The strain energy function of a polymeric material is given by the following hyperelastic potential where c, c and c are material parameters, and , and are respectively the first, second and third principal invariants of the right Cauchy-Green deformation tensor (with components in a Cartesian coordinate system, , = 1,2,3). xp and o are respectively the exponential and logarithm functions.
(1, 2, 3) = c1(1 − 3) + c2 (1 − 3)2 + c3(2 − 3) +
1
2
3 − 1
2
(i) Give the explicit expression of the first principal invariant as a function of the components of [2 marks]
(ii) Define the second Piola-Kirchhoff stress tensor arising from the hyperelastic potential as a function of and .
[2 marks]
TURN OVER (1, 2, 3) = c1(1 − 3) + c2 (1 − 3)2 + c3(2 − 3) + 1 2 3 − 1 2 FEEG6010W1 Copyright 2022 v01 © University of Southampton Page 10 of 11 (iii) Provide the explicit expression of the second Piola-Kirchhoff stress tensor arising from the hyperelastic potential , in compact form (tensor). You will use the following formulas for the derivative of the determinant det() of a second-order tensor : det() = () and the derivative of the trace of the square of a second-order tensor : trace = [15 marks] (iv) Provide the explicit expression of the second Piola-Kirchhoff stress tensor arising from the hyperelastic potential , in matrix form (assuming a 3D problem). You will denote the components of as . To lighten notations replace the explicit expressions of ⁄, ⁄ and ⁄ by respectively the letters A, B and K.

When the source-to-film distance was increased from 60 in. to 120 in., the geometric unsharpness was improved. This means that the image on the radiograph will be sharper and clearer, making it easier to identify any defects or issues with the weld.

For such more question on radiograph

https://brainly.com/question/14318920

#SPJ11

huhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhhh

Answer:

?

Explanation:

what do you mean

4 netherite scrap and 4 gold

in a crafting table

The `INC` assembly command is used to add one to the value stored in a register or memory location. It stands for increment.

The format of the `INC` instruction is as follows:

```assembly INC destination ```

where destination can be a register or a memory location.

Example:

To increment the value stored in the AX register, we use the following syntax:```assembly INC AX ```

This will add one to the value stored in the AX register.

To increment the value stored at a memory location, we use the following syntax:```assembly INC [address] ```

where address represents the memory location whose value needs to be incremented.

For example:```assembly INC [BX] ```will increment the value stored at the memory location whose address is stored in the BX register.

Learn more about increment at

https://brainly.com/question/14294555

#SPJ11

Answer:

  83.6%

Explanation:

On its current schedule, the plant can theoretically produce ...

  (30 pc/h/machine)(10 machine)(8 h/shift)(2 shift/day)(5 day/wk)(50 wk/yr)

  = (30)(10)(8)(2)(5)(50) pc/yr = 1,200,000 pc/yr

__

On the proposed schedule, this production becomes ...

  (30 pc/mach)(10 mach)(8 h/sh)(3 sh/da)(6 da/wk)(51 wk/yr)

  = (30)(10)(8)(3)(6)(51) pc/yr = 2,203,200 pc/yr

The increase in capacity is ...

  (2,203,200/1,200,000 -1) × 100% = 83.6% . . . capacity increase

_____

Additional comment

The number of parts per shift did not change. Only the number of shifts per year changed. It went up by a factor of (3/2)(6/5)(51/50) = 1.836. Hence the 83.6% increase in capacity.

We have to assume that maintenance and repair are done as effectvely as before in the reduced down time that each machine has.

The examples of engineering controls is Biohazard waste containers and Spill clean up kits.

An engineering controls is a workplace process that protect workers by removing hazardous conditions or by placing a barrier between the worker and the hazard.

An example of engineering controls is installation of exhaust ventilation to remove airborne emissions to shield the worker.

Hence, the examples of engineering controls is Biohazard waste containers and Spill clean up kits.

Therefore, the Option C and D is correct.

Read more about engineering controls

brainly.com/question/17483083

The term “Flip-flop” relates to the actual operation of the device, as it can be “flipped” into one logical  Set state or “flopped” back into the opposing logical set.

A flip-flop is a device which stores a single bit (binary digit) of data; one of its two states represents a "one" and the other represents a "zero". Such data storage can be used for storage of state, and such a circuit is described as sequential logic in electronics.

STATIC RAM (SRAM) consists of flip-flops, a circuit composed of four to six transistors. Once a flip-flop stores a bit, it keeps that value until the opposite value is stored in it.

Hence, logical set is used.

To know more about Flip flop from the given link

https://brainly.com/question/4237777

#SPJ1

Answer:

I would check out Coursera. Coursera has a premium membership for around $62 a month, and has Master degrees in Engineering from many universities ranging from University of London to MIT.

The given statement "when running coaxial cable systems, the outer conductive shield must be interrupted as close as possible to the point of entrance to the building" is true. To ensure safety and proper functioning of a coaxial cable system, the outer conductive shield must be interrupted near the building entrance point.

When running coaxial cable systems, the outer conductive shield should indeed be interrupted as close as possible to the point of entrance to the building. This practice helps prevent the shield from acting as a conductor for lightning strikes or other electrical surges, which could cause damage to the equipment or create safety hazards. Proper grounding and bonding of the shield at the entrance point further ensure the safety and effectiveness of the coaxial cable system.

Learn more about cable visit:

https://brainly.com/question/32316511

#SPJ11

Answer:

Transversal

Explanation:

Most 4-cylinder engine are configure in a Transversal configuration.

An access control system controls access to area restricted area or facility using physical and computer-related devices, equipment along with authentication and authorization mechanisms.

We must break down the forces acting on the eyeball into their component parts to calculate the required values ​​of T and (theta), and we must use the concept of equilibrium, which states that the net force acting on an object and net torque are both zero.

Let us examine in more detail the forces affecting the eyeball:

The equations for balancing in the x and y directions will now be presented as:

No pressure is acting in the x-direction, so the tension force is zero in that direction: T * cos(θ) = 0

T * sin(θ) + \(\rm F_1 + F_2 - F_3\)= 1200N (net pull force of 1200N in y-direction due to tension force in y-direction, f1, f2 and f3)

Let us now find the value of T and θ:

From the x-direction equation, we get:

T * cos(θ) = 0

T = 0

From the y-direction equation, we get:

0 + 500N + 800N - 600N = 1200N

T * sin(θ) = 1200N

T = 1200N / sin(θ)

Since T cannot be both 0 and 1200N, it implies that sin(θ) must be equal to 1:

sin(θ) = 1

To find θ, we take the inverse sine (or arcsine) of 1:

θ = arcsin(1)

The arcsine of 1 is 90 degrees or π/2 radians.

Therefore, the values are T = 1200N / sin(θ) = 1200N / 1 = 1200N and θ = 90 degrees or π/2 radians.

Learn more about Force, here:

https://brainly.com/question/13191643

#SPJ7

Fire wall is a home that has its own roof, foundation, and a wall that extends from the roof through the foundation.

This is known to be a form of rated assembly that ranges from the foundation to and via the roof of a building to lower the rate of fire spread.

Note that, Fire wall is a home that has its own roof, foundation, and a wall that extends from the roof through the foundation.

Learn more about Fire wall from

https://brainly.com/question/13024946

#SPJ1

Answer:

The above three conditions are commonly referred to as the equations of equilibrium for planar structures. ∑ Fx and ∑ Fy are the summation of the x and y components of all the forces acting on the structure, and ∑ Mz is the summation of the couple moments and the moments of all the forces about an axis z, perpendicular to the plane xy of the action of the forces.

Explanation:

Answer:

knowledge of animal behavior and anatomy

Explanation:

the qualification that will make Milton successful in his research is a knowledge of animal behaviour and also their anatomy. the knowledge of whales behaviour has opened his eyes into their world so he knows to a great deal about them. it is through his knowledge of the behaviour of whales that he's able to get used to their migrating patterns to know where and when to find them. Also, through the body anatomy of whales he knows what their movement is like.

Answer:

knowledge of animal behavior and anatomy

The specific gravity of each of the tabularized items are given as attached.

To determine the specific gravity, we need to compare the density of each material to the density of water (which is 62.4 lb/ft^3). The specific gravity is defined as the ratio of the density of the material to the density of water.

Therefore, the specific gravity of Gold is 19.36, the specific gravity of Platinum is 21.47, the specific gravity of Silver is 10.48, the specific gravity of Sand is 1.52, the specific gravity of Freshly fallen snow is 0.50, the specific gravity of Tar is 1.19, the specific gravity of Hard Rubber is 1.00, and the specific gravity of Water is 1.00.

Note that Specific gravity is the ratio of the density of a substance to the density of a reference substance, typically water at a specified temperature and pressure. It is a dimensionless quantity that helps determine the buoyancy of a substance.

Learn more about specific gravity  at:

https://brainly.com/question/8808140

#SPJ1

To reflect a triangle about the line y=x+4, follow these steps: find the line's perpendicular, intersect the line, and reflect the vertices.

Reflecting a triangle about a given line involves finding the perpendicular line to the given line and then determining the new positions of the triangle's vertices. In this case, the given line is y=x+4.

To find the perpendicular line, we need to determine its slope. Since the given line has a slope of 1, the perpendicular line will have a slope of -1 (the negative reciprocal).

Next, we find the point of intersection between the given line and the perpendicular line. To do this, we set the equations of the two lines equal to each other and solve for x and y. Let's call the coordinates of the intersection point (a, b).

Now, we can determine the new positions of the triangle's vertices. For each vertex of the original triangle, we calculate the distance between the vertex and the intersection point. Then, we move the same distance in the opposite direction to obtain the reflected position. This is done for all three vertices of the triangle.

Once we have the new positions of the vertices, we can connect them to form the reflected triangle. The resulting triangle will be a mirror image of the original triangle with respect to the line y=x+4.

For more questions on triangle

https://brainly.com/question/2773823

#SPJ8

Answer:

A rectangular shaped tool that functions as a pulley.

Explanation:

i beleive

Answer:

1. 1111.5MPa

2. 56.1GPa

Explanation:

1. Longitudinal tensile stress can be obtained by obtaining the strength and volume of the fiber reinforcement. The derived formula is given by;

σcl = σm (1 - Vf) + σfVf

Substituting the figures, we will have;

45(1 - 0.30) + 3600(0.30)

45(0.70) + 1080

31.5 + 1080

= 1111.5MPa

2. Longitudinal modulus of elasticity or Young's modulus is the ability of an object to resist deformation. The derived formula is given by;

Ecl = EmVm + EfVf

Substituting the formula gives;

= 2.4 (1 - 0.30) + 131 (0.30)

= 2.4(0.70) + 39.3

= 16.8 + 39.3

= 56.1GPa

Using the appropriate relation, the longitudinal tensile stress and the longitudinal modulus are 1111.50 and 56.10 respectively.

Longitudinal tensile stress can be obtained using the relation :

Substituting the values into the relation:

45(1 - 0.30) + 3600(0.30)

45 × 0.70 + 1080

31.5 + 1080

= 1111.50 MPa

2.)

Longitudinal modulus of elasticity is obtained using the relation :

Substituting the values thus :

2.4 (1 - 0.30) + 131 (0.30)

= 2.4 × 0.70 + 39.3

= 16.8 + 39.3

= 56.10 GPa

Hence, the longitudinal tensile stress and the longitudinal modulus are 1111.50 and 56.10 respectively.

Learn more : https://brainly.com/question/22664384

The below code assigns true to duplicates if any two elements in the array have the same value, and that assigns false to duplicates otherwise.

The code is
zipcodelist = ["12345", "67890", "23456", "78901", "34567"]
duplicates = False
for j in range(len(zipcodelist)):
   for k in range(j + 1, len(zipcodelist)):
       if zipcodelist[j] == zipcodelist[k]:
           duplicates = True
print(duplicates)

In this code, we first define the 'zipcodelist' array. Then we initialize the 'duplicates' variable to `False`. After that, we use two nested loops to compare every pair of elements in the 'zipcodelist' array.The outer loop iterates over every index in the zipcodelist' array. The inner loop iterates over every index after the current index of the outer loop. This is because we only need to compare each pair of elements once (e.g. comparing elements at index 0 and 1 is the same as comparing elements at index 1 and 0).Inside the inner loop, we compare the two elements at the current pair of indices. If they are equal, we set the `duplicates` variable to 'True'.

Finally, we print out the value of the zipcodelist' variable. If there are any duplicates in the 'zipcodelist' array, 'zipcodelist' will be 'True'. Otherwise, it will be 'False'.

You can learn more about duplicate value in array at

https://brainly.com/question/30093004

#SPJ11

Answer:

d. A proxy server d. A proxy serverd. A proxy server

Explanation:

d. A proxy server

To cool a given room it is necessary to provide 4 ft³/s of air through an 8-inches diameter pipe, for this Entrance length in this pipe = 17.7 ft

Q = 4ft³/s

Diameter = D = 8 inches

Entrance length in this pipe = \(l_{e}\) = ?

By using flow rate formula:

V = Q/A

V= Q/ π/4*D²

= 4ft³/s / π/4 (8/12 ft)²

V= 11.5 ft/s

Thus, with ν = 1.57 x 10⁻⁴ft²/s (value from table)

Re = VD/ν

Re = 11.5 ft/s (8/12 ft)/1.57x10⁻⁴ft²/s

Re = 48,800 > 4000 (based on the criteria)

so, the flow is turbulent

Hence,

\(l_{e} / D\) = \(4.4 R_{e}^{1/6}\)

\(l_{e}\) = 4.4 (48,800)\(^{1/6}\) (8/12)

\(l_{e}\) = 17.7 ft

Entrance Length of an 8-inch diameter pipe = 17.7 ft

Learn more about Diameter:

https://brainly.com/question/5501950

#SPJ4

When it comes to repairing damaged corrugated sheath, there are several approved methods depending on the extent of the damage. One common repair method involves using a specially designed corrugated sheath repair kit that includes a new section of corrugated sheath and the necessary tools and materials to splice it onto the existing sheath.

This kit typically includes a heat shrink sleeve that is used to secure the new section of sheath in place, as well as adhesive or sealant to ensure a watertight seal. Another approved repair method for damaged corrugated sheath involves using a mechanical repair coupling. This type of coupling is designed to join two sections of corrugated sheath together, creating a strong and durable repair. Mechanical repair couplings are typically made from stainless steel and can be easily installed using basic tools. Overall, it is important to follow manufacturer recommendations and industry standards when repairing damaged corrugated sheath to ensure that the repair is safe, effective, and meets all necessary requirements.

Learn more about manufacturer here-

https://brainly.com/question/30352969

#SPJ11

Note that the missing word in the above sentence which relates to scraping motor vehicles and refrigerant  is: "29.92"

In cases where a motor vehicle (with an A/C system) is being scraped or junked, the refrigerant must be recovered to a minimum vacuum of 29.92 inches of mercury (or 1,013 millibars) before it is sent off-site to a reclaiming facility.

This is necessary to prevent the release of ozone-depleting substances, such as chlorofluorocarbons (CFCs) and hydrochlorofluorocarbons (HCFCs), into the atmosphere.

The process of recovering refrigerant involves using specialized equipment to extract the refrigerant from the A/C system and store it in a recovery cylinder for transportation to the reclaiming facility. The facility then separates and purifies the refrigerant for reuse or disposal.

Learn more about refrigerant  at:

https://brainly.com/question/28265596

#SPJ1

Answer:

a). 139498.24 kg

b). 281.85 ohm

c). 10.2 ohm

Explanation:

Given :

Diameter, d = 22 m

Linear strain, \($\epsilon$\) = 3%

                        = 0.03

Young's modulus, E = 30 GPa

Gauge factor, k = 6.9

Gauge resistance, R = 340 Ω

a). Maximum truck weight

σ = Eε

σ = \($0.03 \times 30 \times 10^9$\)

\($\frac{P}{A} =0.03 \times 30 \times 10^9$\)

\($P = 0.03 \times 30 \times 10^9\times \frac{\pi}{4}\times (0.022)^2$\)

 = 342119.44 N

For the four sensors,

Maximum weight = 4 x P

                            =  4 x 342119.44

                            = 1368477.76 N

Therefore, weight in kg is \($m=\frac{W}{g}=\frac{1368477.76}{9.81}$\)

                     m = 139498.24 kg

b). Change in resistance

\(k=\frac{\Delta R/R}{\Delta L/L}\)

\($\Delta R = k. \epsilon R$\)    , since \($\epsilon= \Delta L/ L$\)

\($\Delta R = 6.9 \times 0.03 \times 340$\)

\($\Delta R = 70.38 $\) Ω

For 4 resistance of the sensors,

\($\Delta R = 70.38 \times 4 = 281.52$\) Ω

c). \($k=\frac{\Delta R/R}{\epsilon}$\)

If linear strain,

\($\frac{\Delta R}{R} \approx \frac{\Delta L}{L}$\)  , where k = 1

\($\Delta R = \frac{\Delta L}{L} \times R$\)

\($\Delta R = 0.03 \times 340$\)

\($\Delta R = 10.2 $\) Ω

This statement is generally true for the automobile industry. Barriers to firms' mobility between different segments in the industry tend to be relatively low, making it easier for firms to enter or exit different segments of the market based on their profitability.

As a result, profitability differences between segments are typically not sustained over long periods of time. When a particular segment becomes more profitable, new firms may enter that segment, increasing competition and driving down prices and profitability. Similarly, when a segment becomes less profitable, firms may exit that segment, reducing competition and potentially increasing profitability.

However, it's worth noting that there may be some barriers to entry or exit in specific segments of the automobile industry. For example, some segments may require specialized knowledge or expertise, or may require significant investments in research and development to develop new technologies. In these cases, profitability differences may be sustained over longer periods of time.

Learn more about  segments  from

https://brainly.com/question/31546199

#SPJ11