in describing temperature and rate dependence of material response as well as strainsoftening and strain-hardening characteristics. Due to limited size of data set used for
determination of viscoplastic flow rule for intermolecular mechanism, it is really
difficult to determine material parameters involved in viscoplastic model which
result in some minor differences in response.
Dual-mechanism viscoplastic model for PMMA is verified and validated for more
challenging non-isothermal conditions as presented in the following section.
Entropy production values are calculated as average of cumulative entropy production of all Gauss integration points at the cross section of center of narrow section of
test sample. Difference between mean entropy production and maximum entropy
production in the cross section is less than 5% for all isothermal test simulations
which indicates that no damage localization is predicted at the cross section which is
similar to case of brittle failure of materials. As brittle failure takes place in the form
of sudden rupture of specimen with concurrent crack formation and propagation at
many locations, damage localization is not observed contrary to ductile failure of
materials for which damage localization is an essential part of crack initiation stage
around microscopic defect regions while crack propagation takes place over a longer
period of time compared to brittle failure. Therefore, damage quantification based on
average entropy production in the cross section is an proper method for brittle
failure, while local thermodynamic state index is essential for damage quantification
in ductile failure. It is also important to note that damage evolution and material
degradation due to mechanical load is assumed to result from only plastic energy
dissipation excluding all other entropy generation mechanisms. Therefore, in order
to fully account for evolution of microscopic defects that lead to stiffness and
strength degradation in material, it is necessary to include all entropy generation
terms associated with energy loss associated with new surface creation at microscopic defect regions, heat generation, and chemical reactions, if there are any. The
latter approach would be more accurate. It is possible to account for difference
between failure in tension and failure in compression or predict damage evolution in
the case of ductile failure, by deriving a more comprehensive fundamental equation.
Total irreversible thermal entropy production in ISO-TEST simulations (S irr, ther,
test ) is completely created by transfer of heat generated due to plastic dissipation
during isothermal stretching. Temperature rise due to plastic dissipation in isothermal stretching is very small; hence, thermal gradients within specimen during testing
is also small, as a result producing negligible amount of irreversible entropy production in comparison with S irr, ther, pre À test and total irreversible mechanical entropy
production during isothermal tests (S irr, mech, test ).
Mechanical damage in materials can be described as formation of micro-cracks
and voids at micro-level with corresponding degradation of stiffness at macro level.
On the other hand, thermal damage in materials is deterioration of material properties
by thermal gradients which weaken chemical bonds between molecules or change
7.7 Numerical Implementation of Dual-Mechanism Viscoplastic Model
389
determination of viscoplastic flow rule for intermolecular mechanism, it is really
difficult to determine material parameters involved in viscoplastic model which
result in some minor differences in response.
Dual-mechanism viscoplastic model for PMMA is verified and validated for more
challenging non-isothermal conditions as presented in the following section.
Entropy production values are calculated as average of cumulative entropy production of all Gauss integration points at the cross section of center of narrow section of
test sample. Difference between mean entropy production and maximum entropy
production in the cross section is less than 5% for all isothermal test simulations
which indicates that no damage localization is predicted at the cross section which is
similar to case of brittle failure of materials. As brittle failure takes place in the form
of sudden rupture of specimen with concurrent crack formation and propagation at
many locations, damage localization is not observed contrary to ductile failure of
materials for which damage localization is an essential part of crack initiation stage
around microscopic defect regions while crack propagation takes place over a longer
period of time compared to brittle failure. Therefore, damage quantification based on
average entropy production in the cross section is an proper method for brittle
failure, while local thermodynamic state index is essential for damage quantification
in ductile failure. It is also important to note that damage evolution and material
degradation due to mechanical load is assumed to result from only plastic energy
dissipation excluding all other entropy generation mechanisms. Therefore, in order
to fully account for evolution of microscopic defects that lead to stiffness and
strength degradation in material, it is necessary to include all entropy generation
terms associated with energy loss associated with new surface creation at microscopic defect regions, heat generation, and chemical reactions, if there are any. The
latter approach would be more accurate. It is possible to account for difference
between failure in tension and failure in compression or predict damage evolution in
the case of ductile failure, by deriving a more comprehensive fundamental equation.
Total irreversible thermal entropy production in ISO-TEST simulations (S irr, ther,
test ) is completely created by transfer of heat generated due to plastic dissipation
during isothermal stretching. Temperature rise due to plastic dissipation in isothermal stretching is very small; hence, thermal gradients within specimen during testing
is also small, as a result producing negligible amount of irreversible entropy production in comparison with S irr, ther, pre À test and total irreversible mechanical entropy
production during isothermal tests (S irr, mech, test ).
Mechanical damage in materials can be described as formation of micro-cracks
and voids at micro-level with corresponding degradation of stiffness at macro level.
On the other hand, thermal damage in materials is deterioration of material properties
by thermal gradients which weaken chemical bonds between molecules or change
7.7 Numerical Implementation of Dual-Mechanism Viscoplastic Model
389