Introduction |
|
1 | (6) |
|
|
7 | (68) |
|
|
7 | (12) |
|
Material and Spatial Representation |
|
|
19 | (4) |
|
|
23 | (9) |
|
|
32 | (6) |
|
|
38 | (4) |
|
|
42 | (4) |
|
|
46 | (4) |
|
Strain Rates in Convective Coordinates |
|
|
50 | (3) |
|
|
53 | (4) |
|
Incompatible Configurations |
|
|
57 | (18) |
|
|
58 | (5) |
|
|
63 | (1) |
|
Conditions of Compatibility |
|
|
64 | (11) |
|
Balance Relations of Mechanics |
|
|
75 | (44) |
|
|
75 | (3) |
|
|
78 | (6) |
|
Balance of Mass: Global Form |
|
|
78 | (1) |
|
Balance of Mass: Local Form |
|
|
79 | (5) |
|
Linear Momentum and Rotational Momentum |
|
|
84 | (20) |
|
Balance of Linear Momentum and Rotational Momentum: Global Formulation |
|
|
84 | (6) |
|
|
90 | (5) |
|
Stress Tensors in Convective Coordinates |
|
|
95 | (1) |
|
Local Formulation of the Balance of Linear Momentum and Rotational Momentum |
|
|
95 | (6) |
|
Initial and Boundary Conditions |
|
|
101 | (3) |
|
Conclusions from the Balance Equations of Mechanics |
|
|
104 | (15) |
|
Balance of Mechanical Energy |
|
|
105 | (4) |
|
The Principle of d'Alembert |
|
|
109 | (5) |
|
Principle of Virtual Work |
|
|
114 | (1) |
|
Incremental Form of the Principle of d'Alembert |
|
|
115 | (4) |
|
Balance Relations of Thermodynamics |
|
|
119 | (36) |
|
|
119 | (1) |
|
|
120 | (5) |
|
|
125 | (5) |
|
Initial and Boundary Conditions |
|
|
130 | (2) |
|
Balance Relations for Open Systems |
|
|
132 | (21) |
|
|
132 | (3) |
|
Balance of Linear Momentum for Systems with Time-Dependent Mass |
|
|
135 | (2) |
|
Balance Relations: Conservation Laws |
|
|
137 | (3) |
|
Discontinuity Surfaces and Jump Conditions |
|
|
140 | (4) |
|
Multi-Component Systems (Mixtures) |
|
|
144 | (9) |
|
Summary: Basic Relations of Thermomechanics |
|
|
153 | (2) |
|
|
155 | (22) |
|
|
155 | (1) |
|
|
156 | (3) |
|
Change of Frame: Passive Interpretation |
|
|
159 | (3) |
|
Change of Frame: Active Interpretation |
|
|
162 | (2) |
|
|
164 | (7) |
|
Observer-Invariant Relations |
|
|
171 | (6) |
|
Classical Theories of Continuum Mechanics |
|
|
177 | (74) |
|
|
177 | (1) |
|
|
178 | (4) |
|
|
182 | (3) |
|
|
185 | (3) |
|
Linear-Viscoelastic Solid |
|
|
188 | (39) |
|
|
227 | (4) |
|
Plasticity with Hardening |
|
|
231 | (12) |
|
Viscoplasticity with Elastic Range |
|
|
243 | (6) |
|
Remarks on the Classical Theories |
|
|
249 | (2) |
|
Experimental Observation and Mathematical Modelling |
|
|
251 | (24) |
|
|
251 | (4) |
|
Information from Experiments |
|
|
255 | (14) |
|
Material Properties of Steel XCrNi 18.9 |
|
|
255 | (8) |
|
Material Properties of Carbon-Black-Filled Elastomers |
|
|
263 | (6) |
|
Four Categories of Material Behaviour |
|
|
269 | (2) |
|
Four Theories of Material Behaviour |
|
|
271 | (2) |
|
Contribution of the Classical Theories |
|
|
273 | (2) |
|
General Theory of Mechanical Material Behaviour |
|
|
275 | (42) |
|
|
275 | (4) |
|
|
279 | (14) |
|
|
279 | (4) |
|
Reduced Forms of the General Constitutive Equation |
|
|
283 | (5) |
|
Simple Examples of Material Objectivity |
|
|
288 | (1) |
|
Frame-Indifference and Observer-Invariance |
|
|
289 | (4) |
|
Properties of Material Symmetry |
|
|
293 | (12) |
|
The Concept of the Symmetry Group |
|
|
293 | (5) |
|
Classification of Simple Materials into Fluids and Solids |
|
|
298 | (7) |
|
Kinematic Conditions of Internal Constraint |
|
|
305 | (6) |
|
|
305 | (3) |
|
Special Conditions of Internal Constraint |
|
|
308 | (3) |
|
Formulation of Material Models |
|
|
311 | (6) |
|
|
311 | (1) |
|
Representation by Means of Functionals |
|
|
312 | (1) |
|
Representation by Means of Internal Variables |
|
|
313 | (2) |
|
|
315 | (2) |
|
|
317 | (28) |
|
Tensor-Valued Evolution Equations |
|
|
317 | (12) |
|
|
317 | (2) |
|
Objective Time Derivatives of Objective Tensors |
|
|
319 | (3) |
|
|
322 | (3) |
|
Example: Rigid-Plastic Solid with Hardening |
|
|
325 | (4) |
|
The Concept of Dual Variables |
|
|
329 | (16) |
|
|
329 | (2) |
|
Strain and Stress Tensors (Summary) |
|
|
331 | (3) |
|
Dual Variables and Derivatives |
|
|
334 | (11) |
|
|
345 | (52) |
|
Elasticity and Hyperelasticity |
|
|
345 | (7) |
|
|
352 | (24) |
|
General Constitutive Equation for Elastic Fluids and Solids |
|
|
352 | (6) |
|
Isotropic Hyperelastic Bodies |
|
|
358 | (5) |
|
Incompressible Isotropic Elastic Materials |
|
|
363 | (2) |
|
Constitutive Equations of Isotropic Elasticity (Examples) |
|
|
365 | (11) |
|
Anisotropic Hyperelastic Solids |
|
|
376 | (21) |
|
Approximation of the General Constitutive Equation |
|
|
376 | (3) |
|
General Representation of the Strain Energy Function |
|
|
379 | (9) |
|
|
388 | (9) |
|
|
397 | (38) |
|
Representation by Means of Functionals |
|
|
397 | (22) |
|
Rate-Dependent Functionals with Fading Memory Properties |
|
|
398 | (12) |
|
Continuity Properties and Approximations |
|
|
410 | (9) |
|
Representation by Means of Internal Variables |
|
|
419 | (16) |
|
|
419 | (7) |
|
Internal Variables of the Strain Type |
|
|
426 | (7) |
|
A General Model of Finite Viscoelasticity |
|
|
433 | (2) |
|
|
435 | (40) |
|
Rate-Independent Functionals |
|
|
435 | (9) |
|
Representation by Means of Internal Variables |
|
|
444 | (6) |
|
|
450 | (25) |
|
|
450 | (4) |
|
Stress-Free Intermediate Configuration |
|
|
454 | (5) |
|
|
459 | (1) |
|
Yield Function and Evolution Equations |
|
|
460 | (3) |
|
|
463 | (12) |
|
|
475 | (34) |
|
|
475 | (2) |
|
Viscoplasticity with Elastic Domain |
|
|
477 | (7) |
|
A General Constitutive Model |
|
|
477 | (3) |
|
Application of the Intermediate Configuration |
|
|
480 | (4) |
|
Plasticity as a Limit Case of Viscoplasticity |
|
|
484 | (15) |
|
The Differential Equation of the Yield Function |
|
|
484 | (5) |
|
|
489 | (2) |
|
Slow Deformation Processes |
|
|
491 | (6) |
|
Elastoplasticity and Arclength Representation |
|
|
497 | (2) |
|
A Concept for General Viscoplasticity |
|
|
499 | (10) |
|
|
499 | (1) |
|
Equilibrium Stress and Overstress |
|
|
500 | (1) |
|
An Example of General Viscoplasticity |
|
|
501 | (6) |
|
Conclusions Regarding the Modelling of Mechanical Material Behaviour |
|
|
507 | (2) |
|
Constitutive Models in Thermomechanics |
|
|
509 | (110) |
|
Thermomechanical Consistency |
|
|
509 | (5) |
|
|
514 | (16) |
|
|
514 | (6) |
|
|
520 | (7) |
|
Linear-Thermoelastic Solids |
|
|
527 | (3) |
|
|
530 | (24) |
|
|
530 | (7) |
|
Thermoelasticity as a Limit Case of Thermoviscoelasticity |
|
|
537 | (4) |
|
Internal Variables of Strain Type |
|
|
541 | (4) |
|
Incorporation of Anisotropic Elasticity Properties |
|
|
545 | (1) |
|
Incompressible Materials: An Extension of the Mooney-Rivlin Model to Thermoviscoelasticity |
|
|
545 | (9) |
|
Thermoviscoplasticity with Elastic Domain |
|
|
554 | (23) |
|
|
554 | (6) |
|
|
560 | (4) |
|
Application of the Intermediate Configuration |
|
|
564 | (4) |
|
Thermoplasticity as a Limit Case of Thermoviscoplasticity |
|
|
568 | (9) |
|
General Thermoviscoplasticity |
|
|
577 | (9) |
|
|
578 | (3) |
|
|
581 | (4) |
|
|
585 | (1) |
|
Anisotropic Material Properties |
|
|
586 | (5) |
|
|
586 | (1) |
|
Axes of Elastic Anisotropy |
|
|
587 | (4) |
|
Anisotropic Viscoplasticity |
|
|
591 | (28) |
|
|
591 | (2) |
|
|
593 | (3) |
|
|
596 | (7) |
|
|
603 | (3) |
|
Summary: A Constitutive Model of Anisotropic Viscoplasticity |
|
|
606 | (2) |
|
|
608 | (10) |
|
|
618 | (1) |
References |
|
619 | (16) |
Index |
|
635 | |