldsymbol \sigma$ is linear, the plastic response is a typical example of a non-linear relationship, because the stress tensor not only depends depends on the current deformation $\bf u$ but also on its history states.
			Generally speaking, for such highly non-linear problems, iterative numerical methods are used to solve the problem. Therefore, the residuum vector $\bf r$ is introduced and above equation is rewritten
			\begin{equation}
			\ \bf r (\bf u_{n + 1}) = \nabla \boldsymbol \sigma (\bf u_{n + 1}) - \bf f = 0.
			\end{equation}


	As previously stated, all of the theory is thoroughly explained in '''Computational Methods for Plasticity - Theory and Applications''' by EA de Souza Neto ~~<ref> de Souza Neto, E.A., Peric, D. and Owen, D.R., 2011. Computational methods for plasticity: theory and applications. John Wiley & Sons</ref>~~, mainly chapters 4-7.		TO BE FINISHED.
			As previously stated, all of the theory is thoroughly explained in '''Computational Methods for Plasticity - Theory and Applications''' by EA de Souza Neto, mainly chapters 4-7.

Mitjajancic at 10:01, 8 October 2021

2021-10-08T10:01:07Z

← Older revision		Revision as of 10:01, 8 October 2021
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	In continuum mechanics, stress is a physical quantity that expresses the internal forces that neighbouring particles of a continuous material exert on each other. When additional external force is applied to the body, the dynamics are described by a second Newton's law		In continuum mechanics, stress is a physical quantity that expresses the internal forces that neighbouring particles of a continuous material exert on each other. When additional external force is applied to the body, the dynamics are described by a second Newton's law
	\begin{equation}		\begin{equation}
	\ \nabla \cdot \bf{\sigma} + \bf{f} = 0		\ \nabla \cdot \boldsymbol{\sigma} + \bf{f} = 0
	\end{equation}		\end{equation}

	As previously stated, all of the theory is thoroughly explained in '''Computational Methods for Plasticity - Theory and Applications''' by EA de Souza Neto <ref> de Souza Neto, E.A., Peric, D. and Owen, D.R., 2011. Computational methods for plasticity: theory and applications. John Wiley & Sons</ref>, mainly chapters 4-7.		As previously stated, all of the theory is thoroughly explained in '''Computational Methods for Plasticity - Theory and Applications''' by EA de Souza Neto <ref> de Souza Neto, E.A., Peric, D. and Owen, D.R., 2011. Computational methods for plasticity: theory and applications. John Wiley & Sons</ref>, mainly chapters 4-7.

Mitjajancic at 10:00, 8 October 2021

2021-10-08T10:00:19Z

← Older revision		Revision as of 10:00, 8 October 2021
Line 11:		Line 11:
	In continuum mechanics, stress is a physical quantity that expresses the internal forces that neighbouring particles of a continuous material exert on each other. When additional external force is applied to the body, the dynamics are described by a second Newton's law		In continuum mechanics, stress is a physical quantity that expresses the internal forces that neighbouring particles of a continuous material exert on each other. When additional external force is applied to the body, the dynamics are described by a second Newton's law
	\begin{equation}		\begin{equation}
	\ \nabla \cdot \bf{sigma} + \bf{f} = 0		\ \nabla \cdot \bf{\sigma} + \bf{f} = 0
	\end{equation}		\end{equation}

	As previously stated, all of the theory is thoroughly explained in '''Computational Methods for Plasticity - Theory and Applications''' by EA de Souza Neto <ref> de Souza Neto, E.A., Peric, D. and Owen, D.R., 2011. Computational methods for plasticity: theory and applications. John Wiley & Sons</ref>, mainly chapters 4-7.		As previously stated, all of the theory is thoroughly explained in '''Computational Methods for Plasticity - Theory and Applications''' by EA de Souza Neto <ref> de Souza Neto, E.A., Peric, D. and Owen, D.R., 2011. Computational methods for plasticity: theory and applications. John Wiley & Sons</ref>, mainly chapters 4-7.

Mitjajancic at 10:00, 8 October 2021

2021-10-08T10:00:09Z

← Older revision		Revision as of 10:00, 8 October 2021
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	Do you want to go back to [[Solid Mechanics]]?		Do you want to go back to [[Solid Mechanics]]?

	On this page we conduct numerical studies of '''plastic deformation ~~with~~ von Mises plasticity model ~~and~~ isotropic hardening'''. The majority of the theory is explained in detail in '''Computational Methods for Plasticity - Theory and Applications''' by EA de Souza Neto <ref> de Souza Neto, E.A., Peric, D. and Owen, D.R., 2011. Computational methods for plasticity: theory and applications. John Wiley & Sons</ref>.		On this page we conduct numerical studies of '''plastic deformation by employing the von Mises plasticity model with isotropic hardening'''. The majority of the theory is explained in detail in '''Computational Methods for Plasticity - Theory and Applications''' by EA de Souza Neto <ref> de Souza Neto, E.A., Peric, D. and Owen, D.R., 2011. Computational methods for plasticity: theory and applications. John Wiley & Sons</ref>. For a more detailed theory description, we strongly recommend reading the book.

			= Introduction =
			In physics and materials science, ''plasticity'', also known as plastic deformation, is observed when the solid material undergoes permanent deformation in response to applied forces. There are different small-strain elastoplastic constitutive models of plasticity known. The most popular theories are the von Mises, Tresca, Mohr-Coulomb and Drucker-Prager models. The main difference between them is in the computation of yield condition - threshold value after which the deformation transits from elastic to plastic range.

			This demonstration uses ''the von Mises model, with nonlinear isotropic hardening'', due to its computational implementation simplicity and appropriateness for real-world examples.

			= Theory of plasticity =
			In continuum mechanics, stress is a physical quantity that expresses the internal forces that neighbouring particles of a continuous material exert on each other. When additional external force is applied to the body, the dynamics are described by a second Newton's law
			\begin{equation}
			\ \nabla \cdot \bf{sigma} + \bf{f} = 0
			\end{equation}

			As previously stated, all of the theory is thoroughly explained in '''Computational Methods for Plasticity - Theory and Applications''' by EA de Souza Neto <ref> de Souza Neto, E.A., Peric, D. and Owen, D.R., 2011. Computational methods for plasticity: theory and applications. John Wiley & Sons</ref>, mainly chapters 4-7.

Mitjajancic at 09:28, 8 October 2021

2021-10-08T09:28:42Z

← Older revision		Revision as of 09:28, 8 October 2021
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	Do you want to go back to [[Solid Mechanics]]?		Do you want to go back to [[Solid Mechanics]]?

	On this page we conduct numerical studies of '''~~bending of a cantilever loaded at the end~~'''~~, a common numerical benchmark in elastostatics~~. ~~<ref> Augarde, Charles E. and Deeks, Andrew J.. "~~The ~~use~~ of ~~Timoshenko~~'~~s exact solution for a cantilever beam in adaptive analysis" ,~~ ''~~Finite Elements in Analysis~~ and ~~Design~~''~~. (2008)~~, ~~doi: [http://dx~~.~~doi~~.~~org/10~~.~~1016/j~~.~~finel~~.~~2008~~.~~01.010 10.1016/j.finel.2008~~.~~01.010]~~ </ref>		On this page we conduct numerical studies of '''plastic deformation with von Mises plasticity model and isotropic hardening'''. The majority of the theory is explained in detail in '''Computational Methods for Plasticity - Theory and Applications''' by EA de Souza Neto <ref> de Souza Neto, E.A., Peric, D. and Owen, D.R., 2011. Computational methods for plasticity: theory and applications. John Wiley & Sons</ref>.

Mitjajancic at 09:21, 8 October 2021

2021-10-08T09:21:57Z

← Older revision		Revision as of 09:21, 8 October 2021
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			Do you want to go back to [[Solid Mechanics]]?

	On this page we ~~showcase some basic examples from linear elasticity~~. ~~To read more about the governing equations~~, ~~refer to the [[Solid Mechanics]] page~~		On this page we conduct numerical studies of '''bending of a cantilever loaded at the end''', a common numerical benchmark in elastostatics. <ref> Augarde, Charles E. and Deeks, Andrew J.. "The use of Timoshenko's exact solution for a cantilever beam in adaptive analysis" , ''Finite Elements in Analysis and Design''. (2008), doi: [http://dx.doi.org/10.1016/j.finel.2008.01.010 10.1016/j.finel.2008.01.010] </ref>
	and ~~examples therein~~, ~~which are considered~~ in ~~more detail~~.

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2021-10-08T09:21:02Z

Created page with " On this page we showcase some basic examples from linear elasticity. To read more about the governing equations, refer to the Solid Mechanics page and examples therein, w..."

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On this page we showcase some basic examples from linear elasticity. To read more about the governing equations, refer to the [[Solid Mechanics]] page
and examples therein, which are considered in more detail.