Common Properties: Nonlinear
Description
Nonlinear material properties commonly found in beam, plate and brick property sets.
Properties
In nonlinear analysis, the modulus (or stiffness) can be temperature and/or time dependent, by associating the modulus (or stiffness) with a Factor vs Temperature and/or a Factor vs Time table. This option specifies how changes in stiffness due to these tables affect the response.
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Elastic
The new modulus (or stiffness) will be used to equilibrate the current total applied load. This means that a modulus (or stiffness) change will disturb the equilibrium even if there is no change in external load.
Changes in stiffness due to the tables will require the current internal forces in the element to be re-equilibrated. Under constant loading, these changes in stiffness will cause additional displacements and/or out-of-balance forces.
A physical example of this might be a steel structure subjected to a high ambient temperature that softens the steel (reduces the modulus). The structure will continue to deform as the steel softens, even though the external load remains constant (ignoring effects of thermal expansion due to the temperature change).
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Plastic
The new modulus (or stiffness) will be used to equilibrate only the changes in applied load. This means that a modulus (or stiffness) change will have no effect on the current equilibrium until there is a change in external load; load changes act on the new modulus (or stiffness).
Changes in stiffness due to the tables will not affect the current equilibrium (all previously equilibrated loads remain equilibrated after the stiffness change). Under constant loading, therefore, a change in stiffness will not cause an out-of-balance force; displacements and stresses will not change as the stiffness changes.
A physical example of this might be a just-cast concrete structure under the action of gravity. As the concrete sets, the modulus (stiffness) of the concrete increases, but the deflections do not change (ignoring the effects of heat of concrete hydration). Additional deflection due to the application of additional external load will be based on the concrete modulus at the time the external load is applied.
Specifies the type of material nonlinearity represented by an associated stress-strain table.
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Elastic
Allows for a nonlinear elastic relationship between stress and strain, but no plastic deformation is produced. Response of the material is path independent, and deformation will return to zero when all load is removed. As there is no plasticity, loading and unloading paths are identical.
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Elastic-Plastic
Allows for a nonlinear elasto-plastic relationship between stress and strain. Before yielding, an increment in stress produces an increment in elastic strain only. After yielding, an increment in stress may produce an increment in elastic strain as well as an increment in plastic strain; the elastic strain is recoverable upon unloading, whereas the plastic strain is not recoverable. The response of the material therefore depends on the loading history (i.e., it is path dependent). Unloading takes a different path to that of loading, and residual strains will remain when the loads are removed.
Specifies the criterion that defines the onset of yield for the material, or the effective stress to be used in a multi-dimensional stress state when referencing the table. See Material Nonlinearity: Yield Criteria.
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Fibre Stress
The one dimensional fibre stress is used directly in the stress-strain table.
As fibre stress is a signed stress, both the positive and negative sides of the stress-strain table are considered.
Applicable only to the beam element, for both Elastic and Elastic-Plastic materials.
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Tresca
The Tresca stress is used in the stress-strain table.
As Tresca stress is always positive, the negative side of the stress-strain table is ignored.
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von Mises
The von Mises stress is used in the stress-strain table.
As von Mises stress is always positive, the negative side of the stress-strain table is ignored.
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Max Stress
The principal stresses are used in the stress-strain table.
As principal stresses are signed, both the positive and negative sides of the stress-strain table are considered.
Applicable only when Material is set to Elastic.
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Mohr-Coulomb
Stress-strain tables are not used with this yield criterion. Instead, the yield surface is defined by a cohesion value and a friction angle.
Available only when Material is set to Elastic-Plastic.
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Drucker-Prager
Stress-strain tables are not used with this yield criterion. Instead, the yield surface is defined by a cohesion value and a friction angle.
Available only when Material is set to Elastic-Plastic.
Specifies the hardening rule for Elastic-Plastic materials. Hardening rules govern the behaviour of the material when it is strained beyond the yield point. A hardening material will develop both additional elastic strains and additional plastic strains, whereas a non-hardening material can only develop additional plastic strains. During the initial unloading, both material types unload elastically (i.e., elastic strains are reduced without changes to plastic strains). For further details see Material Nonlinearity: Hardening Laws.
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Isotropic
Yield stress in compression and tension are equal.
In principal stress space this corresponds to the yield surface expanding uniformly but remaining centred at the origin.
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Kinematic
Yield stress in compression and tension will generally not be equal and will depend on the loading-unloading-reloading history. Yielding in one direction will result in a subsequently lower yield stress in the other direction.
In principal stress space this corresponds to the yield surface translating to a new position but remaining the same size.
Typically used in situations with repeated loading and unloading cycles.
Applicable only to spring-damper, truss and beam elements.
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Takeda
Specialised rule normally used to model reinforced concrete frame structures in nonlinear transient dynamic analysis. The Takeda model has specific hysteresis rules evaluated from physical testing of reinforced concrete members under load reversal.
Applicable only to spring-damper, truss and beam elements.
Stress vs Strain table used in material nonlinear analysis.
The elastic modulus entered in the Property dialog is ignored when a stress vs strain table is specified in material nonlinear analysis. The elastic modulus used is calculated as the gradient in the stress-strain table passing through the origin.
Cohesion used to define the Mohr-Coulomb and Drucker-Prager yield surfaces.
Units are Pressure (e.g., MPa, psi).
Friction angle used to define the Mohr-Coulomb and Drucker-Prager yield surfaces.
Units are Degrees.
Creep data used in creep analysis.
See Also