Plasticity - Revision history

Mitjajancic at 10:23, 8 October 2021

2021-10-08T10:23:13Z

Mitjajancic at 10:22, 8 October 2021

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Mitjajancic at 10:20, 8 October 2021

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Mitjajancic at 10:20, 8 October 2021

2021-10-08T10:20:07Z

Mitjajancic at 10:01, 8 October 2021

2021-10-08T10:01:07Z

Mitjajancic at 10:00, 8 October 2021

2021-10-08T10:00:19Z

Mitjajancic at 10:00, 8 October 2021

2021-10-08T10:00:09Z

Mitjajancic at 09:28, 8 October 2021

2021-10-08T09:28:42Z

Mitjajancic at 09:21, 8 October 2021

2021-10-08T09:21:57Z

Mitjajancic: 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..."

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..."

New page

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.

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 \end{equation}
 =References=
 <references/>

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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.
-<div class="mw-collapsible-content">
 = 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.
@@ Line 19: / Line 20: @@
 \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.

@@ Line 2: / Line 2: @@
 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 =
 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.

@@ Line 1: / Line 1: @@
 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 =
-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 =
-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}
-\ \nabla \cdot \boldsymbol{\sigma} + \bf{f} = 0
+\ \nabla \cdot \boldsymbol{\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.
+TO BE FINISHED.

@@ 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
 \begin{equation}
-\ \nabla \cdot \bf{\sigma} + \bf{f} = 0
+\ \nabla \cdot \boldsymbol{\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.

← Older revision		Revision as of 10:00, 8 October 2021
Line 1:		Line 1:
	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.

← Older revision		Revision as of 09:28, 8 October 2021
Line 1:		Line 1:
	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>.

← Older revision		Revision as of 09:21, 8 October 2021
Line 1:		Line 1:
		+	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~~.